B chapter.indd - Charles Babbage Institute - University of Minnesota
B chapter.indd - Charles Babbage Institute - University of Minnesota
B chapter.indd - Charles Babbage Institute - University of Minnesota
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Erwin Tomash Library<br />
<strong>Babbage</strong>, <strong>Charles</strong> <strong>Babbage</strong>, <strong>Charles</strong><br />
Blagrave, Mathematical jewel, 1585<br />
B 1<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
On the action <strong>of</strong> ocean-currents in the formation <strong>of</strong> the<br />
strata <strong>of</strong> the earth (Abstract).<br />
See any biographical dictionary for details on <strong>Babbage</strong>’s<br />
life and the entry Macrosty and Bonar, Annals <strong>of</strong> the<br />
Royal Statistical Society, 1934, for a photographic<br />
portrait.<br />
While <strong>Charles</strong> <strong>Babbage</strong> may be considered to be the<br />
grandfather <strong>of</strong> the modern computer, his work was limited<br />
to mechanical technology. Though electrical technology<br />
(particularly telegraph and relay technology) was being<br />
developed towards the end <strong>of</strong> his life, he seems not to<br />
have considered them for any <strong>of</strong> his engines. Despite this<br />
he was able to design mechanical machines that were the<br />
functional equivalent <strong>of</strong> the modern electronic computer.<br />
Today all encyclopedias will have some mention <strong>of</strong> him<br />
or his achievements—a situation that only arose after the<br />
development <strong>of</strong> the modern computer. He was essentially<br />
forgotten, or at least relegated to an obscure corner <strong>of</strong><br />
the history <strong>of</strong> mathematics, before his involvement with<br />
calculating machines came to be appreciated. Interested<br />
in all aspects <strong>of</strong> science, he made contributions to areas<br />
as diverse as mathematics, geology, chemistry, statistics,<br />
astronomy, railroads and lighthouses. Short introductions<br />
to each <strong>of</strong> <strong>Babbage</strong>’s publications can be found in The<br />
Works <strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong>, edited by Martin Campbell-<br />
Kelly, published in London by Pickering and Chatto in<br />
1989. Many <strong>of</strong> the remarks in the <strong>Babbage</strong> entries <strong>of</strong> this<br />
work are adapted from the introductions by Campbell-<br />
Kelly.<br />
See entry for Works <strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong>, M.A., F.R.S., &c.<br />
[A Collection <strong>of</strong> seventeen items by or about <strong>Babbage</strong>].<br />
B 2<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Addition to the memoir <strong>of</strong> M. Menabrea on the<br />
analytical engine. In The London, Edinburgh and<br />
Dublin Philosophical Magazine, and Journal <strong>of</strong><br />
Science. Third Series. Vol. 23, No. 151, September<br />
1843.<br />
Year: 1843<br />
Place: London<br />
Publisher: Taylor and Francis<br />
Edition: 1st<br />
Language: English<br />
Binding: original paper wrappers; unopened<br />
Pagination: pp. 235–239<br />
Size: 223x140 mm<br />
Reference: Van S CBCP, #55; Ran ODC, p. 405; MCK CBCW,<br />
v. 3, pp. 83–88; Not in Babb CBLP<br />
This paper was published anonymously a few weeks after<br />
the Ada Lovelace translation <strong>of</strong> the Menabrea paper on<br />
the Analytical Engine appeared (see Menabrea, Luigi<br />
Federico; translated by Byron, Augusta Ada, Lady<br />
Lovelace, Sketch <strong>of</strong> the Analytical Engine invented by<br />
<strong>Charles</strong> <strong>Babbage</strong>, Esq. … with notes by the translator,<br />
extract from the “Scientific Memoirs” vol. III, 1843).<br />
The attribution to <strong>Babbage</strong> was by the editors <strong>of</strong><br />
Astronomische Nachtrichen, who reprinted the paper in<br />
1844 and learned <strong>of</strong> the author’s identity through David<br />
Brewster.<br />
In this paper <strong>Babbage</strong> presents his side <strong>of</strong> the dispute<br />
with the British government over financial support for<br />
the Difference Engine. <strong>Babbage</strong> evidently intended the<br />
paper be published as an addendum to the Lovelace<br />
translation, but both the translator and the publishers<br />
were reluctant to involve themselves in the controversy.<br />
<strong>Babbage</strong> then turned to his friend and admirer David<br />
Journal cover, B2<br />
67
68<br />
Erwin Tomash Library<br />
<strong>Babbage</strong>, <strong>Charles</strong> <strong>Babbage</strong>, <strong>Charles</strong><br />
Brewster, an editor <strong>of</strong> the Philosophical Magazine.<br />
The paper also appears in <strong>Babbage</strong>, H. P.; <strong>Babbage</strong>’s<br />
calculating engines, being a collection <strong>of</strong> papers relating<br />
to them, their history and construction, London, 1889,<br />
under the title Statement <strong>of</strong> the circumstances attending<br />
the invention and construction <strong>of</strong> Mr. <strong>Babbage</strong>’s<br />
calculating engines.<br />
Illustrations available:<br />
Cover page:<br />
B 3<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
An analysis <strong>of</strong> the statistics <strong>of</strong> the clearing house during<br />
the year 1839.<br />
See <strong>Babbage</strong>, <strong>Charles</strong>; Works <strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong>,<br />
M.A., F.R.S., &c. [A Collection <strong>of</strong> seventeen items<br />
by or about <strong>Babbage</strong>].<br />
B 4<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
On the application <strong>of</strong> analysis to the discovery <strong>of</strong> local<br />
theorems and porisms. In Transactions <strong>of</strong> the Royal<br />
Society <strong>of</strong> Edinburgh, vol. 9.<br />
Year: 1823<br />
Place: Edinburgh<br />
Publisher: Royal Society <strong>of</strong> Edinburgh<br />
Edition: 1st (<strong>of</strong>fprint)<br />
Language: English<br />
Binding: extract; paper wrappers<br />
Pagination: pp. 337–352<br />
Reference: Van S CBCP, #21; Babb CBLP #14; Ran ODC, p.<br />
405; Dub MWCB, p. 231<br />
This journal extract is a technical mathematical paper.<br />
Illustrations available:<br />
First page:<br />
B 5<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Autograph letter.<br />
Year: 1820 or 1826<br />
Place: London<br />
Edition: manuscript<br />
Language: English<br />
Pagination: 1 page<br />
Dated 24 April, <strong>Babbage</strong> sends invitations to Mrs. Butler<br />
and Miss Kemble (likely the celebrated actress Fanny<br />
Kemble), via Mrs. Milman, for one <strong>of</strong> his gatherings.<br />
The text mentions Saturday, April 29, and Saturday,<br />
May 6, and these dates are a Saturday in both 1820 and<br />
B 5<br />
1826. Mrs. Milman was a poet and scholar, according to<br />
a notation by the seller.<br />
Illustrations available:<br />
Letter<br />
B 6<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Autograph letter.<br />
Year: 1838<br />
Place: London<br />
Edition: manuscript<br />
Language: English<br />
Pagination: 2 pages<br />
A letter from <strong>Babbage</strong> to an anonymous recipient dated<br />
10 January 1838. <strong>Babbage</strong> says he cannot come out<br />
because he is having a hot water apparatus installed and<br />
cannot leave the workmen.<br />
Illustrations available:<br />
Letter (2)<br />
B 7<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Autograph letter.<br />
Year: 1862<br />
Place: London<br />
Edition: manuscript<br />
Language: English<br />
Size: 180x126 mm<br />
A letter from <strong>Babbage</strong> to a Mrs. Robinson dated 25<br />
August 1862. It mentions the excitement <strong>of</strong> the Exhibition<br />
and the fact that <strong>Babbage</strong> was writing a book that will<br />
gain his revenge over those who used all the small<br />
power and wit they possess to destroy the Analytical
Erwin Tomash Library<br />
<strong>Babbage</strong>, <strong>Charles</strong> <strong>Babbage</strong>, <strong>Charles</strong><br />
Engine. He presumably means Passages from the life <strong>of</strong><br />
a philosopher, which was first published in 1864.<br />
Illustrations available:<br />
Letter (2)<br />
B 8<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Carte de visite.<br />
Year: n/d<br />
Place: London<br />
Edition: photograph and autograph<br />
Language: English<br />
Size: 104x62 mm<br />
This bears a photograph <strong>of</strong> <strong>Babbage</strong> with his autograph<br />
on the verso.<br />
Illustrations available:<br />
Card<br />
B 9<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
A <strong>chapter</strong> on street nuisances.<br />
Year: 1864<br />
Place: London<br />
Publisher: John Murray<br />
Edition: 2nd<br />
Language: English<br />
Binding: paper wrappers<br />
Pagination: pp. 32<br />
Reference: Van S CBCP, #76; Ran ODC, p. 405; MCK CBCW,<br />
v. 11; Not in; Babb CBLP<br />
This is an <strong>of</strong>fprint from Passages from the life <strong>of</strong> a<br />
philosopher (misnoted on the title page as Passages in<br />
the life <strong>of</strong> a philosopher).<br />
Illustrations available:<br />
Title page<br />
<strong>Charles</strong> <strong>Babbage</strong>, B 8<br />
B 10<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
B 9<br />
A comparative view <strong>of</strong> the various institutions for the<br />
assurance <strong>of</strong> lives.<br />
Year: 1826<br />
Place: London<br />
Publisher: J. Mawman<br />
Edition: 1st<br />
Language: English<br />
Figures: 1 folding table<br />
Binding: three-quarter leather over marbled boards<br />
Pagination: pp. xxxii, 170, [28]<br />
Collation: A–N 8 O 3<br />
Size: 214x132 mm<br />
Reference: Van S CBCP, #26; Babb CBLP, #30; Ran ODC, p.<br />
405; MCK CBCW, v.6<br />
This volume is illustrative <strong>of</strong> <strong>Babbage</strong>’s broad range <strong>of</strong><br />
interests and grew out <strong>of</strong> his experience as an actuary<br />
for the Protector Life Assurance Society. The insurance<br />
business was in its infancy at the time, and many<br />
companies were being formed in England. The Protector<br />
did not, in fact, issue any policies. It was within a few<br />
days <strong>of</strong> opening its doors when, for reasons still not clear,<br />
the directors unexpectedly decided to cease business.<br />
Rather than a book for the insurance industry, <strong>Babbage</strong><br />
aimed this volume at the interested layman. In 1827 it<br />
was translated into German.<br />
This book carries the signature <strong>of</strong> Henry P. <strong>Babbage</strong><br />
(<strong>Charles</strong>’ son) as well as being a presentation copy<br />
69
70<br />
Inscription, B 10<br />
Erwin Tomash Library<br />
<strong>Babbage</strong>, <strong>Charles</strong> <strong>Babbage</strong>, <strong>Charles</strong><br />
from Richard H. <strong>Babbage</strong> (<strong>Charles</strong>’ great-grandson<br />
who lived in Montreal) to Richard Bedford Bennett, a<br />
Canadian lawyer and politician. Bennett later (1930)<br />
became Prime Minister <strong>of</strong> Canada. Richard <strong>Babbage</strong>’s<br />
inscription reads:<br />
Presented to R. B. Bennett K.C. MP by Richard H.<br />
<strong>Babbage</strong> M.C. Great grandson <strong>of</strong> the Author as a<br />
small token <strong>of</strong> gratitude for many kindnesses Dec.<br />
1919<br />
Richard <strong>Babbage</strong> was correct in addressing Bennett as<br />
a King’s Counsel (K.C.); however, Bennett was not, at<br />
the time, a Member <strong>of</strong> Parliament (MP). Bennett was an<br />
MP from 1911 until 1917, then was not elected again<br />
until 1925.<br />
A review <strong>of</strong> this work by David Brewster (see entry for<br />
<strong>Babbage</strong>; Works <strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong>, M.A., F.R.S., &c.<br />
[A Collection <strong>of</strong> seventeen items by or about <strong>Babbage</strong>])<br />
is also available in the collection.<br />
Illustrations available:<br />
Title page<br />
Inscription<br />
B 11<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
On currency, on a new system <strong>of</strong> manufacturing and<br />
on the effect <strong>of</strong> machinery on human labour. Being<br />
three <strong>chapter</strong>s extracted from the third edition <strong>of</strong> “The<br />
Economy <strong>of</strong> Machinery and Manufactures.”<br />
B 10<br />
Year: 1833<br />
Place: London<br />
Publisher: <strong>Charles</strong> Knight<br />
Edition: 1st (Separate)<br />
Language: English<br />
Binding: original paper wrappers<br />
Pagination: pp. 31<br />
Size: 174x109 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 8<br />
This is an extract from one <strong>of</strong> <strong>Babbage</strong>’s most important<br />
works.<br />
Illustrations available:<br />
Title page<br />
B 12<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Demonstration <strong>of</strong> a theorem relating to prime numbers<br />
In The Edinburgh Philosophical Journal, Vol. 1, No. 1,<br />
June 1819.<br />
Year: 1819<br />
Place: Edinburgh<br />
Publisher: Archibald Constable<br />
Edition: 1st<br />
Language: English<br />
Binding: half bound over marbled boards<br />
Pagination: pp. 46–49<br />
Size: 207x125 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 1, pp. 279–282; Dub<br />
MWCB, p. 230
<strong>Babbage</strong>, <strong>Charles</strong><br />
This is one <strong>of</strong> <strong>Babbage</strong>’s earlier mathematical papers.<br />
It is simply an extension <strong>of</strong> one relating to which<br />
mathematical forms are divisible by n when n is a prime<br />
number but not otherwise. <strong>Babbage</strong>’s theorem extends<br />
the situation to include n 2 .<br />
Illustrations available:<br />
First page<br />
Erwin Tomash Library<br />
B 11<br />
Journal cover, B 13<br />
B 13<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
<strong>Babbage</strong>, <strong>Charles</strong><br />
Demonstrations <strong>of</strong> some <strong>of</strong> Dr. Matthew Stewart’s<br />
general theorems; to which is added, an account <strong>of</strong><br />
some new properties <strong>of</strong> the circle. In the Journal <strong>of</strong><br />
Science and the Arts Vol. I, Art II,1817.<br />
Year: 1816<br />
Place: New York<br />
Publisher: James Eastburn<br />
Edition: 1st (U. S.)<br />
Language: English<br />
Figures: 4 engraved plates<br />
Binding: Cloth spine over paper boards<br />
Pagination: pp. 6–24<br />
Collation: A 4 B–I 8 K 7 L–X 8 Y 4 Z 2<br />
Size: 234x140 mm<br />
Reference: Van S CBCP, #5; Babb CBLP, #5; MCK CBCW,<br />
v.1, pp. 194–212; Dub MWCB, p. 230<br />
This is a prime example <strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong>’s early<br />
mathematical work. After graduation from Cambridge<br />
in 1814, <strong>Babbage</strong> sought to establish his career as a<br />
mathematician, a calling in which he was both talented<br />
and prolific. From 1813 to 1827, <strong>Babbage</strong>, according<br />
to his own List <strong>of</strong> works, wrote no less than thirty-three<br />
books and papers.<br />
Illustrations available:<br />
Title page<br />
B 14<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
On the determination <strong>of</strong> the general term <strong>of</strong> a new class<br />
<strong>of</strong> infinite series In The Philosophical Magazine and<br />
Journal, Vol. 67, No. 336, April 1826.<br />
Year: 1826<br />
Place: London<br />
Publisher: Richard Taylor<br />
Edition: 1st<br />
Language: English<br />
Binding: half-bound leather over marbled paper boards<br />
Pagination: pp. 259–265<br />
Size: 208x125 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v.1, pp. 61–68<br />
This is another <strong>of</strong> <strong>Babbage</strong>’s early mathematical papers.<br />
Illustrations available:<br />
None<br />
B 15<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Sulla economia delle macchine e della manifatture.<br />
Year: 1834<br />
Place: Florence<br />
71
<strong>Babbage</strong>, <strong>Charles</strong><br />
72<br />
Publisher: Presso Guglielmo Piatti in Vacchereccia – Luigi<br />
Casini in Via Martelli e al Gabinetto Scientifico<br />
Lettrario di Vieusseux<br />
Edition: 1st (Italian)<br />
Language: Italian<br />
Binding: original paper wrappers; untrimmed<br />
Pagination: pp. [8], 311, [1], [7], [1]<br />
Collation: π 4 1–20 8<br />
Size: 218x145 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 8<br />
See the entry for <strong>Babbage</strong>, <strong>Charles</strong>; On the economy <strong>of</strong><br />
machinery and manufactures, 1832.<br />
Illustrations available:<br />
Title page<br />
B 16<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
On the economy <strong>of</strong> machinery and manufactures.<br />
Year: 1832<br />
Place: London<br />
Publisher: <strong>Charles</strong> Knight<br />
Edition: 1st<br />
Language: English<br />
Binding: later buckram boards<br />
Pagination: pp. xvi, 320<br />
Collation: A–X 8<br />
Size: 174x105 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 8<br />
<strong>Babbage</strong>’s work on his calculating engines aroused his<br />
keen interest in the workshops and factories <strong>of</strong> Great<br />
Britain and Europe. His observation and study <strong>of</strong> their<br />
Erwin Tomash Library<br />
B 15 B 16<br />
<strong>Babbage</strong>, <strong>Charles</strong><br />
methods during his visits led him to write this classic<br />
treatise, one <strong>of</strong> his major works, and its publication<br />
established him as a major figure in the economics field.<br />
It is due to this study that <strong>Babbage</strong> is sometimes referred<br />
to as the founder <strong>of</strong> the field <strong>of</strong> Operations Research.<br />
This remarkable work considers not only the productive<br />
function <strong>of</strong> machines and processes but also their<br />
administration and control. <strong>Babbage</strong> referred to the<br />
subject as the domestic economy <strong>of</strong> the factory. As was<br />
his usual predilection, <strong>Babbage</strong> sought to establish the<br />
governing general principles based on scientific analysis<br />
<strong>of</strong> the subject at hand. Hence, it is not surprising that in<br />
this work he covers a broad range <strong>of</strong> topics, including<br />
process control, production efficiency, plant location and<br />
labor incentives (pr<strong>of</strong>it sharing).<br />
Many <strong>of</strong> the contents were first published in the<br />
introduction to Peter Barlow’s long essay on<br />
manufacturing and machinery in Great Britain (see that<br />
entry) in the Encyclopedia Metropolitana in 1829 and a<br />
few years later as this volume. The book went through<br />
several editions and was translated into all the major<br />
European languages. <strong>Babbage</strong> added minor items from<br />
one edition to the next, but essentially all the material is<br />
present in this first edition.<br />
This first edition had two issues: a presentation version,<br />
<strong>of</strong> which a small number were printed in large paper<br />
format, and three thousand copies in the standard octavo<br />
size usually encountered.<br />
Illustrations available:<br />
Title page
<strong>Babbage</strong>, <strong>Charles</strong><br />
B 17<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Erwin Tomash Library<br />
B 17<br />
On the economy <strong>of</strong> machinery and manufactures.<br />
Year: 1832<br />
Place: Philadelphia<br />
Publisher: Carey & Lea<br />
Edition: 1st (U.S.)<br />
Language: English<br />
Binding: later leather<br />
Pagination: pp. xx, 15–282, [36]<br />
Collation: π 4 1–23 6 24 2 χ 18<br />
Size: 160x92 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 8<br />
This is the American edition <strong>of</strong> <strong>Babbage</strong>’s major work,<br />
published in the same year as the British first edition.<br />
Illustrations available:<br />
Title page<br />
B 18<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
On the economy <strong>of</strong> machinery and manufactures.<br />
Year: 1832<br />
Place: London<br />
Publisher: <strong>Charles</strong> Knight<br />
Edition: 2nd<br />
Language: English<br />
Figures: steel engraved title page<br />
Binding: contemporary leather; spine gilt; gilt edges<br />
<strong>Babbage</strong>, <strong>Charles</strong><br />
B 18<br />
Pagination: pp. xxiv, 388<br />
Collation: a 8 b 4 B–2B 8 2C 2<br />
Size: 165x100 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 8<br />
This is the second edition <strong>of</strong> <strong>Babbage</strong>’s work—published<br />
in the same year as the first.<br />
Illustrations available:<br />
Title page<br />
B 19<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
On the economy <strong>of</strong> machinery and manufactures.<br />
Year: 1833<br />
Place: London<br />
Publisher: <strong>Charles</strong> Knight<br />
Edition: 3rd<br />
Language: English<br />
Figures: steel engraved title page<br />
Binding: original moiré grained buff cloth boards; gilt spine<br />
Pagination: pp. xxiv, 392, [4]<br />
Collation: a 8 b 4 B–2B 8 2C 4 2D 2<br />
Size: 171x105 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 8<br />
This third edition <strong>of</strong> <strong>Babbage</strong>’s major work features a<br />
new preface.<br />
Illustrations available:<br />
Title page<br />
73
<strong>Babbage</strong>, <strong>Charles</strong><br />
B 20<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
On the economy <strong>of</strong> machinery and manufactures.<br />
74<br />
Year: 1835<br />
Place: London<br />
Publisher: <strong>Charles</strong> Knight<br />
Edition: 4th<br />
Language: English<br />
Figures: steel engraved title page<br />
Binding: original cloth boards<br />
Pagination: pp. iii–xii, [2], xiii–xxiv, 408<br />
Collation: a 8 b 4 B–2B 8 C–E 4<br />
Size: 160x95 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 8<br />
This is the fourth edition. The work was a popular<br />
success, with four editions in a little over two years.<br />
Illustrations available:<br />
Title page<br />
B 21<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
On electrical and magnetic rotations. In Philosophical<br />
Transactions <strong>of</strong> the Royal Society for the year<br />
MDCCCXXVI.<br />
Year: 1826<br />
Place: London<br />
Publisher: Royal Society <strong>of</strong> London<br />
Edition: 1st<br />
Language: English<br />
Figures: 19 engraved plates (5 folding)<br />
Binding: original paper wrappers<br />
Pagination: pp. 494 –528.<br />
Collation: 3Sv 4 –3V 4 3Y 2<br />
Size: 295x230 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405<br />
This is a paper on the magnetic properties <strong>of</strong> matter. See<br />
the entry <strong>Babbage</strong>, <strong>Charles</strong>; On a method <strong>of</strong> expressing<br />
signs, 1826, for an illustration <strong>of</strong> the title page <strong>of</strong> this<br />
volume <strong>of</strong> the Philosophical Transactions.<br />
Illustrations available:<br />
Title page (see above)<br />
B 22<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
An examination <strong>of</strong> some questions connected with<br />
games <strong>of</strong> chance.<br />
Year: 1821<br />
Place: London<br />
Publisher: Royal Society <strong>of</strong> Edinburgh<br />
Edition: 1st<br />
Language: English<br />
Erwin Tomash Library<br />
<strong>Babbage</strong> title page, B 23<br />
<strong>Babbage</strong>, <strong>Charles</strong><br />
Binding: disbound extract<br />
Pagination: pp. 153–177<br />
Size: 272x215 mm.<br />
Reference: Van S CBCP, #14; Babb CBLP, #12; Ran ODC, p.<br />
5; MCK CBCW, v. 1, pp. 327–343; Dub MWCB, p. 231<br />
This is an extract <strong>of</strong> one <strong>of</strong> <strong>Babbage</strong>’s technical<br />
mathematical papers.<br />
Illustrations available:<br />
First page<br />
B 23<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Examples <strong>of</strong> the solutions <strong>of</strong> functional equations.<br />
b/w: Herschel, J. F. W.; A collection <strong>of</strong> examples <strong>of</strong> the<br />
applications <strong>of</strong> the calculus <strong>of</strong> finite differences.<br />
Year: 1820<br />
Place: Cambridge<br />
Publisher: J. Smith for J. Deighton et. al.<br />
Edition: 1st<br />
Language: English<br />
Figures: one engraved plate<br />
Binding: green cloth boards<br />
Pagination: pp. vi, 172, [iv], 42<br />
Collation: *a 3 *A–*X 4 *Y 2 * 2 A–E 4 F 1<br />
Size: 225x140 mm<br />
Van S CBCP #70; Babb CBLP #71, #73; Ran ODC, p. 405;<br />
MCK CBCW, v. 1, pp. 283–326; Dub MWCB, p. 230<br />
While undergraduate students at Cambridge in 1812,<br />
<strong>Charles</strong> <strong>Babbage</strong> and his two friends George Peacock<br />
and John Herschel, formed the Analytical Society to<br />
bring mathematics teaching in England up to the standards<br />
<strong>of</strong> the European continent. Their first undertaking<br />
was to translate into English a French calculus book<br />
by Sylvestre François Lacroix (Traité du calcul
<strong>Babbage</strong>, <strong>Charles</strong><br />
Herschel title page, B 23<br />
Peacock title page, B 23<br />
différentiel et du calcul integral, 1797–1800) (see entry<br />
for [<strong>Babbage</strong>, et al., translators] – Lacroix, Sylvestre<br />
François; An elementary treatise on the differential and<br />
integral calculus. Translated from the French with an<br />
appendix and notes, 1816).<br />
This volume consists <strong>of</strong> a large set <strong>of</strong> examples <strong>of</strong> the<br />
applications <strong>of</strong> the calculus <strong>of</strong> differences, initially<br />
intended to accompany that translation but ultimately<br />
published separately. It contains examples (171 pp.)<br />
by Herschel for the calculus <strong>of</strong> finite differences<br />
and <strong>Babbage</strong>’s smaller (42 pp.), eighty-three worked<br />
examples <strong>of</strong> the calculus <strong>of</strong> functions.<br />
The printer, J. Smith, printer to the <strong>University</strong>, issued<br />
the work in two forms. One was in two volumes, the<br />
first containing the work <strong>of</strong> Peacock and the second<br />
containing the work <strong>of</strong> <strong>Babbage</strong> and Herschel. Smith<br />
also produced an issue containing the work <strong>of</strong> all three<br />
Erwin Tomash Library<br />
<strong>Babbage</strong>, <strong>Charles</strong><br />
authors. A copy <strong>of</strong> this later edition is available in the<br />
collection.<br />
Peacock (1791–1858) held the Lowndean chair <strong>of</strong><br />
astronomy and geometry at Cambridge from 1836 to<br />
1858 but stopped lecturing there when he became Dean<br />
<strong>of</strong> Ely Cathedral in 1839.<br />
The translation became very popular and was used for<br />
many years as a calculus text in British universities.<br />
Illustrations available:<br />
Title page <strong>of</strong> <strong>Babbage</strong> section<br />
Title page <strong>of</strong> Herschel section<br />
Title page from Peacock’s section (from the second copy)<br />
B 24<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
The exposition <strong>of</strong> 1851; or, views <strong>of</strong> the industry, the<br />
science, and the government <strong>of</strong> England.<br />
Year: 1851<br />
Place: London<br />
Publisher: London<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards; spine and cover gilt stamped<br />
Pagination: pp. xvi, 290, [4], 16<br />
Collation: A–T 8 U 3 χ 8<br />
Size: 226x138 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 10<br />
Martin Campbell-Kelly, editor <strong>of</strong> The works <strong>of</strong> <strong>Charles</strong><br />
<strong>Babbage</strong> (London, 1989), describes this as a vitriolic<br />
volume. It was written after <strong>Charles</strong> <strong>Babbage</strong> was not<br />
invited to take part in the organization <strong>of</strong> the International<br />
Exposition <strong>of</strong> 1851. The exhibition, held to celebrate<br />
progress in arts and manufactures, was opened by Queen<br />
Victoria and took place in Hyde Park in Joseph Paxton’s<br />
newly erected, eye-catching Crystal Palace. In the<br />
Dictionary <strong>of</strong> National Biography, the work is described<br />
as the diatribe <strong>of</strong> a disappointed man. <strong>Babbage</strong> had sought<br />
permission from the organizing committee to display the<br />
model <strong>of</strong> his Difference Engine and had been refused.<br />
In this polemic, <strong>Babbage</strong> not only criticized the policies<br />
<strong>of</strong> the organizers <strong>of</strong> the exhibition but also broadened<br />
his censure to include the low estate to which science<br />
in Great Britain had fallen. To remedy the Exposition<br />
Committee’s failure to recognize the importance and<br />
value <strong>of</strong> the Difference Engine, <strong>Babbage</strong> included a<br />
<strong>chapter</strong> on the machine and its history (pp. 173–188) in<br />
the main body <strong>of</strong> the text. In an appendix he provided<br />
a copy <strong>of</strong> a previously published (1849) pamphlet<br />
containing articles by <strong>Charles</strong> Weld and Augustus<br />
DeMorgan that present <strong>Babbage</strong> and his work on the<br />
Difference Engine in an objective and factual light.<br />
75
<strong>Babbage</strong>, <strong>Charles</strong><br />
76<br />
B 24<br />
Within a few years, this work inspired a reply in<br />
defense <strong>of</strong> the British establishment written by Richard<br />
Sheepshanks, A letter to the Board <strong>of</strong> Visitors <strong>of</strong> the<br />
Greenwich Royal Observatory in reply to the calumnies<br />
<strong>of</strong> Mr. <strong>Babbage</strong> at their meeting in June 1853, and in his<br />
book entitled The Exposition <strong>of</strong> 1851 (London, 1854).<br />
Illustrations available:<br />
Title page<br />
B 25<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
The exposition <strong>of</strong> 1851; or, views <strong>of</strong> the industry, the<br />
science, and the government <strong>of</strong> England.<br />
Year: 1851<br />
Place: London<br />
Publisher: John Murray<br />
Edition: 2nd<br />
Language: English<br />
Binding: original cloth boards; spine and cover gilt stamped<br />
Pagination: pp. xvi, 290, [4], 16<br />
Collation: A–T 8 U 3 χ 8<br />
Size: 226x138 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 10<br />
In the second edition <strong>Babbage</strong> added significant new<br />
material and incorporated the description <strong>of</strong> his Difference<br />
Engine into the main body <strong>of</strong> the work. See also the entry<br />
for the first edition (also published in 1851).<br />
Illustrations available:<br />
Title page<br />
Erwin Tomash Library<br />
B 26<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
<strong>Babbage</strong>, <strong>Charles</strong><br />
B 26<br />
On the influence <strong>of</strong> signs in mathematical reasoning.<br />
From: Transactions <strong>of</strong> the Cambridge Philosophical<br />
Society. 1826, Vol. II.<br />
Year: 1826<br />
Place: Cambridge<br />
Publisher: Cambridge Philosophical Society<br />
Edition: 1st (<strong>of</strong>fprint)<br />
Language: English<br />
Binding: yellow paper wrappers<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 1, pp. 371–408<br />
This is another <strong>of</strong> <strong>Babbage</strong>’s mathematical papers.<br />
In this paper, <strong>Babbage</strong> turns from the advancement<br />
<strong>of</strong> mathematics to a discussion <strong>of</strong> the importance <strong>of</strong><br />
mathematical notation and the facilitating role a good<br />
system can have in leading researchers to discoveries.<br />
He began this type <strong>of</strong> research several years earlier: see<br />
the entry for <strong>Babbage</strong>, Observations on the notation<br />
employed in the calculus <strong>of</strong> functions, 1822.<br />
Illustrations available:<br />
Title page<br />
B 27<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
An introductory view <strong>of</strong> the principles <strong>of</strong> manufactures.<br />
b/w: Barlow, Peter; A treatise on the manufactures<br />
and machinery <strong>of</strong> Great Britain… To which is<br />
prefaced, an introductory view <strong>of</strong> the principles<br />
<strong>of</strong> manufactures by <strong>Charles</strong> <strong>Babbage</strong>. Forming
<strong>Babbage</strong>, <strong>Charles</strong><br />
a portion <strong>of</strong> the Encyclopaedia Metropolitana. 3<br />
volumes.<br />
Year: 1836<br />
Place: London<br />
Publisher: Baldwin and Braddock<br />
Edition: 2nd<br />
Language: English<br />
Figures: 87 engraved plates bound at end <strong>of</strong> v.3<br />
Binding: contemporary leather<br />
Pagination: v.1: pp. Iii–viii, 412; v.2: pp. 413–828; pp. 829-834<br />
Collation: v.1: π 3 B–L 4 M 2 N–3G 4 ; v.2: 3H–5N 4 ; v.3: 5O 3<br />
Size: 274x208 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 10<br />
In 1829, Peter Barlow wrote an extensive tract on the<br />
subject <strong>of</strong> machinery as applied to manufacturing for<br />
the Encyclopedia Metropolitana, for which <strong>Charles</strong><br />
<strong>Babbage</strong> provided the introduction. The two items were<br />
also published separately, as here (first edition in 1829,<br />
third in 1845). <strong>Babbage</strong> had a very strong interest in<br />
manufacturing techniques and the first section <strong>of</strong> his<br />
classic book On the economy <strong>of</strong> machinery and<br />
manufactures, published in 1832, was based on this<br />
introduction. He also rewrote this eighty-four page<br />
introduction substantially for each new edition.<br />
Characteristically, the treatise is thorough and<br />
comprehensive. It ranges from the gathering and<br />
regulating <strong>of</strong> power needed to properly operate machinery<br />
to a discussion <strong>of</strong> the division <strong>of</strong> labor and the needs<br />
for capital in a manufacturing enterprise, concluding<br />
Erwin Tomash Library<br />
B 27<br />
<strong>Babbage</strong>, <strong>Charles</strong><br />
B 28<br />
with a checklist <strong>of</strong> data to be acquired when gathering<br />
information about a factory and its production <strong>of</strong> goods.<br />
Illustrations available:<br />
Title page<br />
B 28<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Letter from Mr. <strong>Babbage</strong> to the members <strong>of</strong> the British<br />
Association for the Promotion <strong>of</strong> Science.<br />
Year: 1839<br />
Place: London<br />
Publisher: Richard Clay<br />
Edition: 1st<br />
Language: English<br />
Binding: original paper wrappers<br />
Pagination: pp. 15, [1]<br />
Size: 213x135 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 4, pp. 151–159<br />
This small pamphlet puts forth <strong>Babbage</strong>’s explanation <strong>of</strong><br />
a disagreement between himself and the other members<br />
<strong>of</strong> the Board <strong>of</strong> the British Association. He had been<br />
asked to let his name stand for president, but his friend<br />
John Herschel had also been asked, and this led both<br />
men to withdraw their names. Subsequent disagreements<br />
also led <strong>Babbage</strong> to resign from the board. The BAAS<br />
had been founded partly in the belief that the Royal<br />
Society had become too political—apparently the BAAS<br />
had also fallen into that state.<br />
77
<strong>Babbage</strong>, <strong>Charles</strong><br />
See also entry for Works <strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong>, M.A.,<br />
F.R.S., &c. [A Collection <strong>of</strong> seventeen items by or about<br />
<strong>Babbage</strong>].<br />
78<br />
Illustrations available:<br />
Title page<br />
B 29<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
A letter to Sir Humphry Davy, Bart. President <strong>of</strong> the<br />
Royal Society, etc. etc. on the application <strong>of</strong> machinery<br />
to the purpose <strong>of</strong> calculating and printing mathematical<br />
tables from <strong>Charles</strong> <strong>Babbage</strong>, Esq. M.A.<br />
Year: 1822<br />
Place: London<br />
Publisher: J. Booth<br />
Edition: 1st<br />
Language: English<br />
Binding: disbound; in cloth case<br />
Pagination: pp. 12<br />
Collation: π 1 B 5 (-B6)<br />
Size: 269x216 mm<br />
Reference: Van S CBCP, #18; Babb CBLP, #19; Ran ODC, p.<br />
405; MCK CBCW, v. 2, pp. 5–14<br />
<strong>Babbage</strong> was only a few years out <strong>of</strong> Cambridge when<br />
he decided to devote his efforts to the production <strong>of</strong> a<br />
Difference Engine. He announced this by writing an open<br />
letter to Sir Humphry Davy, the president <strong>of</strong> the Royal<br />
Society. In it he describes the concept, his pilot project,<br />
his critical results and eventually, in the last sentence, an<br />
indirect request for financial support:<br />
It must however be attained at a very considerable<br />
expense, which would not probably be replaced,<br />
Erwin Tomash Library<br />
B 29 Journal cover, B 30<br />
<strong>Babbage</strong>, <strong>Charles</strong><br />
by the works it might produce, for a long period<br />
<strong>of</strong> time, and which is an undertaking I should feel<br />
unwilling to commence, as altogether foreign to<br />
my habits and pursuits.<br />
The letter was widely circulated and eventually resulted<br />
in the government granting funds for the construction <strong>of</strong><br />
<strong>Babbage</strong>’s Difference Engine. Significantly, the letter<br />
also contains remarks showing that <strong>Babbage</strong> had been<br />
thinking <strong>of</strong> other forms <strong>of</strong> calculating machines.<br />
Illustrations available:<br />
Title page<br />
B 30<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Note sur machine suédoise de MM. Scheutz pour<br />
calculer les tables mathématiques par la méthode<br />
des différences, et en imprimer la les resultats<br />
sur des planches stéréotypes. In Comptes Rendus<br />
Hebdomadaires des séances de l’Académie des<br />
Sciences, Vol. XLI, No. 15, 8 October 1855.<br />
Year: 1855<br />
Place: Paris<br />
Publisher: Mallet-Bachelier<br />
Edition: 1st<br />
Language: French<br />
Binding: original paper wrappers<br />
Pagination: pp. 557–560<br />
Size: 283x226 mm<br />
Reference: Van S CBCP, #70; #71, #73; Ran ODC, p. 405;<br />
MCK CBCW, v. 3, pp. 233–236
Erwin Tomash Library<br />
<strong>Babbage</strong>, <strong>Charles</strong> <strong>Babbage</strong>, <strong>Charles</strong><br />
A short communication by <strong>Babbage</strong> regarding the<br />
Scheutz Difference Engine. <strong>Babbage</strong> uses this note to<br />
bring his system <strong>of</strong> mechanical notation to the attention<br />
<strong>of</strong> the French Academy. The article mentions several<br />
graphical illustrations, evidently drawn by <strong>Charles</strong>’ son<br />
Henry P. <strong>Babbage</strong> for the occasion, but these were not<br />
reproduced in the printed version.<br />
An English translation <strong>of</strong> this paper is in The works <strong>of</strong><br />
<strong>Charles</strong> <strong>Babbage</strong>, Martin Campbell-Kelly, ed., 1989.<br />
Illustrations available:<br />
Cover page<br />
B 31<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871) [G. Friedenberg,<br />
translator]<br />
Ueber Maschinen und Fabrikenwesen.<br />
Year: 1833<br />
Place: Berlin<br />
Publisher: Stuhrschen Buchhandlung<br />
Edition: 1st (German)<br />
Language: German<br />
Binding: contemporary marbled boards; rebacked<br />
Pagination: pp. [4], lii, 462<br />
Collation: π 2 a–b 12 c 2 1–19 12 20 3<br />
Size: 166x95 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 8<br />
See entry for <strong>Babbage</strong>, On the economy <strong>of</strong> machinery<br />
and manufactures, 1832 edition—this is the German<br />
translation.<br />
Illustrations available:<br />
Title page<br />
B 31<br />
B 32<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Memoirs <strong>of</strong> the Astronomical Society <strong>of</strong> London.<br />
Year: 1822–1829<br />
Place: London<br />
Publisher: v.1 & v.2: Baldwin, Cradock and Joy; v.3: Priestley<br />
and Weale<br />
Edition: 1st<br />
Language: English<br />
Figures: v.1: 6 plates (1 folding); 1 folding table; v.2: 8 plates<br />
(1 folding)<br />
Binding: contemporary three-quarter leather; spine gilt<br />
Pagination: v.1. pp. viii, iii–vi, 532; v.2. pp. iii–viii, iii–viii,<br />
564, ccxxiv, [4]; v.3. pp. viii, v–viii, 432<br />
Collation: v.1. A 6 B–2C 4 2D 2 2E 2 2F–3Y 4 3Z 2 ; v.2. A 6 B–<br />
2R 4 2S 2 2T–4C 4 a–2d 4 2e 6 ; v.3. A 6 B–3I 4<br />
Size: 267x208 mm<br />
These three volumes, the only ones published, contain a<br />
number <strong>of</strong> papers by <strong>Babbage</strong>:<br />
1. A note respecting the application <strong>of</strong> machinery to<br />
the calculation <strong>of</strong> astronomical tables<br />
2. Address <strong>of</strong> Henry Thomas Colebrooke, president<br />
<strong>of</strong> the Astronomical Society <strong>of</strong> London, on<br />
presenting the gold medal to <strong>Charles</strong> <strong>Babbage</strong><br />
3. Notice respecting some errors common to many<br />
tables <strong>of</strong> logarithms<br />
4. Observations on the application <strong>of</strong> machinery to<br />
the computation <strong>of</strong> mathematical tables<br />
5. On a new zenith micrometer<br />
Each <strong>of</strong> these papers has its own entry in this catalog.<br />
<strong>Babbage</strong> was one <strong>of</strong> the founders <strong>of</strong> the Astronomical<br />
Society.<br />
Illustrations available:<br />
Title page<br />
B 33<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
On a method <strong>of</strong> expressing signs by the action <strong>of</strong><br />
machinery. In Philosophical Transactions <strong>of</strong> the Royal<br />
Society 116, pt. 3, (1826) for the year MDCCCXXVI.<br />
Year: 1826<br />
Place: London<br />
Publisher: Royal Society <strong>of</strong> London<br />
Edition: 1st<br />
Language: English<br />
Figures: 19 engraved plates (5 folding)<br />
Binding: original paper wrappers; unopened<br />
Pagination: pp. 250–265<br />
Collation: 2K 3 ,2K 4 ,2L 4 ,2M 1 ,2M 2<br />
Size: 295x230 mm<br />
Reference: MCK CBCW, v. 3, pp. 209–223<br />
Ever the generalist, this paper is <strong>Babbage</strong>’s attempt to<br />
formally describe the movements <strong>of</strong> a complex piece <strong>of</strong><br />
79
80<br />
Erwin Tomash Library<br />
<strong>Babbage</strong>, <strong>Charles</strong> <strong>Babbage</strong>, <strong>Charles</strong><br />
machinery and to make it understandable by means <strong>of</strong><br />
letters and signs that indicate how each piece moves and<br />
at what time in the cycle.<br />
A second copy <strong>of</strong> this work is available in the<br />
collection.<br />
Illustrations available:<br />
Title page<br />
B 34<br />
[<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)]<br />
Mr. <strong>Babbage</strong>’s Invention. Copies <strong>of</strong> the correspondence<br />
between the Lord’s Commissioners <strong>of</strong> his Majesty’s<br />
treasury and the President and council <strong>of</strong> the Royal<br />
Society, relative to an Invention <strong>of</strong> Mr. <strong>Babbage</strong>.<br />
Year: 1823<br />
Place: London<br />
Publisher: Royal Society <strong>of</strong> London<br />
Edition: 1st<br />
Language: English<br />
Binding: extract, disbound<br />
Size: 328x203 mm<br />
This contains the letter that <strong>Babbage</strong> wrote to Humphry<br />
Davy indirectly asking for government support <strong>of</strong> his<br />
efforts at building a Difference Engine. The government<br />
passed the letter along to the Royal Society with a letter<br />
<strong>of</strong> their own (also printed here) asking<br />
… that their lordships request to be favoured with<br />
the opinion <strong>of</strong> the Royal Society on the merits and<br />
utility <strong>of</strong> his invention.<br />
The Royal Society wrote back (letter also printed here):<br />
That it appears to the Committee, that Mr.<br />
<strong>Babbage</strong> has displayed great talents and<br />
ingenuity in the construction <strong>of</strong> his machine<br />
for computation, which the Committee think<br />
fully adequate to the attainment <strong>of</strong> the objects<br />
proposed by the Inventor, and that they consider<br />
Mr. <strong>Babbage</strong> as highly deserving <strong>of</strong> public<br />
encouragement in the prosecution <strong>of</strong> his arduous<br />
undertaking.<br />
Illustrations available:<br />
First page<br />
B 35<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
On some new methods <strong>of</strong> investigating the sums <strong>of</strong><br />
several classes <strong>of</strong> infinite series. In Philosophical<br />
Transactions <strong>of</strong> the Royal Society <strong>of</strong> London, Vol. 109<br />
(1819).<br />
Year: 1819<br />
Place: London<br />
B 34<br />
Publisher: Royal Society <strong>of</strong> London<br />
Edition: 1st (Extract)<br />
Language: English<br />
Binding: extract-uncut, disbound<br />
Pagination: pp. 249–282<br />
Size: 292x232 mm.<br />
Reference: Van S CBCP, #11; Babb CBLP, #10; Dub MWCB,<br />
pp. 136–143, 230; MCK CBCW, v. 1, pp. 248–278<br />
This extract from the journal is uncut and disbound. It is<br />
one <strong>of</strong> <strong>Babbage</strong>’s early papers on mathematics.<br />
Illustrations available:<br />
Title page<br />
B 36<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
On a new zenith micrometer. In Memoirs <strong>of</strong> the<br />
Astronomical Society <strong>of</strong> London, Volume 2.<br />
Year: 1826<br />
Place: London<br />
Publisher: Baldwin, Cradock and Joy<br />
Edition: 1st<br />
Language: English<br />
Figures: 1<br />
Binding: contemporary three-quarter leather; spine gilt<br />
Pagination: v.1, pp. viii, iii–vi, 530, [2]; v.2, pp. iii–viii, iii–viii,<br />
564, ccxxviii; v.3, pp. viii, v–viii, 432<br />
Collation: v.1, a 4 b 2 B–2C 4 2D–2E 2 2F–3Y 4 3Z 2 ; v.2, a 6 B–<br />
2R 4 2S 2 2T–4C 4 a–2d 4 e 6 ; v.3, a 6 B–3I 4<br />
Size: 267x208 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, vol. 4, pp. 42–45
Erwin Tomash Library<br />
<strong>Babbage</strong>, <strong>Charles</strong> <strong>Babbage</strong>, <strong>Charles</strong><br />
This paper is indicative <strong>of</strong> <strong>Babbage</strong>’s wide range <strong>of</strong><br />
interests and his willingness to apply his intellect to a<br />
variety <strong>of</strong> topics. It is a short description <strong>of</strong> an anglemeasuring<br />
device <strong>of</strong> his invention. Previous astronomical<br />
angular measurement systems relied on a finely divided<br />
scale that could be read by the aid <strong>of</strong> a magnifying glass.<br />
<strong>Babbage</strong> proposes a system in which a telescope is<br />
attached to one arm <strong>of</strong> a parallelogram; any shift <strong>of</strong> the<br />
configuration <strong>of</strong> the parallelogram being magnified by<br />
attachments to the other arms makes it easy to determine<br />
the angle <strong>of</strong> shift. There is one small figure describing the<br />
system that is to be found as part <strong>of</strong> the plate illustrating<br />
the previous paper in the volume.<br />
Illustrations available:<br />
None<br />
B 37<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
The ninth Bridgewater treatise, a fragment.<br />
Year: 1837<br />
Place: London<br />
Publisher: John Murray<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards<br />
Pagination: pp. [4], xxii (iii misnumbered as i), 23–240, (103<br />
misnumbered as 101),[2], 8<br />
Collation: π 2 B–Q 8 R 1 χ 4<br />
Size: 225x142 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 9<br />
As modern science began to conflict with traditional<br />
religious values, in 1829 the Earl <strong>of</strong> Bridgewater (Rev.<br />
Francis Egerton, F.R.S.) left the Royal Society a bequest<br />
<strong>of</strong> £8,000 to pay for the writing <strong>of</strong> several books on the<br />
Power, Wisdom and Goodness <strong>of</strong> God, as manifested<br />
in the Creation. Eight <strong>of</strong> these treatises were produced,<br />
but none seems to have had lasting value. The most<br />
successful treatise, titled Astronomy and general physics,<br />
was written by William Whewell, a tutor <strong>of</strong> mathematics<br />
at Cambridge. In it, Whewell condemned the growing<br />
influence <strong>of</strong> scientists and mathematicians and described<br />
them as mechanical philosophers without any authority<br />
with regard to their view <strong>of</strong> the administration <strong>of</strong> the<br />
Universe. In passing, Whewell singled out mechanized<br />
analytical calculation for particular condemnation.<br />
<strong>Babbage</strong> felt the need to respond and privately produced<br />
this un<strong>of</strong>ficial Ninth treatise. The work is curious in<br />
that <strong>Babbage</strong> decided to leave large sections blank (or<br />
perhaps removed them before publication)—hence the<br />
term fragment in the title. Martin Campbell-Kelly (The<br />
Works <strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong>) reports that it had been<br />
suggested that some may have been removed after<br />
<strong>Babbage</strong>’s friends, upon reading the pro<strong>of</strong>s, objected to<br />
certain passages.<br />
The work argues for example, that miracles can easily<br />
occur without divine intervention and gives examples<br />
relating to his calculating machines and mathematics<br />
in general. The appendix contains a section on the<br />
calculating engine.<br />
For a modern discussion, see Topham, J., “Science and<br />
popular education: The role <strong>of</strong> the Bridgewater treatises,”<br />
British Journal for the History <strong>of</strong> Science, Vol. 25, 1992,<br />
pp. 397–430.<br />
Illustrations available:<br />
Title page<br />
B 38<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
The ninth Bridgewater treatise, a fragment.<br />
Year: 1838<br />
Place: London<br />
Publisher: John Murray<br />
Edition: 2nd<br />
Language: English<br />
Binding: original cloth boards<br />
Pagination: pp. viii, xxii, 23–270, [14]<br />
Collation: A 4 B–S 8 χ 6<br />
Size: 223x140 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 9<br />
B 37<br />
81
82<br />
Erwin Tomash Library<br />
<strong>Babbage</strong>, <strong>Charles</strong> <strong>Babbage</strong>, <strong>Charles</strong><br />
This second edition was considerably revised and<br />
enlarged with the help <strong>of</strong> Dr. W. H. Fitton, a longtime<br />
friend <strong>of</strong> <strong>Babbage</strong>’s.<br />
A second copy <strong>of</strong> this edition is available in the<br />
collection. It is a presentation copy from <strong>Babbage</strong> to<br />
W. R. Grove. William Robert Grove (1811–1896) was<br />
trained as a lawyer, but his interest was in science. He<br />
served as pr<strong>of</strong>essor <strong>of</strong> experimental philosophy at the<br />
London Institution and was elected a fellow <strong>of</strong> the Royal<br />
Society in 1840.<br />
Illustrations available:<br />
Title page<br />
B 39<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
The ninth Bridgewater treatise, a fragment.<br />
B 39<br />
Year: 1841<br />
Place: Philadelphia<br />
Publisher: Lea & Blanchard<br />
Edition: 1st (U.S.)<br />
Language: English<br />
Binding: original cloth boards; paper label on spine<br />
Pagination: pp. xii, xvii–xxxii, 33–250, [2], 3–32<br />
Collation: 1 2 2–31 4 32 2 χ 15<br />
Size: 226x142 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 9<br />
This first American edition was produced from the<br />
second (1838) London edition.<br />
Illustrations available:<br />
Title page<br />
B 40<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
A note respecting the application <strong>of</strong> machinery to the<br />
calculation <strong>of</strong> astronomical tables. In Memoirs <strong>of</strong> the<br />
Astronomical Society <strong>of</strong> London, v.1, pt. 2.<br />
Year: 1822<br />
Place: London<br />
Publisher: Baldwin, Cradock and Joy<br />
Edition: 1st<br />
Language: English<br />
Binding: contemporary three-quarter leather; spine gilt<br />
Pagination: v.1: pp. viii, iii–vi, 532; v.2: pp. iii–viii, iii–viii,<br />
564, ccxxiv, [4] v.3: pp. viii, v–viii, 432<br />
Collation: v.1: A 6 B–2C 4 2D 2 2E 2 2F–3Y 4 3Z 2 ; v.2: A 6 B–<br />
2R 4 2S 2 2T–4C 4 a–2d 4 2e 6 v.3: A 6 B–3I 4<br />
Size: 267x208 mm<br />
Reference: Van S CBCP, #17; Babb CBLP, #18; Ran ODC, p.<br />
405; MCK CBCW, v. 2, pp. 3–4<br />
This one page item, in a three-volume set, simply<br />
announces the fact that <strong>Babbage</strong>’s small trial Difference<br />
Engine was working correctly.<br />
Illustrations available:<br />
None<br />
B 41<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Notice respecting some errors common to many tables<br />
<strong>of</strong> logarithms. In Memoirs <strong>of</strong> the Astronomical Society<br />
<strong>of</strong> London, Volume 3, part 1.<br />
Year: 1829<br />
Place: London<br />
Publisher: Baldwin, Cradock and Joy<br />
Edition: 1st<br />
Language: English<br />
Binding: contemporary three-quarter leather; spine gilt<br />
Pagination: v.1: pp. viii, iii–vi, 532; v.2: pp. iii–viii, iii–viii,<br />
564, ccxxiv, [4] v.3: pp. viii, v–viii, 432<br />
Collation: v.1: A 6 B–2C 4 2D 2 2E 2 2F–3Y 4 3Z 2 ; v.2: A 6 B–<br />
2R 4 2S 2 2T–4C 4 a–2d 4 2e 6 v.3: A 6 B–3I 4<br />
Size: 267x208 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 2, pp. 69–71; Dub<br />
MWCB, p. 196<br />
This is an important paper in which <strong>Babbage</strong> points out<br />
that almost all logarithmic tables had been copied from<br />
earlier versions and consequently contained the same<br />
errors. He points out that the source <strong>of</strong> six common<br />
errors was the table produced by Vlacq in 1628. He also<br />
notes the same errors were found in a set <strong>of</strong> tables, in the<br />
library <strong>of</strong> the Royal Society, produced in China. This was<br />
two years after publishing his own logarithm tables.<br />
Illustrations available:<br />
List <strong>of</strong> the six common errors.
Erwin Tomash Library<br />
<strong>Babbage</strong>, <strong>Charles</strong> <strong>Babbage</strong>, <strong>Charles</strong><br />
B 42<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Notice respecting some errors common to many tables<br />
<strong>of</strong> logarithms. In Memoirs <strong>of</strong> the Astronomical Society<br />
<strong>of</strong> London. V. 3, pt. 1.<br />
Year: 1829<br />
Place: London<br />
Publisher: Astronomical Society <strong>of</strong> London<br />
Edition: 1st<br />
Language: English<br />
Binding: extract; disbound<br />
Pagination: pp. 65–67<br />
Size: n/a<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 2, pp. 69–71; Dub<br />
MWCB, p. 196<br />
This second copy is an extract from the journal. See also<br />
the entry for <strong>Babbage</strong>, <strong>Charles</strong>; Notice respecting some<br />
errors common to many tables <strong>of</strong> logarithms, 1829.<br />
Illustrations available:<br />
First page with table <strong>of</strong> errors<br />
[<strong>Babbage</strong>, <strong>Charles</strong>]<br />
Obituary notice.<br />
See <strong>Babbage</strong>, <strong>Charles</strong>; Works <strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong>,<br />
M.A., F.R.S., &c. [A Collection <strong>of</strong> seventeen items by or<br />
about <strong>Babbage</strong>].<br />
B 43<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Common errors, B 42<br />
Observations addressed, at the last anniversary, <strong>of</strong> the<br />
President and Fellows <strong>of</strong> the Royal Society, after the<br />
delivery <strong>of</strong> the medals …<br />
Year: 1856<br />
Place: London<br />
Publisher: John Murray<br />
Edition: 1st<br />
Language: English<br />
Binding: original paper wrappers<br />
Pagination: pp. 10, [2]<br />
Size: 243x155 mm<br />
Van S CBCP #73; Babb CBLP #76; Ran ODC, p. 405; MCK<br />
CBCW, v. 2, pp. 187–193<br />
A committee <strong>of</strong> the Royal Society decides who will be<br />
awarded various medals in any given year. At one <strong>of</strong> the<br />
medal ceremonies, <strong>Babbage</strong> observed that the Scheutz<br />
Difference Engine had been in the Royal Society rooms<br />
for many months, and he was distressed that, perhaps<br />
through his own oversight, the Scheutz team had not been<br />
nominated for one <strong>of</strong> the medals. He briefly summarizes<br />
the history <strong>of</strong> the Scheutz team and their Difference<br />
Engine and concludes by hoping that the committee<br />
would keep them in mind in future years. <strong>Babbage</strong> goes<br />
on to make it quite plain that he was not questioning the<br />
competency <strong>of</strong> those who were awarded the medals.<br />
Illustrations available:<br />
Title page<br />
83
84<br />
Erwin Tomash Library<br />
<strong>Babbage</strong>, <strong>Charles</strong> <strong>Babbage</strong>, <strong>Charles</strong><br />
B 44<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Observations on the analogy which subsists between the<br />
calculus <strong>of</strong> functions and other branches <strong>of</strong> analysis.<br />
In Philosophical Transactions <strong>of</strong> the Royal Society <strong>of</strong><br />
London, Vol. 107, Part II, 1817.<br />
Year: 1817<br />
Place: London<br />
Publisher: The Royal Society<br />
Edition: 1st<br />
Language: English<br />
Binding: contemporary leather<br />
Pagination: pp. 197–216<br />
Size: 269x205 mm<br />
Van S CBCP #7; Babb CBLP #6; Dub MWCB, p. 230;<br />
In this mathematical paper <strong>Babbage</strong> shows how one may<br />
use analogies from one branch <strong>of</strong> mathematics to find<br />
truths in another. He is careful, however, to point out that<br />
analogy can only be used as a guide and not as a pro<strong>of</strong>.<br />
Illustrations available:<br />
Title page<br />
B 45<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Observations on the application <strong>of</strong> machinery to the<br />
computation <strong>of</strong> mathematical tables. In Memoirs <strong>of</strong> the<br />
Astronomical Society <strong>of</strong> London. v.1 pt. 2.<br />
Year: 1822<br />
Place: London<br />
Publisher: Baldwin, Cradock and Joy<br />
Edition: 1st<br />
Language: English<br />
Binding: contemporary three-quarter leather; spine gilt<br />
Pagination: v.1, pp. viii, iii–vi, 532; v.2, pp. iii–viii, iii–viii,<br />
564, ccxxiv, [4] v.3, pp. viii, v–viii, 432<br />
Collation: v.1, A 6 B–2C 4 2D 2 2E 2 2F–3Y 4 3Z 2 ; v.2, A 6 B–<br />
2R 4 2S 2 2T–4C 4 a–2d 4 2e 6 v.3, A 6 B–3I 4<br />
Size: 267x208 mm<br />
Reference: Van S CBCP, #19; Babb CBLP, #21; Ran ODC, p.<br />
405; MCK CBCW, v. 2, pp. 33–37<br />
<strong>Babbage</strong> was a leading figure in the formation <strong>of</strong> the<br />
Astronomical Society and read several papers there. The<br />
first volume <strong>of</strong> this three-volume set contains a paper on<br />
difference equations that was inspired by his attempt to<br />
build a Difference Engine. It also indicates that he was<br />
considering a different arrangement <strong>of</strong> the figure wheels<br />
(so that they could add to any other axle and not just to<br />
that <strong>of</strong> the immediately preceding difference). This more<br />
flexible arrangement <strong>of</strong> the organization <strong>of</strong> the system<br />
was one <strong>of</strong> the factors that eventually led to his ideas for<br />
an Analytical Engine (see illustrations). This early paper<br />
on his Difference Engine was written in the same year as<br />
his letter to Sir Humphry Davy.<br />
Illustrations available:<br />
Quotation regarding the rearrangement <strong>of</strong> the figure wheels.<br />
B 46<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Observations on the discovery in various localities<br />
<strong>of</strong> the remains <strong>of</strong> human art mixed with the bones <strong>of</strong><br />
extinct races <strong>of</strong> animals.<br />
Year: 1847<br />
Place: London<br />
Publisher: Taylor and Francis<br />
Edition: 1st<br />
Language: English<br />
Binding: <strong>of</strong>fprint<br />
Pagination: 16 pp.<br />
Size: 212x137 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 4, pp. 165–217<br />
Recent discoveries in France and Sicily <strong>of</strong> human and<br />
extinct animal bones in the same deposit had led to<br />
questions concerning the antiquity <strong>of</strong> humans. <strong>Babbage</strong><br />
points out here that one had to be cautious in assuming<br />
that they were <strong>of</strong> the same age and presents arguments<br />
as to how natural geological processes might have been<br />
responsible for commingling the remains <strong>of</strong> species from<br />
two different ages. This is a presentation copy to George<br />
Ticknor.<br />
Illustrations available:<br />
Title page<br />
B 47<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Observations on the notation employed in the calculus<br />
<strong>of</strong> functions.<br />
Year: 1822<br />
Place: Cambridge<br />
Publisher: Cambridge Philosophical Society<br />
Edition: 1st<br />
Language: English<br />
Binding: modern paper wrappers<br />
Pagination: pp. 63–76<br />
Size: 272x212 mm.<br />
Reference: Van S CBCP, #19; Babb CBLP, #21; Ran ODC, p.<br />
405; MCK CBCW, v. 2, pp. 33–37<br />
In this extract from Transactions <strong>of</strong> the Cambridge<br />
Philosophical Society, <strong>Babbage</strong> begins his commentary<br />
with the assertion that many mathematical discoveries<br />
are dependent on the development <strong>of</strong> a suitable<br />
mathematical notation. See also the entry for <strong>Babbage</strong>,<br />
On the influence <strong>of</strong> signs in mathematical reasoning,<br />
1826.<br />
Illustrations available:<br />
First page
Erwin Tomash Library<br />
<strong>Babbage</strong>, <strong>Charles</strong> <strong>Babbage</strong>, <strong>Charles</strong><br />
B 48<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
B 48<br />
Observations on the Temple <strong>of</strong> Serapis at Pozzuoli near<br />
Naples, with an attempt to explain the causes <strong>of</strong> the<br />
frequent elevation and depression <strong>of</strong> large portions <strong>of</strong><br />
the earth’s surface in remote periods, and to prove that<br />
those causes continue in action at the present time. With<br />
a supplement. Conjectures on the physical condition <strong>of</strong><br />
the surface <strong>of</strong> the moon.<br />
Year: 1847<br />
Place: London<br />
Publisher: Privately printed (for the author) by Richard and<br />
John Taylor<br />
Edition: 1st<br />
Language: English<br />
Figures: 2 double lithographed plates (1 colored)<br />
Binding: original cloth boards; gilt embossed covers<br />
Pagination: pp. 42, [4]<br />
Collation: A–B 8 C 5 χ 2<br />
Size: 222x136 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 4, pp. 165–217<br />
This small work testifies once more to <strong>Babbage</strong>’s wide-<br />
ranging curiosity. During one <strong>of</strong> his several trips to Italy,<br />
he noted evidence <strong>of</strong> the Temple <strong>of</strong> Serapis having been<br />
submerged. In this booklet he attempts an explanation for<br />
ground movement based on information first presented<br />
as a paper in the Proceedings <strong>of</strong> the Geological Society,<br />
March 1834, Vol. ii, p. 72. <strong>Babbage</strong> theorized that the<br />
area had been heated and cooled by movements <strong>of</strong> the<br />
liquid core <strong>of</strong> the earth. His reasoning was that a onemile<br />
thickness <strong>of</strong> rock would expand twenty-five feet if<br />
heated a hundred degrees Fahrenheit and thus raise or<br />
lower the ground surface above it by the same amount.<br />
Illustrations available:<br />
Title page<br />
B 49<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Passages from the life <strong>of</strong> a philosopher.<br />
B 49<br />
Year: 1864<br />
Place: London<br />
Publisher: Longman, Green, Longman, Roberts & Green<br />
Edition: 1st<br />
Language: English<br />
Figures: engraved frontispiece<br />
Binding: contemporary leather—special presentation copy<br />
inscribed by <strong>Babbage</strong>: “To her Majesty, Eugenie,<br />
Empress <strong>of</strong> the French, most respectfully presented by<br />
the author”<br />
Pagination: pp. xii, 496<br />
Collation: A 6 B–2I 8<br />
Size: 218x133 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 11<br />
This autobiographical work notably comprises the<br />
history <strong>of</strong> both the Difference Engine and the Analytical<br />
Engine. It also treats his many other inventions and<br />
contributions including the speedometer, the cowcatcher,<br />
encoded lighthouse signaling and what is today known<br />
as operations research.<br />
This example, in a deluxe Royal binding, with silk<br />
endpapers by Robert Rivière, is inscribed To her Majesty,<br />
Eugenie, Empress <strong>of</strong> the French, most respectfully<br />
presented by the author.<br />
A second presentation copy <strong>of</strong> this work (original cloth<br />
boards, unopened) is in the collection. It is inscribed:<br />
To [Mm] M. Mignet, member <strong>of</strong> the <strong>Institute</strong> <strong>of</strong> France,<br />
from the author.<br />
Illustrations available:<br />
Title page<br />
Frontispiece<br />
Design on the front and back cover <strong>of</strong> the leather binding<br />
85
86<br />
Frontispiece, B 49<br />
Erwin Tomash Library<br />
<strong>Babbage</strong>, <strong>Charles</strong> <strong>Babbage</strong>, <strong>Charles</strong><br />
B 50<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Pensieri sui principii dell’imposta in relazione ad una<br />
tassa sulla propietà e sue eccezioni… Tradotti dall<br />
Inglese in Italiano.<br />
Year: 1850<br />
Place: Turin<br />
Publisher: Cugini Pomba e C. Editori<br />
Edition: 1st<br />
Language: Italian<br />
Binding: contemporary roan-backed marbled boards<br />
Pagination: pp. 40<br />
Size: 161x97 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 5, pp. 31–56<br />
This is the Italian translation <strong>of</strong> <strong>Babbage</strong>’s Thoughts on<br />
the principles <strong>of</strong> taxation with reference to a property<br />
tax and its exceptions (see entry for <strong>Babbage</strong>, Works<br />
<strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong>, M.A., F.R.S., &c. [A Collection<br />
<strong>of</strong> seventeen items by or about <strong>Babbage</strong> bound in one<br />
volume]).<br />
Illustrations available:<br />
Title page<br />
B 51<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Reflections on the decline <strong>of</strong> science in England, and on<br />
some <strong>of</strong> its causes.<br />
Year: 1830<br />
Place: London<br />
Publisher: B. Fellowes<br />
Edition: 1st<br />
Language: English<br />
Binding: three-quarter leather over moirè cloth boards; red<br />
leather label<br />
Pagination: pp. xvi, 228<br />
Collation: A–P 8 Q 2<br />
Size: 216x130 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 7<br />
<strong>Babbage</strong> was courageously outspoken all his life. This<br />
is an attack on the leadership <strong>of</strong> the Royal Society that<br />
led to the formation <strong>of</strong> the British Association for the<br />
Promotion <strong>of</strong> Science in the following year. In this<br />
work <strong>Babbage</strong> reveals his love <strong>of</strong> science and his deep<br />
understanding <strong>of</strong> the nature <strong>of</strong> scientific inquiry. This<br />
work excited a vigorous correspondence in the pages<br />
<strong>of</strong> the Philosophical Magazine that led to <strong>Babbage</strong>’s<br />
reputation as a thorn in the side <strong>of</strong> the British scientific<br />
establishment. Nevertheless, the reforms that <strong>Babbage</strong><br />
sought were eventually realized, not only in the Royal<br />
Society but in British science in general.<br />
The title page has been signed by <strong>Babbage</strong>’s son Henry<br />
<strong>Babbage</strong>.<br />
Illustrations available:<br />
Title page<br />
B 52<br />
[<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)]<br />
B 51<br />
Report from the select committee on the laws respecting<br />
Friendly Societies [Evidence contributed to].<br />
Year: 1827<br />
Place: London<br />
Publisher: HMSO<br />
Edition: 1st (extract)
Erwin Tomash Library<br />
<strong>Babbage</strong>, <strong>Charles</strong> <strong>Babbage</strong>, <strong>Charles</strong><br />
Language: English<br />
Binding: none—extracted from a volume <strong>of</strong> parliamentary<br />
reports<br />
Pagination: pp. 135, [1]<br />
Collation: A–R 4<br />
Size: 335x200 mm<br />
<strong>Babbage</strong> was interested in all aspects <strong>of</strong> the developing<br />
life insurance industry and the statistics upon which<br />
it based rates. As a director <strong>of</strong> the aborted firm <strong>of</strong> The<br />
Protector Life Insurance Co. (see <strong>Babbage</strong>, Protector<br />
Life Assurance Society. In Works <strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong>,<br />
Collection <strong>of</strong> seventeen items …), he, together with<br />
Benjamin Gompertz, was called in to give evidence<br />
to a Select Committee <strong>of</strong> the House <strong>of</strong> Commons<br />
investigating the laws governing the insurance industry.<br />
The testimony concerned the accuracy <strong>of</strong> the tables upon<br />
which the insurance rates were based. While <strong>Babbage</strong><br />
did not, in general, think they were accurate, he <strong>of</strong>ten<br />
tempered his opinion. For example, when asked about<br />
death rates for higher and lower classes <strong>of</strong> society and<br />
whether differing tables should be used for each, he<br />
responded that he thought different tables should be used<br />
but that he would need to see more facts and figures to<br />
see how soundly that opinion was founded.<br />
Illustrations available:<br />
Title page<br />
B 53<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871) [J. E. Isoard, translator]<br />
Science économique des manufactures, traduit de<br />
l’Anglais de Ch. <strong>Babbage</strong>, sur le troisiéme édition par<br />
M. Isoard.<br />
Year: 1834<br />
Place: Paris<br />
Publisher: A la Librairie Orientale de Doney - Dupré<br />
Edition: 2nd (French)<br />
Language: French<br />
Binding: contemporary leather; red leather label<br />
Pagination: pp. xxiii, [1], 392<br />
Collation: π 12 1–24 8 25 4<br />
Size: 206x128 mm<br />
Reference: MCK CBCW, v. 8<br />
Two translations into French <strong>of</strong> <strong>Babbage</strong>’s On the<br />
economy <strong>of</strong> machinery and manufactures appeared in<br />
Paris almost simultaneously. Both were based on the<br />
third English edition <strong>of</strong> 1833. This one by J. M. Isoard,<br />
an <strong>of</strong>ficial at the Ministry <strong>of</strong> Commerce, covered only<br />
<strong>chapter</strong>s 13 to 34 <strong>of</strong> the original. Isoard felt that <strong>Babbage</strong>’s<br />
earlier <strong>chapter</strong>s on machinery were too specialized<br />
for the French reader. For a complete translation, see<br />
<strong>Babbage</strong>, <strong>Charles</strong>; Traité sur l’économie des machines<br />
et des manufactures, 1833.<br />
Illustrations available:<br />
Title page<br />
B 54<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Table <strong>of</strong> logarithms <strong>of</strong> the natural numbers from 1 to<br />
108000.<br />
Year: 1829<br />
Place: London<br />
Publisher: B. Fellowes<br />
Edition: 1st (2nd issue)<br />
Language: English<br />
Binding: original paper boards, printed label on spine<br />
Pagination: pp. xx, 202, [2]<br />
Collation: a 8 b 2 B–N 8 O 4 P 2<br />
Size: 262x158 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405<br />
This is the first edition <strong>of</strong> <strong>Babbage</strong>’s logarithms, printed<br />
on light yellow paper.<br />
<strong>Babbage</strong>’s interest in calculating machines arose from<br />
his desire to mechanically compute complete sets <strong>of</strong><br />
mathematical tables and thus eliminate the errors that<br />
inevitably crept into them when they were calculated and<br />
typeset by hand. He created this table <strong>of</strong> logarithms not<br />
by calculating them, but by comparing many different<br />
tables against one another. When differences were noted,<br />
he would recalculate the correct value, thus producing<br />
the first error-free table <strong>of</strong> logarithms. Not content with<br />
accuracy, he also experimented with their layout and their<br />
printing. He used variously colored papers in combination<br />
B 54<br />
87
88<br />
Erwin Tomash Library<br />
<strong>Babbage</strong>, <strong>Charles</strong> <strong>Babbage</strong>, <strong>Charles</strong><br />
with differently colored inks. He notes in his preface (see<br />
illustration) that all his test subjects agreed that colored<br />
papers were easier to read, but subjects differed as to<br />
which color they preferred. The first edition was printed<br />
on a variety <strong>of</strong> colors: light yellow, green, etc.<br />
<strong>Babbage</strong> also took great pains with the layout <strong>of</strong> the<br />
tables experimenting with type fonts and various<br />
columnar approaches. For example, a comparison <strong>of</strong><br />
these tables with an earlier set (see, for example, the<br />
entry for Hutton, Mathematical tables, 1785) reveals<br />
the obvious difference in ease <strong>of</strong> use.<br />
The only complete set <strong>of</strong> these experimental volumes<br />
extant is held in the Crawford Collection now at the<br />
Royal Observatory in Edinburgh.<br />
Illustrations available:<br />
Title page<br />
B 55<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Table <strong>of</strong> the logarithms <strong>of</strong> the natural numbers from 1<br />
to 108000.<br />
Year: 1831<br />
Place: London<br />
Publisher: B. Fellowes<br />
Edition: 2nd<br />
Language: English<br />
Binding: original paper boards rebacked<br />
Pagination: pp. xx, 202, [2]<br />
Collation: a 8 b 2 B–N 8 O 4 P 2<br />
Size: 262x158 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 2, pp. 72–107<br />
<strong>Babbage</strong> had the pro<strong>of</strong>s <strong>of</strong> the first edition <strong>of</strong> these tables<br />
checked as many as nine times; despite these efforts, nine<br />
errors were found. These were corrected in this second<br />
edition, which in this example is printed on yellow paper<br />
with gray undertones.<br />
Illustrations available:<br />
Title page<br />
Preface remark on colored papers<br />
First page <strong>of</strong> table (color)<br />
B 56<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Table <strong>of</strong> the logarithms <strong>of</strong> the natural numbers from 1<br />
to 108000.<br />
Year: 1834<br />
Place: London<br />
Publisher: <strong>Charles</strong> Knight.<br />
Edition: 3rd<br />
Language: English<br />
Binding: modern half-leather marbled boards<br />
Pagination: pp. xx, 202, [2]<br />
Collation: [A] 8 b 2 B–N 8 O 4 P 2<br />
Size: 241x154 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 2, pp. 72–107<br />
This copy <strong>of</strong> the third edition is printed on light green<br />
paper. There was also a second issue <strong>of</strong> the third edition<br />
in 1838.<br />
Illustrations available:<br />
Title page<br />
Page 1 <strong>of</strong> the tables (color)<br />
B 57<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Table <strong>of</strong> the logarithms <strong>of</strong> the natural numbers from 1<br />
to 108000.<br />
Year: 1841<br />
Place: London<br />
Publisher: William Clowes and Sons<br />
Edition: 4th<br />
Language: English<br />
Binding: original paper boards; red leather label<br />
Pagination: pp. xx, 202, [2]<br />
Collation: [A] 8 b 2 B–N 8 O 4 P 2<br />
Size: 236x146 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 2, pp. 72–107<br />
This copy <strong>of</strong> the fourth edition is printed on light yellow<br />
(sienna) paper. A second copy is also available.<br />
Illustrations available:<br />
Title page<br />
Page 1 <strong>of</strong> the tables (color)<br />
B 58<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Table <strong>of</strong> the logarithms <strong>of</strong> the natural numbers from 1<br />
to 108000.<br />
Year: 1844<br />
Place: London<br />
Publisher: John Murray<br />
Edition: 5th<br />
Language: English<br />
Binding: half bound leather<br />
Pagination: pp. xx, 202<br />
Collation: A 8 b 2 B–N 8 O 4 P 1<br />
Size: 229x135 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 2, pp. 72–107<br />
This copy <strong>of</strong> the fifth edition is printed on light yellow<br />
paper.<br />
Illustrations available:<br />
Title page<br />
Page 1 <strong>of</strong> tables (color)
<strong>Babbage</strong>, <strong>Charles</strong><br />
B 59<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
On tables <strong>of</strong> the constants <strong>of</strong> nature and art. In Annual<br />
report <strong>of</strong> the Board <strong>of</strong> Regents <strong>of</strong> the Smithsonian<br />
Institution, 1857.<br />
Year: 1857<br />
Place: Washington, D.C.<br />
Publisher: A. O. P. Nicholson<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards<br />
Pagination: pp. 298–302 (<strong>of</strong> 468)<br />
Collation: 1–29 8 30 2<br />
Size: 224x140 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 5, pp. 138–154<br />
In this paper <strong>Babbage</strong> proposes an ambitious project<br />
to tabulate all natural features (chemical properties,<br />
measurements) <strong>of</strong> all plants and animals, etc.<br />
Illustrations available:<br />
Title page<br />
B 60<br />
[<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)] – David Brewster<br />
(1781–1868)<br />
On the theoretical principles <strong>of</strong> the machinery for<br />
calculating tables. In a letter from <strong>Charles</strong> <strong>Babbage</strong>,<br />
Esq. F. R. S. Lond. & Edin. to Dr. Brewster. In<br />
Edinburgh Philosophical Journal Vol. VIII. No. 15,<br />
January 1823.<br />
Year: 1823<br />
Journal cover, B 60<br />
Erwin Tomash Library<br />
<strong>Babbage</strong>, <strong>Charles</strong><br />
Place: Edinburgh<br />
Publisher: Archibald Constable and Co.<br />
Edition: 1st<br />
Language: English<br />
Binding: modern paper wrappers<br />
Pagination: pp. 122–128<br />
Size: 207x128 mm<br />
Reference: Van S CBCP, #20; Babb CBLP, #20; Ran ODC, p.<br />
405; MCK CBCW, v. 2, pp. 38–43<br />
<strong>Babbage</strong> appreciated Brewster’s support and seems to<br />
have kept in touch with him. This letter describes the<br />
interesting developments that occur when the Difference<br />
Engine, rather than simply adding differences, was set<br />
to add multiples <strong>of</strong> differences. This material was also<br />
communicated to the Astronomical Society <strong>of</strong> London<br />
(<strong>Babbage</strong>, Memoirs <strong>of</strong> the Astronomical Society <strong>of</strong><br />
London, 1822). Brewster, who had presented a paper<br />
on <strong>Babbage</strong>’s Difference Engine to the Society just<br />
a few months previously, was editor <strong>of</strong> the Edinburgh<br />
Philosophical Society Journal and arranged for it to be<br />
printed it in that publication.<br />
Illustrations available:<br />
Title page<br />
B 61<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Thoughts on the principles <strong>of</strong> taxation with reference to<br />
a property tax and its exceptions.<br />
Year: 1851<br />
Place: London<br />
Publisher: John Murray<br />
Edition: 2nd<br />
Language: English<br />
Binding: new marbled paper wrappers<br />
Pagination: pp. 28, [4]<br />
Size: 198x128 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 5, pp. 31–56<br />
<strong>Babbage</strong> had published this small pamphlet earlier but<br />
was impelled to produce a second edition because <strong>of</strong> a<br />
Parliamentary debate on the imposition <strong>of</strong> an income<br />
tax. In the preface, he also indicates that he was moved<br />
to reprint it … because <strong>of</strong> the prevalence <strong>of</strong> what I<br />
conceive to be unsound principles, even in quarters<br />
where it should be the least expected. His basic political<br />
leanings are revealed when he states: I regard the large<br />
exemptions from the tax admitted in the present act as<br />
leading directly towards Socialism …<br />
See also the entry for <strong>Babbage</strong>, <strong>Charles</strong>; Works <strong>of</strong><br />
<strong>Charles</strong> <strong>Babbage</strong>, M.A., F.R.S., &c. [A Collection <strong>of</strong><br />
seventeen items by or about <strong>Babbage</strong>].<br />
Illustrations available:<br />
Title page<br />
89
90<br />
Erwin Tomash Library<br />
<strong>Babbage</strong>, <strong>Charles</strong> <strong>Babbage</strong>, <strong>Charles</strong><br />
B 62<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
B 61<br />
Traité sur l’économie des machines et des manufactures<br />
… Traduit de l’Anglais sur la troisieme edition, par Éd.<br />
Biot.<br />
Year: 1833<br />
Place: Paris<br />
Publisher: Bachelier<br />
Edition: 1st (French)<br />
Language: French<br />
Binding: contemporary green parchment-backed marbled<br />
boards<br />
Pagination: pp. [4], xvi, 515, [1]<br />
Collation: π 2 a 8 1–32 8 33 2<br />
Size: 208x124 mm<br />
Reference: MCK CBCW, v. 8<br />
See the entry for <strong>Babbage</strong>, <strong>Charles</strong>; On the economy <strong>of</strong><br />
machinery and manufactures, 1832. Unlike J. E. Isoard’s<br />
translation, Science économique des manufactures, Paris<br />
1834, this translation by Biot includes <strong>Babbage</strong>’s work<br />
in its entirety. This is the first French translation and is<br />
based on the third English edition <strong>of</strong> 1833.<br />
Illustrations available:<br />
Title page<br />
B 63<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871) [Jose Diez Imbrechts,<br />
translator]<br />
Tratado de mecánica práctica y economia politica que<br />
con el titulo de Economia de máquinas y manufacturas<br />
escribe in inglis, C. <strong>Babbage</strong> traducido de la 3 a edicion<br />
y ampliado con notas.<br />
Year: 1833<br />
Place: Madrid<br />
Publisher: [I. Sancha]<br />
Edition: 1st (Spanish)<br />
Language: Spanish<br />
Figures: lithographed portrait frontispiece; lithographed title<br />
page<br />
Binding: contemporary leather<br />
Pagination: pp. xx, 356<br />
Collation: * 4 ** 4 *** 2 1–44 4 45 2<br />
Size: 202x135 mm<br />
Reference: MCK CBCW, v. 8<br />
See entry for <strong>Babbage</strong>, On the economy <strong>of</strong> machinery<br />
and manufactures, 1832 edition.<br />
Illustrations available:<br />
Title page<br />
B 64<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
<strong>Charles</strong> <strong>Babbage</strong>’s vergleichende Darstellung der<br />
verschiedenen Lebens - Assecuranz - Gesellschaften.<br />
Aus dem Englischen.<br />
Year: 1827<br />
Place: Weimar<br />
Publisher: Landes - Industrie - Comptoirs<br />
Edition: 1st (German)<br />
Language: German<br />
Figures: 1 folding plate (follows p. 12)<br />
Binding: contemporary quarter-leather marbled boards<br />
Pagination: pp. xvi, 138, [30], 12, 8<br />
Collation: π 8 1–10 8 11 4 χ 10<br />
Size: 206x116 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405; MCK CBCW, v. 6<br />
B 63
<strong>Babbage</strong>, <strong>Charles</strong><br />
Within a year <strong>of</strong> the publication <strong>of</strong> A comparative view<br />
<strong>of</strong> the various institutions for the assurance <strong>of</strong> lives, in<br />
1826, a German translation appeared that <strong>Babbage</strong> noted<br />
with some pride in his List <strong>of</strong> Works, 1847 (see entry for<br />
<strong>Babbage</strong>, Works <strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong>, M.A., F.R.S., &c.<br />
[A Collection <strong>of</strong> seventeen items by or about <strong>Babbage</strong>]).<br />
The German edition was published for the purpose <strong>of</strong><br />
establishing, at Gotha, a Society for the Assurance <strong>of</strong><br />
Lives, by the Life Assurance Bank <strong>of</strong> Gotha, in 1829.<br />
According to the above-mentioned List <strong>of</strong> Works:<br />
At the commencement <strong>of</strong> 1847, the number <strong>of</strong><br />
persons whose lives had been assured, was 14,564,<br />
and the amount then assured was 23,218,700 Thlr.<br />
Illustrations available:<br />
Title page<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
A word to the Wise. Observations on peerage for life.<br />
See <strong>Babbage</strong>, <strong>Charles</strong>; Works <strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong>,<br />
M.A., F.R.S., &c. [A Collection <strong>of</strong> seventeen items<br />
by or about <strong>Babbage</strong>].<br />
B 65<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
Works <strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong>, M.A., F.R.S, &c. [A<br />
Collection <strong>of</strong> seventeen items by or about <strong>Babbage</strong><br />
bound in one volume].<br />
Year: 1815–1864 (but 1824–1872)<br />
Place: London<br />
Edition: 1st<br />
Language: English<br />
Figures: engraved portrait pasted on frontispiece<br />
Binding: contemporary three-quarter leather; marbled<br />
endpapers<br />
Size: 206x131 mm<br />
Reference: MCK CBCW, v. 1, pp. 34–47<br />
This is much more a <strong>Babbage</strong> miscellany than the usual<br />
sammelband (the binding together <strong>of</strong> a set <strong>of</strong> related<br />
books or papers <strong>of</strong> similar size). It would seem that this<br />
volume was being readied for publication as it has a title<br />
page and a pasted-up frontispiece complete with a portrait<br />
<strong>of</strong> <strong>Babbage</strong>, as well as typeset half-title pages preceding<br />
many <strong>of</strong> the individual articles. While the List <strong>of</strong> Works<br />
contains none later than 1847, an auction notice <strong>of</strong> 1872<br />
is included, as is <strong>Charles</strong> <strong>Babbage</strong>’s obituary notice <strong>of</strong><br />
1871. The volume was discovered with a cache <strong>of</strong> papers<br />
held by <strong>Babbage</strong> descendants in Ireland. Items 1 and 16<br />
can only be described as ephemera while 3 and 4 are book<br />
reviews, and 2 is the well-known article by Brewster.<br />
Item 6 was written with <strong>Charles</strong> Holzappfel (1806–1847)<br />
Erwin Tomash Library<br />
B 64<br />
<strong>Babbage</strong>, <strong>Charles</strong><br />
a skilled mechanical engineer and technical writer, who<br />
was well acquainted with workshop practice.<br />
A brief list <strong>of</strong> the contents is as follows:<br />
1. Rates <strong>of</strong> the Protector Life Assurance Society<br />
2. On Mr. <strong>Babbage</strong>’s new Machine for Calculating<br />
and printing Mathematical and Astronomical<br />
Tables. Philosophical Magazine, May 1824<br />
3. A Comparative View <strong>of</strong> the Various Institutions<br />
for the Assurance <strong>of</strong> Lives. Quarterly Review, Vol.<br />
xxxv, No. lxix (review)<br />
4. Reflections on the Decline <strong>of</strong> Science in England.<br />
Quarterly Review, Vol. Xliii No. lxxxvi (review)<br />
5. Letter from Mr. <strong>Babbage</strong> to the members <strong>of</strong> the<br />
British Association for the Promotion <strong>of</strong> Science,<br />
1839<br />
6. Paper on the principles <strong>of</strong> Tools for Turning and<br />
Planing Metals, 1846<br />
7. Thoughts on the Principles <strong>of</strong> Taxation, third<br />
edition, 1852<br />
8. On Mechanical Notation as exemplified in the<br />
Swedish calculating machine by Henry P. <strong>Babbage</strong><br />
(from the Report <strong>of</strong> the British Association, 1855)<br />
9. Report <strong>of</strong> a Committee appointed by the Council<br />
to examine the Calculating Machine <strong>of</strong> M. Scheutz<br />
(Royal Society)<br />
10. An Analysis <strong>of</strong> the Statistics <strong>of</strong> the Clearing House<br />
During the Year 1839, 1856<br />
11. On the Calculation and Printing <strong>of</strong> Mathematical<br />
Tables by Machinery; The Inventor and His<br />
Treatment by Judex Juris (a pseudonym for James<br />
Jerwood)<br />
12. Observations on Peerage for Life, 1856<br />
91
92<br />
Erwin Tomash Library<br />
<strong>Babbage</strong>, <strong>Charles</strong> <strong>Babbage</strong>, <strong>Charles</strong><br />
13. On the Action <strong>of</strong> Ocean Currents in the Formation<br />
<strong>of</strong> the Strata <strong>of</strong> the Earth. Quarterly Journal <strong>of</strong> the<br />
Geological Society <strong>of</strong> London, November 1856<br />
14. Address <strong>of</strong> Dr. Farr, President <strong>of</strong> the Statistical<br />
Society, Session 1871–1872<br />
15. Obituary Notice <strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong>, Esq.<br />
F.R.S.: from the Monthly Notices <strong>of</strong> the Royal<br />
Astronomical Society<br />
16. A catalogue <strong>of</strong> a collection <strong>of</strong> Engineers’ Tools<br />
and Plant Used by the late Mr. Baggage (auction<br />
notice), 1872<br />
17. A list <strong>of</strong> works <strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong>.<br />
Illustrations available:<br />
Title page<br />
Obituary Notice and Catalogue <strong>of</strong> tools<br />
B 66<br />
[<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)]<br />
Auction notice, B 65<br />
The Art Journal illustrated catalogue <strong>of</strong> the Industry <strong>of</strong><br />
All Nations - 1851.<br />
Year: 1851<br />
Place: London<br />
Publisher: George Virtue for the Proprietors<br />
Edition: 1st<br />
Language: English<br />
Figures: engraved frontispiece<br />
Binding: original gilt-embossed cloth boards and spine<br />
Pagination: pp. xxvi, 328, xvi, viii, viii, viii, xxii<br />
Collation: a(-a1)–g 2 B–4O 2 * 8 ‡ 4 † 4 ** 4 *** 12 (-***12)<br />
Size: 327x240 mm<br />
B 65<br />
<strong>Babbage</strong> was incensed at the exclusion <strong>of</strong> his Difference<br />
Engine from the Great Exhibition <strong>of</strong> 1851, and his bitter<br />
feelings were compounded by his not being asked to<br />
play a leading role in its organization. The latter <strong>of</strong>fense<br />
probably resulted from his not entirely undeserved<br />
reputation for refractoriness. There is nothing in this<br />
volume that directly concerns <strong>Babbage</strong> (other than the<br />
omission <strong>of</strong> his engines), but it represents a troubled era<br />
in which he wrote several diatribes against the British<br />
establishment.<br />
Illustrations available:<br />
Title page<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871)<br />
See American magazine <strong>of</strong> useful and entertaining<br />
knowledge; Vol. 1, pp. 88–96, <strong>Babbage</strong>’s<br />
calculating engine<br />
See Baily, Francis; On Mr. <strong>Babbage</strong>’s new machine<br />
for calculating and printing mathematical and<br />
astronomical tables<br />
See Bass, Michael T.; Street music in the metropolis<br />
See Brewster, David; On machinery for calculating<br />
and printing mathematical tables<br />
See Buxton, Leonard Halford Dudley; <strong>Charles</strong><br />
<strong>Babbage</strong> and his difference engines<br />
See Colebrooke, Henry Thomas; Address <strong>of</strong> Henry<br />
Thomas Colebrooke, president <strong>of</strong> the Astronomical<br />
Society <strong>of</strong> London, on presenting the gold medal to<br />
<strong>Charles</strong> <strong>Babbage</strong><br />
See Dodd, George; The curiosities <strong>of</strong> industry and the
<strong>Babbage</strong>, <strong>Charles</strong><br />
applied sciences, 1852 and 1854<br />
See Dodge, Nathaniel Shatswell; <strong>Charles</strong> <strong>Babbage</strong>,<br />
1874<br />
See Knight’s Cyclopædia, Calculating machines<br />
See Lardner, Dionysius; <strong>Babbage</strong>’s calculating<br />
engines<br />
See Marshall, William P.; <strong>Babbage</strong>’s calculating<br />
machine, 1879<br />
See Menabrea, Luigi Federico; Sur la machine<br />
analytique de <strong>Charles</strong> <strong>Babbage</strong><br />
See Menabrea, Luigi Federico [Augusta Ada<br />
Lovelace, translator]; Sketch <strong>of</strong> the Analytical<br />
Engine invented by <strong>Charles</strong> <strong>Babbage</strong>, Esq… with<br />
notes by the translator<br />
See Quetelet, Lambert Adolphe Jacques; Notice <strong>of</strong><br />
<strong>Charles</strong> <strong>Babbage</strong><br />
See Sheepshanks, Richard; Correspondence<br />
respecting the Liverpool Observatory<br />
See Strand Magazine - William G. Fitzgerald, The<br />
romance <strong>of</strong> the museums.<br />
B 67<br />
<strong>Babbage</strong>, <strong>Charles</strong> (1791–1871) and John F. W. Herschel<br />
(1792–1871)<br />
Memoirs <strong>of</strong> the Analytical Society 1813.<br />
b/w: Agnesi, Donna Maria Gaetena, [John Colson,<br />
translator]; Analytical institutions, in four books:<br />
originally written in Italian…. Translated into<br />
English by the late Rev. John Colson…<br />
Year: 1813<br />
Place: Cambridge<br />
Publisher: Printed by J. Smith<br />
Edition: 1st<br />
Language: English<br />
Binding: contemporary three-quarter leather over marbled<br />
boards<br />
Pagination: pp. [4], xxii, [2], 114<br />
Collation: π 2 a–f 2 A–2E 2 2F 1<br />
Size: 271x212 mm<br />
Reference: Van S CBCP, #1; Babb CBLP, #1; Ran ODC, p.<br />
405; MCK CBCW, v. 1, pp. 37–60; Dub MWCB, p. 230<br />
Driven by their desire to modernize the teaching<br />
<strong>of</strong> mathematics at Cambridge when they were<br />
undergraduates there, <strong>Babbage</strong>, Herschel and Peacock<br />
founded the Analytical Society in 1813. The contents<br />
were <strong>of</strong> surprisingly high quality (<strong>of</strong>ten written by the<br />
founders and their friends). This volume contains a<br />
preface and three articles. <strong>Babbage</strong> was certainly the<br />
author <strong>of</strong> the preface and the first article, and he might<br />
well have written the second.<br />
Illustrations available:<br />
Title page<br />
Erwin Tomash Library<br />
<strong>Babbage</strong>, Henry Prevost<br />
B 67<br />
<strong>Babbage</strong>, <strong>Charles</strong> and <strong>Charles</strong> Holtzapffel (1806–1847)<br />
See <strong>Babbage</strong>, <strong>Charles</strong>; Works <strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong><br />
M.A. F.R. S. &c. [A Collection <strong>of</strong> seventeen items<br />
by or about <strong>Babbage</strong> bound in one volume] - Paper<br />
on principles <strong>of</strong> tools, for turning and planing<br />
metals from: Holtzapffel, <strong>Charles</strong>, Turning and<br />
mechanical manipulation, Vol. 2, London, 1847,<br />
pp. 984–991.<br />
[<strong>Babbage</strong>, <strong>Charles</strong>; George Peacock and John<br />
Frederick William Herschel, translators]<br />
See Lacroix, Sylvestre François, An elementary<br />
treatise on the differential and integral calculus.<br />
Translated from the French with an appendix and<br />
notes.<br />
B 68<br />
<strong>Babbage</strong>, Henry Prevost (1824–1925)<br />
<strong>Babbage</strong>’s analytical engine. In Monthly notices <strong>of</strong> the<br />
Royal Astronomical Society, v. LXX, No. 6, April 1910.<br />
Year: 1910<br />
Place: London<br />
Publisher: Royal Astronomical Society<br />
Edition: 1st<br />
Language: English<br />
Figures: 1 photolith plate; 1 table<br />
Binding: original paper wrappers<br />
Pagination: pp. 517–520<br />
Size: 225x145 mm<br />
Reference: Ran ODC, p. 406; Flet MT vol. I, p. 121; Dub<br />
MWCB, p. 196<br />
The youngest son <strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong>, Henry Prevost<br />
<strong>Babbage</strong>, rose to the rank <strong>of</strong> Major-General in the British<br />
93
94<br />
Erwin Tomash Library<br />
<strong>Babbage</strong>, Henry Prevost <strong>Babbage</strong>, Henry Prevost<br />
Army. At <strong>Charles</strong>’ death, he took possession <strong>of</strong> all his<br />
father’s materials relating to the calculating engines<br />
and used them both to promote his father’s work and to<br />
construct a portion <strong>of</strong> the analytical engine.<br />
Henry <strong>Babbage</strong> reports that he had managed to assemble<br />
the mill (arithmetic unit) <strong>of</strong> his father’s analytical engine<br />
to the point where it would do simple calculations—in<br />
this case produce multiples <strong>of</strong> π. Also, in this work Henry<br />
explains his reasons for melting down the remaining<br />
portions <strong>of</strong> his father’s Difference Engine.<br />
This copy remains uncut, rendering the introductory<br />
material on the first page difficult to read. The plate<br />
shows the mill and the table <strong>of</strong> multiples.<br />
Illustrations available:<br />
Last two pages <strong>of</strong> text<br />
Plate <strong>of</strong> mill and table<br />
B 69<br />
<strong>Babbage</strong>, Henry Prevost (1824–1925)<br />
On the mechanical arrangements <strong>of</strong> the Analytical<br />
Engine <strong>of</strong> the late <strong>Charles</strong> <strong>Babbage</strong>, F.R.S. In Report <strong>of</strong><br />
the Fifty-Eighth Meeting <strong>of</strong> the British Association for<br />
the Advancement <strong>of</strong> Science. Held at Bath in September<br />
1888.<br />
Year: 1889<br />
Place: London<br />
Publisher: John Murray<br />
Edition: 1st<br />
Language: English<br />
Binding: contemporary buckram<br />
Pagination: pp. 616–617<br />
Size: 215x138 mm<br />
Reference: Van S CBCP, #70; Babb CBLP, #71, #73; Ran<br />
ODC, p. 405<br />
This is a brief report <strong>of</strong> the presentation made by Henry P.<br />
<strong>Babbage</strong> at the 1888 meeting <strong>of</strong> the British Association.<br />
The closing sentences are <strong>of</strong> interest:<br />
It may here be stated that a piece <strong>of</strong> machinery<br />
working to 29 places <strong>of</strong> figures, and embodying<br />
the anticipating carriage, was shown during the<br />
meeting to several who desired to see it. The<br />
anticipating carriage works perfectly, and was<br />
much admired by those who saw it.<br />
Illustrations available:<br />
None<br />
B 70<br />
<strong>Babbage</strong>, Henry Prevost (1824–1925)<br />
Memoirs and correspondence <strong>of</strong> Major-General H. P.<br />
<strong>Babbage</strong>.<br />
Year: 1910<br />
Place: London<br />
Publisher: W. Clowes<br />
Edition: 1st<br />
Language: English<br />
Figures: engraved portrait frontispiece<br />
Binding: original cloth boards; gilt spine<br />
Pagination: vii, [1], 264<br />
Collation: A 4 B–R 8 S 4<br />
Size: 214x135 mm<br />
Reference: DSB, v. 1, p. 356a<br />
The Mill, B 68<br />
<strong>Charles</strong> <strong>Babbage</strong>’s son, Henry Prevost, was his intellectual<br />
heir. Having joined the Indian army, Henry’s language<br />
skills enabled him to pass examinations in some <strong>of</strong> the<br />
major Indian languages, thus securing him administrative<br />
positions, mainly in the Indian judicial system. Although<br />
many <strong>of</strong> his siblings had moved to Australia and other<br />
British colonies, Henry eventually retired to England<br />
with the rank <strong>of</strong> Major General and wrote his memoirs.<br />
His writing is not fluid, and much <strong>of</strong> the work seems<br />
to have been based upon short extracts from his diary.<br />
However, there are some well-written sections. For<br />
example, his description <strong>of</strong> service in India during the<br />
Great Indian Mutiny <strong>of</strong> 1857, notably the execution <strong>of</strong><br />
forty men from his regiment by being blown away from<br />
guns on the parade ground at Peshawar. There is also<br />
a moving account <strong>of</strong> his father’s deathbed, the dying<br />
<strong>Charles</strong> tormented by the racket from organ grinders in<br />
the street, and another <strong>of</strong> the circumstances when, after<br />
attempting to assemble his father’s Difference Engine<br />
from the parts Clement had made, he finally recognized<br />
its futility and had most <strong>of</strong> the parts melted down.
Erwin Tomash Library<br />
<strong>Babbage</strong>, Henry Prevost Bachmann, Udalricum<br />
Illustrations available:<br />
Title page<br />
Frontispiece portrait <strong>of</strong> H.P. <strong>Babbage</strong><br />
B 70<br />
B 71<br />
<strong>Babbage</strong>, Henry Prevost (1824–1925) [<strong>Charles</strong> Manby,<br />
editor]<br />
Scheutz’ difference engine and <strong>Babbage</strong>’s mechanical<br />
notation. In Minutes <strong>of</strong> Proceedings <strong>of</strong> the Institution <strong>of</strong><br />
Civil Engineers with Abstracts <strong>of</strong> the Discussions, Vol.<br />
XV.<br />
Year: 1856<br />
Place: London<br />
Publisher: Institution <strong>of</strong> Civil Engineers<br />
Edition: 1st<br />
Language: English<br />
Binding: three-quarter bound over marbled paper boards; gilt<br />
spine<br />
Pagination: pp. 497–514<br />
Size: 207x125 mm<br />
Reference: DSB, v. 1, p. 356a<br />
Manby, the editor <strong>of</strong> the Proceedings <strong>of</strong> the Institution <strong>of</strong><br />
Civil Engineers, reports on a presentation given at one <strong>of</strong><br />
their meetings by <strong>Charles</strong> <strong>Babbage</strong> and his son, Henry<br />
P. <strong>Babbage</strong>. They first described the Scheutz Difference<br />
Engine, and <strong>Charles</strong> praised many aspects <strong>of</strong> the machine,<br />
noting that they differed completely from his own. This<br />
was followed by a presentation on the notation <strong>Babbage</strong><br />
Sr. had developed for detailing movements in complex<br />
Henry Prevost <strong>Babbage</strong>, B 70<br />
mechanical devices, and parts <strong>of</strong> the Scheutz engine were<br />
explained using this form <strong>of</strong> notation. Unfortunately, the<br />
charts used during the presentation are not preserved as<br />
part <strong>of</strong> Manby’s report.<br />
Illustrations available:<br />
First page<br />
<strong>Babbage</strong>, Henry Prevost (1824–1925)<br />
See <strong>Babbage</strong>, <strong>Charles</strong>; Works <strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong><br />
M.A. F.R.S. &c [A collection <strong>of</strong> seventeen items by<br />
and about <strong>Babbage</strong>] — On mechanical notation, as<br />
exemplified in the Swedish calculating machine <strong>of</strong><br />
Messrs. Scheütz.<br />
B 72<br />
Bachmann, Udalricum<br />
Neues Creuz-Rechen-Buchlein, Dergleichen niemalen<br />
in Druck aussgegangen. In welchem unterschiedlich<br />
aussgegangne Tarriffae Rechen-Buchlein, so von<br />
Kauffen und Verkauffen, auch anderen Zinsen,<br />
Besoldungen, und Hauss-Rechnungen handlen, um vil<br />
vermehrt, und gebessert zu finden.<br />
Year: 1693<br />
Place: Augsburg<br />
Publisher: Jacob Koppmayer<br />
Edition: 1st<br />
Language: German<br />
Figures: engraved frontispiece<br />
Binding: tall, narrow, quarter-bound leather<br />
Pagination: ff. [190]<br />
Collation: ][ 10 A–2Q 4 2T–2Z 4 3A 4<br />
Size: 198x80 mm<br />
Reference: Bru MLAL<br />
95
Baehne, George Walter<br />
This unusual ready reckoner was produced for use<br />
in southern Germany. Of interest is the allegorical<br />
frontispiece depicting merchants discussing units <strong>of</strong><br />
measure, together with a quotation from the Bible about<br />
cheating in small things leading to cheating in larger ones.<br />
It is uncommon to see all the tables presented entirely<br />
in Roman numerals, referred to here as Baurenziffer or<br />
farmer’s digits. The tables present various weights and<br />
measures in terms <strong>of</strong> fractions—usually eighths, twentyfourths,<br />
etc.<br />
96<br />
Illustrations available:<br />
Frontispiece and title page<br />
Dedication page<br />
First page <strong>of</strong> tables<br />
B 73<br />
Baehne, George Walter<br />
Roman numeral table, B 72<br />
Practical applications <strong>of</strong> the punch card method in<br />
colleges and universities.<br />
Year: 1935<br />
Place: New York<br />
Publisher: Columbia <strong>University</strong> Press<br />
Edition: 1st<br />
Language: English<br />
Figures: 6 plates, figures in text<br />
Binding: original cloth boards<br />
Size: 253x174 mm<br />
Reference: Enc Brit, v.12, p. 344<br />
Erwin Tomash Library<br />
Baehne, George Walter<br />
B 72<br />
Dedication, B 72<br />
Thanks to a 1929 grant <strong>of</strong> punched card equipment from<br />
IBM, Columbia <strong>University</strong> became a leader in the use<br />
<strong>of</strong> this equipment among colleges and universities. This<br />
volume shows that interest in the processing <strong>of</strong> punched<br />
card data in universities was not confined to Columbia.<br />
The work, edited by Baehne, is mainly devoted to the<br />
administrative uses <strong>of</strong> punched card equipment, though<br />
it does also describe their use in psychological, medical,<br />
agricultural, scientific, legal and statistical areas.<br />
Astronomical usage for the equipment is presented by<br />
W. J. Eckert, who would later head up the IBM Watson<br />
Laboratory at Columbia <strong>University</strong>.
Erwin Tomash Library<br />
Baehne, George Walter Baeza, Lodoico<br />
The problems faced by university registrars seem to<br />
have changed little since this volume was written—only<br />
the numbers <strong>of</strong> students and equipment available to<br />
process them have modified the situation. The methods<br />
used to process data were based on the capabilities <strong>of</strong><br />
the equipment. For example, it was possible to sort<br />
punched cards on a single column (character) at a time.<br />
A digit was represented by a single punch in any <strong>of</strong> ten<br />
possible rows in the column, but an alphabetic character<br />
required two punches out <strong>of</strong> each column. This meant<br />
that sorting cards alphabetically required two passes<br />
through the sorter for each column <strong>of</strong> the data field. Thus<br />
alphabetizing a class list would take two passes through<br />
the sorter for each character in the student’s name<br />
field—a non-trivial amount <strong>of</strong> work. The <strong>University</strong> <strong>of</strong><br />
Oregon describes a system it adopted to break the range<br />
<strong>of</strong> possible student names into ten thousand parts and<br />
assign a four-digit code number to each – thus the list<br />
could be alphabetized by only sorting on 4 digits instead<br />
<strong>of</strong> many alphabetic columns.<br />
This volume is valuable in that it contains a complete<br />
description <strong>of</strong> the IBM/Hollerith equipment <strong>of</strong> the pre–<br />
World War II period. The machines are reproduced in the<br />
illustrations.<br />
Illustrations available:<br />
Title page<br />
Equipment essay ( 6 pages)<br />
<strong>University</strong> <strong>of</strong> Oregon name code<br />
Punched card equipment, B 73<br />
Card sorter, B 73<br />
B 74<br />
Baeza, Lodoico (ca.1550)<br />
B 73<br />
Numerandi doctrina præ clara methodo exposita, in<br />
qua breviter continentur, & exponuntur apertè ea, quæ<br />
ex universa arithmetica sunt ad usum potiora.<br />
Year: 1555<br />
Place: Paris<br />
Publisher: Gulielmum Cavellat<br />
Edition: 1st<br />
Language: Latin<br />
Figures: 1 folding plate (f.54)<br />
Binding: contemporary paper wrappers<br />
Pagination: ff. 67, [1]<br />
Collation: A–H 8 I 4<br />
Size: 161x97 mm<br />
Reference: Smith Rara, p. 269<br />
B 74<br />
Lodoico Baeza is known only as a Spanish scholar from<br />
the mid-sixteenth century.<br />
97
98<br />
Erwin Tomash Library<br />
Bagay, Valentin Baily, Francis<br />
This is a work on arithmetic. It begins by presenting<br />
the Hindu-Arabic numerals, addition and multiplication<br />
tables, squares, cubes and square roots—all in quite<br />
modern form. These elementary ideas occupy only the<br />
first few pages, and the text is thereafter devoted to<br />
topics such as mixed radix arithmetic (addition <strong>of</strong> days,<br />
hours, minutes, etc.), including a table that could be used<br />
to convert days to hours, etc.<br />
The text is heavily interspersed, particularly in the first<br />
half, with Greek quotations.<br />
Illustrations available:<br />
Title page<br />
B 75<br />
Bagay, Valentin (1772–1851)<br />
Nouvelles tables astronomiques et hydrographiques,<br />
contenant un traité abrégé des cercles de la sphère;<br />
- la description des instruments a réflexion; - diverses<br />
méthodes pour obtenir les latitudes et les longitudes<br />
terrestres; - une nouvelle table des logarithmes, des<br />
sinus, cosinus, tangentes et cotangentes, de seconde en<br />
seconde, pour les quatre-vingt-dix degrés du quart du<br />
cercle.<br />
Year: 1829<br />
Place: Paris<br />
Publisher: Firmin Didot Père et Fils<br />
Edition: 1st<br />
Language: French<br />
Figures: 5 engraved plates<br />
Binding: contemporary half-leather boards<br />
Pagination: pp. [8], lxxxvi, [iv], 125, 615<br />
Collation: π 4 1–11 4 1–15 4 16 3 1–77 4<br />
Size: 265x205 mm<br />
Reference: Glais RCMT, p. 86; Hend BTM, #134.0, p. 111;<br />
Soth/Zeit BCM, Vol III, #875–#804, p. 65<br />
Bagay was pr<strong>of</strong>essor <strong>of</strong> Hydrographie at Lorient.<br />
This very extensive set <strong>of</strong> tables for astronomy and<br />
navigation is an example <strong>of</strong> the best tabular technique in<br />
use as <strong>Charles</strong> <strong>Babbage</strong> began his efforts to mechanize<br />
table making. A series <strong>of</strong> introductory essays discuss<br />
topics from spherical geometry to observational<br />
instruments such as the sextant and octant. The<br />
detailed tables provide corrections for temperature and<br />
humidity. Logarithms are given for natural numbers and<br />
trigonometric functions for both decimal and sexagesimal<br />
numbers to every minute <strong>of</strong> the arc. Bagay introduced<br />
one, easily visible, typographical improvement on earlier<br />
tables to remove a potential source <strong>of</strong> error: a large black<br />
dot notes where the first figures <strong>of</strong> logarithms change.<br />
Illustrations available:<br />
Title page<br />
Table page illustrating the typographical innovation<br />
B 76<br />
Baily, Francis (1774–1844)<br />
Table typography, B 75<br />
B 75<br />
Astronomical tables and formulae together with a<br />
variety <strong>of</strong> problems explanatory <strong>of</strong> their use and<br />
application. To which are prefixed the elements <strong>of</strong> the<br />
solar system.<br />
Year: 1827<br />
Place: London<br />
Publisher: Richard Taylor<br />
Edition: 1st<br />
Language: English<br />
Binding: original morocco grained blue cloth boards; rebacked<br />
Pagination: pp. xvi, 120, 119*–120*, [2], 123–152, 153*–158*,<br />
153–194, 193*–194*, 195–267, [3], 267–304<br />
Collation: a–b 4 B–P 4 Q 5 R–T 4 U 7 X–2B 4 2C 5 2D–2L 4 2M 2 2M–2Q 4<br />
Size: 208x128 mm<br />
Reference: DSB, v. 1, pp. 402–403
Erwin Tomash Library<br />
Baily, Francis Baker, Humphrey<br />
Francis Baily, after whom Baily’s Beads (caused by<br />
the sun shining through mountain valleys on the moon<br />
during an eclipse) are named, was a member <strong>of</strong> the Royal<br />
Society, one <strong>of</strong> the founders <strong>of</strong> the Astronomical Society,<br />
and later its president for two terms. He left England, aged<br />
twenty-one, and spent the next two years at sea and as an<br />
adventurer in America. During that time he endured two<br />
shipwrecks, a voyage in an open boat from Pittsburgh<br />
to New Orleans, and a return trip to New York over two<br />
thousand miles <strong>of</strong> wilderness. He evidently attempted to<br />
obtain American citizenship by marriage, but when that<br />
failed, he returned to England in 1798. Thereafter, he<br />
attempted to join various expeditions to Africa, but when<br />
these also fell through, he became a stockbroker. His first<br />
publications, Tables for the purchasing and renewing<br />
<strong>of</strong> leases (1802), The doctrine <strong>of</strong> interest and annuities<br />
(1808), and The doctrine <strong>of</strong> life-annuities and assurances<br />
(1810), made his reputation in the financial world. He<br />
first published on astronomy in 1811 and became one <strong>of</strong><br />
the founders <strong>of</strong> the Royal Astronomical Society in 1820.<br />
In 1825, at the age <strong>of</strong> fifty, having made a fortune in<br />
banking, he retired to devote his life to astronomy.<br />
These tables are a collection <strong>of</strong> items that Baily found<br />
useful in his calculations. The first 120 pages are divided<br />
equally between a description <strong>of</strong> the solar system and<br />
lists <strong>of</strong> formulae useful for astronomical calculation.<br />
The section <strong>of</strong> tables seems short, occupying only about<br />
one quarter <strong>of</strong> the volume. The last section is devoted<br />
to a brief description <strong>of</strong> the tables and a number <strong>of</strong><br />
astronomical problems illustrating their use.<br />
An appendix, dated January 1829, bound at the back<br />
<strong>of</strong> this volume, was written after Baily had received<br />
comments from other astronomers. He had sent a few<br />
copies for comment before it was released and then<br />
modified some <strong>of</strong> the original tables in light <strong>of</strong> the<br />
remarks. Thus the work, while dated 1827, was not<br />
available to any but a select few prior to 1829. This is<br />
copy #113, with presentation to the Royal Institution.<br />
Illustrations available:<br />
Title page<br />
B 77<br />
Baily, Francis (1774–1844) [H. C. Schumacher, editor]<br />
On Mr. <strong>Babbage</strong>’s new machine for calculating and<br />
printing mathematical and astronomical tables.<br />
London, November 28, 1823. In Astronomische<br />
Nachrichten No. 46, 1/2.<br />
Year: 1824<br />
Place: Altona<br />
Publisher: Astronomische Nachrichten<br />
Edition: 1st<br />
B 76<br />
Language: English<br />
Binding: original marbled boards<br />
Pagination: pp. 409–422<br />
Size: 258x226 mm<br />
Reference: DSB, v. 1, pp. 402–403; Ran ODC, p. 406; MCK<br />
CBCW, v. 2, pp. 44–56<br />
A report on <strong>Babbage</strong>’s Difference Engine given by<br />
Francis Baily, an astronomer and friend <strong>of</strong> <strong>Babbage</strong>. For<br />
a biographical note on Baily, see Baily, Astronomical<br />
tables, 1827.<br />
Illustrations available:<br />
None<br />
B 78<br />
Baker, Humphrey (fl.1557–1587) [Henry Phillippes (fl.<br />
1648–77), editor]<br />
Baker’s arithmetick: teaching the perfect work and<br />
practice <strong>of</strong> arithmetick both in whole numbers &<br />
fractions. Whereunto are added many rules and tables<br />
<strong>of</strong> interest, rebate, and purchases, & c. Also, the art <strong>of</strong><br />
decimal fractions, intermixed with common fractions,<br />
for the better understanding there<strong>of</strong>. Newly corrected<br />
and enlarged, and made more plain and easie by Henry<br />
Phillippes.<br />
Year: 1670<br />
Place: London<br />
Publisher: Edward Thomas<br />
Edition: 1st<br />
99
100<br />
Erwin Tomash Library<br />
Baker, Humphrey Baker, Humphrey<br />
Language: English<br />
Binding: contemporary leather; rebacked; red leather label<br />
Pagination: pp. [16], 128, 139–362, 367–398 (misnumbering<br />
390 as 388, 391 as 389, 394 as 392, 395 as 393, 398 as<br />
396)<br />
Collation: A–2B 8<br />
Size: 163x106 mm<br />
Reference: Smi Rara, p. 327<br />
Henry Phillippes, the editor, was a teacher <strong>of</strong> mathematics,<br />
surveying and gauging in London. He lived for most <strong>of</strong><br />
his life in a house built on London Bridge. He took part<br />
in the Royal Society investigations <strong>of</strong> the variation <strong>of</strong> the<br />
compass and was considered an authority on the subject.<br />
He is known to have published a number <strong>of</strong> works on<br />
mathematical subjects (see entries under Phillippes).<br />
A comparison with the Baker 1583 edition reveals this<br />
to be an almost completely new work. It seems likely<br />
that the publisher sought to take advantage <strong>of</strong> Baker’s<br />
better-known name. It does contain many <strong>of</strong> the same<br />
tables (although they have been updated and <strong>of</strong>ten show<br />
different values—compare the illustration <strong>of</strong> the table for<br />
Roan here with the one in the entry for the 1583 edition—<br />
see illustrations) with the addition <strong>of</strong> tables such as ones<br />
showing the decimal equivalent <strong>of</strong> common fractions<br />
and decimal equivalents <strong>of</strong> sterling money. Baker’s more<br />
difficult passages, for example, the definition <strong>of</strong> number,<br />
have been rewritten.<br />
Illustrations available:<br />
Title page<br />
Roan table<br />
Decimal tables<br />
B 79<br />
Baker, Humphrey (fl.1557–1587)<br />
The well spring <strong>of</strong> sciences. Which teacheth the perfect<br />
worke and practise <strong>of</strong> arithmeticke, both in whole<br />
numbers and fractions …<br />
Year: 1583<br />
Place: [London]<br />
Publisher: [Thomas Purfoot]<br />
Edition: 7th<br />
Language: English<br />
Binding: contemporary leather<br />
Pagination: ff. [8], 198, 18<br />
Collation: A 8 (-A1, title page replaced by title <strong>of</strong> 1580 edition)<br />
B–V 8 (-T2 torn away) W– 2C 8 D 6 a 2 (a 2 misbound at end)<br />
Size: 144x89 mm<br />
Reference: H&J<br />
Humphrey Baker was a native <strong>of</strong> London, but <strong>of</strong> him<br />
little else is known other than that he translated, from the<br />
French, a book on astrology (The rules touching the use<br />
and practice <strong>of</strong> the common almanacs, 1587).<br />
B 78<br />
B 79<br />
When Baker first published this small pocket arithmetic<br />
in 1562, the only other work on arithmetic in the English<br />
language was Robert Recorde’s Ground <strong>of</strong> Artes.<br />
Record’s book had been criticized as weak, particularly<br />
on the continent, for it was, indeed, inferior to several<br />
works available there. This criticism prompted Baker<br />
to compose this volume, first published in 1568, which<br />
proved to be quite popular.<br />
Baker’s descriptions are lengthy and not easily understood<br />
by a modern reader because they rely on outmoded
Erwin Tomash Library<br />
Baker, Humphrey Baker, Humphrey<br />
concepts. For example, when defining number, he used<br />
the Pythagorean approach that one (1) is not a proper<br />
number, but the progenitor <strong>of</strong> all other numbers (see the<br />
illustration <strong>of</strong> number definition page).<br />
After discussing the simple arithmetic operations, he<br />
covers fractions and makes a few remarks on mixedradix<br />
arithmetic (days, hours, minutes; pounds, shillings,<br />
pence) and the usual procedures for rule <strong>of</strong> three, etc.<br />
The last half <strong>of</strong> the book deals with problems <strong>of</strong> concern<br />
to merchants and others participating in commerce, and<br />
closes with tables giving equivalents <strong>of</strong> weights and<br />
measures in various cities.<br />
Sample table, B 79<br />
Number definition, B 79<br />
Illustrations available:<br />
Title page (not contemporary with this volume – see collation<br />
above)<br />
Number definition page<br />
Sample tables page<br />
B 80<br />
Baker, Humphrey (fl.1557–1587)<br />
B 80<br />
The wel spring <strong>of</strong> sciences. Which teacheth the<br />
perfect worke and practise <strong>of</strong> arithmeticke, both in<br />
whole numbers and fractions : set foorth by Humfrey<br />
Baker Londoner. 1562. And now once againe perused<br />
augmented, and amended in all the three parts, by the<br />
sayde authour: whereunto he hath also added certain<br />
tables <strong>of</strong> the agreement <strong>of</strong> measures and waights <strong>of</strong><br />
diverse places <strong>of</strong> Europe, the one with the other, as by<br />
the table following it may appeare.<br />
Year: 1591<br />
Place: London<br />
Publisher: Thomas Purfoote<br />
Edition: 9th<br />
Language: English<br />
Binding: later full red morocco leather with raised bands on<br />
spine; gilt decorations<br />
Pagination: ff. [7], 137, 137–198 (misnumbering 196 as 198),<br />
[24]<br />
Collation: A 8 (-A2) B–V 8 W–Z 8 2A–2D 8 2E 7<br />
Size: 136x90 mm<br />
Reference: H&J<br />
This is the ninth edition <strong>of</strong> Baker’s Well spring <strong>of</strong> sciences.<br />
It is in much better condition than the copy <strong>of</strong> the seventh<br />
edition described above. A contemporary hand has made<br />
101
102<br />
Colophon and printer’s mark, B 80<br />
Erwin Tomash Library<br />
Baldi, Bernardino Ball, Walter William Rouse<br />
occasional ink notations in the wide margin and another<br />
has added pencil notations. The pencil notations appear<br />
to be <strong>of</strong> two types, one working the examples to check<br />
the arithmetic and another attempting to correct misprints<br />
or clarify hard-to-read text. The pencil annotations leave<br />
the impression <strong>of</strong> someone preparing another edition.<br />
Illustrations available:<br />
Title page<br />
Printer’s mark<br />
Baldi, Bernardino, translator<br />
See Hero <strong>of</strong> Alexandria; De gli automati, overo<br />
machine se moventi, libri due, tradotti dal Greco<br />
da Bernardino Baldi Abbate di Guastalla, 1589<br />
B 81<br />
Ball, Walter William Rouse (1850–1925) [H. M. S.<br />
Coxeter (1907–2003), editor]<br />
Mathematical recreations and essays.<br />
Year: 1947<br />
Place: New York<br />
Publisher: Macmillan<br />
Edition: late<br />
Language: English<br />
Figures: 2 photolith plates<br />
Binding: original cloth boards; with dust jacket<br />
Pagination: pp. xvi, 418<br />
Size: 203x136 mm<br />
W. W. R. Ball was a mathematician at Trinity College,<br />
Cambridge. He is well known as a writer on the history<br />
B 81<br />
<strong>of</strong> mathematics and on ancillary subjects such as<br />
mathematical recreations, e.g., string figures.<br />
This is one <strong>of</strong> the more famous books on recreational<br />
mathematics. It was produced by a master in the field<br />
and has remained continuously in print from its first<br />
publication in 1892. It spans the field from simple<br />
arithmetical series to cryptography and cryptanalysis.<br />
Of particular interest is the section on calculating<br />
prodigies. The editor <strong>of</strong> this edition, H. M. S. Coxeter, a<br />
mathematician at the <strong>University</strong> <strong>of</strong> Toronto, was known<br />
for his interest in recreational mathematics as well as<br />
more traditional mathematical fields.<br />
Illustrations available:<br />
Title page<br />
B 82<br />
Ball, Walter William Rouse (1850–1925)<br />
A primer <strong>of</strong> the history <strong>of</strong> mathematics.<br />
Year: 1914<br />
Place: London<br />
Publisher: Macmillan<br />
Edition: 4th<br />
Language: English<br />
Binding: original cloth boards<br />
Pagination: pp. iv, 164<br />
Collation: π 2 A–K 8 γ 2<br />
Size: 174x114 mm<br />
Reference: Cre CL, p. 102<br />
This highly condensed version <strong>of</strong> Ball’s History <strong>of</strong><br />
mathematics makes no pretense to be anything except a<br />
short, popular description <strong>of</strong> the history <strong>of</strong> mathematics
Erwin Tomash Library<br />
Ball, Walter William Rouse Bardeen, John<br />
and to provide a few stories about pioneers <strong>of</strong> the subject.<br />
The early editions <strong>of</strong> this work were 1895, 1903 and<br />
1906.<br />
Illustrations available:<br />
Title page<br />
B 83<br />
Ball, Walter William Rouse (1850–1925)<br />
A short account <strong>of</strong> the history <strong>of</strong> mathematics.<br />
Year: 1901<br />
Place: London<br />
Publisher: Macmillan and Co.<br />
Edition: 3rd<br />
Language: English<br />
Binding: original cloth boards; gilt spine and front cover<br />
Pagination: pp. xxiv, [2], 527, [15]<br />
Collation: π 4 b 9 1–33 8 γ 7<br />
Size: 188x125 mm<br />
Reference: Cre CL, p. 102; Pul HA, p. 117<br />
This is a standard reference work on the history <strong>of</strong><br />
mathematics from the time <strong>of</strong> ancient Egypt to near<br />
the end <strong>of</strong> the nineteenth century. It has been reprinted<br />
several times since its first appearance in 1888.<br />
Illustrations available:<br />
Title page<br />
B 84<br />
Bamford, Philip<br />
The practical gauger: Being a summary <strong>of</strong> what is<br />
necessary to be understood by all pretenders to that art.<br />
Wherin the nature <strong>of</strong> such superficies and solids as are<br />
usually the subject <strong>of</strong> gauging are fully discuss’d. With<br />
the method <strong>of</strong> finding their area’s or solidites, either<br />
whole or in part. Performed by the pen and the sliding<br />
- rule. To which is added, many useful tables proper for<br />
such a work, never before printed.<br />
Year: 1714<br />
Place: London<br />
Publisher: Richard Mount, John Sprint and Nathaniel Cliff<br />
Edition: 1st<br />
Language: English<br />
Binding: contemporary panelled leather; spine gilt in<br />
compartments; morocco label<br />
Pagination: pp. 128<br />
Collation: A 4 B–I 8<br />
Size: 184x113 mm<br />
The introduction to this work begins by describing<br />
decimal arithmetic and its use in the rule <strong>of</strong> three and<br />
other such operations, and also contains the abbreviations<br />
used. This is followed by tables relating measures <strong>of</strong><br />
wine and beer to cubic inches, pints, quarts, gallons,<br />
firkins and other lesser-known units <strong>of</strong> measure: the but<br />
and ton. The remainder <strong>of</strong> the book presents the usual<br />
gauging problems but with greater clarity than most.<br />
It describes the different shapes <strong>of</strong> barrels, casks, tubs,<br />
etc. and how they should be measured. The final section<br />
contains tables <strong>of</strong> excise rates for different liquids, tables<br />
for determining the number <strong>of</strong> days between any two<br />
dates, salary tables and so forth.<br />
Illustrations available:<br />
Title page<br />
Sample table page<br />
B 85<br />
Bardeen, John (1908–1991)<br />
B 84<br />
On the theory <strong>of</strong> the A-C. impedance <strong>of</strong> a contact<br />
rectifier. In Some contributions to transistor electronics.<br />
Monograph 1726<br />
Year: 1949<br />
Place: New York<br />
Publisher: American Telephone & Telegraph Company<br />
Edition: 1st<br />
Language: English<br />
Pagination: pp. 94–100<br />
Size: 277x213 mm<br />
A thoughtful, respectful biography <strong>of</strong> John Bardeen is<br />
Hoddeson, Lillian, and Vicki Daitch, True genius. The<br />
life and science <strong>of</strong> John Bardeen, Joseph Henry Press,<br />
Washington, DC, 2002.<br />
This is the same Bardeen paper that appeared in the Bell<br />
Systems Technical Journal, Semiconductor issue. See<br />
103
entry for American Telephone & Telegraph Company,<br />
Some contributions to transistor electronics.<br />
104<br />
Illustrations available:<br />
None<br />
B 86<br />
Bardeen, John (1908–1991)<br />
On the theory <strong>of</strong> the A-C. impedance <strong>of</strong> a contact<br />
rectifier. In Bell System Technical Journal Vol. XXVIII<br />
No. 3, July 1949.<br />
Year: 1949<br />
Place: New York<br />
Publisher: American Telephone & Telegraph Company<br />
Edition: 1st<br />
Language: English<br />
Binding: original paper wrappers<br />
Pagination: pp. 428–434.<br />
Size: 228x152 mm<br />
See entry for American Telephone, Bell System<br />
Technical Journal, Semiconductor issue.<br />
B 87<br />
Illustrations available:<br />
None<br />
Bardeen, John (1908–1991) and Walter Hauser<br />
Brattain (1902–1987)<br />
Physical principles involved in transistor action. In<br />
Bell System Technical Journal Vol. XXVIII No. 2, April<br />
1949.<br />
Year: 1949<br />
Place: New York<br />
Publisher: American Telephone & Telegraph Company<br />
Edition: 1st<br />
Language: English<br />
Binding: original paper wrappers<br />
Pagination: pp. 239–277<br />
Size: 228x152 mm<br />
See entry for American Telephone and Telegraph,<br />
Semiconductor issue.<br />
John Bardeen received his Ph.D. degree from Princeton<br />
<strong>University</strong> in 1936. During World War II, he served at<br />
the Naval Ordnance Laboratory. After the war, he joined<br />
Bell Telephone Laboratories, where his research was<br />
concerned with the properties <strong>of</strong> semiconductors. This<br />
work led to the invention <strong>of</strong> the transistor, for which<br />
he shared the Nobel Prize. He received a second Nobel<br />
Prize for his work on super-conductivity.<br />
Walter Brattain obtained his doctorate in physics from the<br />
<strong>University</strong> <strong>of</strong> <strong>Minnesota</strong>. He was a gifted experimental<br />
physicist who spent the majority <strong>of</strong> his career at Bell<br />
Erwin Tomash Library<br />
Bardeen, John Bardeen, John<br />
Telephone Laboratories. Working with Bardeen and<br />
Shockley, Brattain constructed the first semiconductor<br />
amplifier.<br />
John Bardeen, Walter Brattain and William Shockley<br />
were awarded the Nobel Prize for their invention <strong>of</strong> the<br />
transistor. This article describes the history <strong>of</strong> transistor<br />
development and the physical properties <strong>of</strong> the device. It<br />
was, other than a brief announcement by a letter to the<br />
editor, the first publication describing these devices.<br />
Illustrations available:<br />
None<br />
B 88<br />
Bardeen, John (1908–1991) and Walter Hauser<br />
Brattain (1902–1987)<br />
The transistor, a semi-conductor triode. In The Physical<br />
Review, Vol. 74, No. 2, July 15 1948.<br />
Year: 1948<br />
Place: Lancaster, PA, and New York, NY<br />
Publisher: American Physical Society<br />
Edition: 1st<br />
Language: English<br />
Binding: original paper wrappers<br />
Pagination: pp. 230–231<br />
Size: 268x200 mm<br />
This is the original announcement <strong>of</strong> the invention <strong>of</strong> the<br />
transistor by means <strong>of</strong> a series <strong>of</strong> letters to the editor <strong>of</strong> the<br />
Physical Review. The authors recognized the importance<br />
<strong>of</strong> their work and used this letter to the editor technique<br />
to permit timely communication <strong>of</strong> their breakthrough<br />
without the delay inherent in the peer review system.<br />
There are three letters in this series: this one announcing<br />
the device, one by Brattain and Bardeen on forward<br />
currents in germanium, and one by Shockley and Pearson<br />
on the modulation <strong>of</strong> currents in the device. All three<br />
letters are reproduced in the illustrations.<br />
Illustrations available:<br />
Letters (4)<br />
B 89<br />
Bardeen, John (1908–1991) and Walter Hauser<br />
Brattain (1902–1987)<br />
Nature <strong>of</strong> the forward current in germanium point<br />
contacts. In The Physical Review, Vol. 74, No. 2, July<br />
15 1948.<br />
Year: 1948<br />
Place: Lancaster, PA, and New York, NY<br />
Publisher: American Physical Society<br />
Edition: 1st<br />
Language: English
Erwin Tomash Library<br />
Barker, John Barlow, Fred<br />
Binding: original paper wrappers<br />
Pagination: pp. 231–232<br />
Size: 268x200 mm<br />
This is a very early paper by two <strong>of</strong> the three Nobel<br />
laureates who developed the transistor. The first account<br />
<strong>of</strong> the invention <strong>of</strong> the semiconductor was by means<br />
<strong>of</strong> a letter, from the same authors, (q.v.) to this journal<br />
(“Nature <strong>of</strong> the forward current in germanium point<br />
contacts,” The Physical Review, Vol. 74, No. 2, July 15,<br />
1948, pp. 231–232). See also entries for Shockley.<br />
Illustrations available:<br />
None<br />
B 90<br />
Barker, John<br />
The measurer’s guide enlarg’d: or, the whole art <strong>of</strong><br />
measuring made short, plain and easy. Containing<br />
full directions how to measure 1. Any plain superfices.<br />
2. All sorts <strong>of</strong> solids; with particular instructions for<br />
measuring <strong>of</strong> timber, &c. 3. All sorts <strong>of</strong> artificers work,<br />
viz. carpenters, joyners, plaisterers, painters, paviors,<br />
glasiers, bricklayers, sawyers, masons, earthwork. 4.<br />
The art <strong>of</strong> gauging: being <strong>of</strong> singular use to ingineers,<br />
gentlemen, artificers, and others.<br />
Year: 1718<br />
Place: London<br />
Publisher: Printed for Samuel Ballard<br />
Edition: 2nd<br />
B 90<br />
Language: English<br />
Binding: contemporary leather gilt; gilt compartmented spine<br />
Pagination: pp. [12], 204<br />
Collation: A–B 6 B–S 6<br />
Size: 152x87 mm<br />
As is common in many <strong>of</strong> these books, the author<br />
indicates in the introduction that:<br />
These sheets were composed for my own private<br />
Use, Thirty Years since, I not in the least intending<br />
to Publish them, but at the Importunities <strong>of</strong> some<br />
Friends, not without Reluctancy, I, agreed to have<br />
them Printed…<br />
This is a general book on measurement for carpenters,<br />
masons, timber merchants, etc.<br />
Illustrations available:<br />
Title page<br />
B 91<br />
Barlow, Fred (1888–1963)<br />
Mental prodigies. An enquiry into the faculties <strong>of</strong><br />
arithmetical, chess and musical prodigies, famous<br />
memorizers, precocious children and the like, with<br />
numerous examples <strong>of</strong> “lightning” calculations and<br />
mental magic.<br />
Year: 1952<br />
Place: New York<br />
Publisher: Philosophical Library<br />
Edition: 1st (U.S.)<br />
Language: English<br />
Binding: original cloth boards; with dust jacket<br />
Pagination: pp. 256<br />
Size: 183x126 mm<br />
B 91<br />
105
For obvious reasons, calculating prodigies have<br />
always been <strong>of</strong> interest to the developers <strong>of</strong> computing<br />
machinery. This 1952 (first U.S.) edition incorporates a<br />
few corrections not present in the 1951 (first English)<br />
edition. The opening third <strong>of</strong> the work discusses famous<br />
calculating prodigies such as Zerah Colburn and describes<br />
some <strong>of</strong> the feats they could perform. The rest <strong>of</strong> the book<br />
is devoted to a discussion <strong>of</strong> these, and related, abilities.<br />
The distinction is drawn between calculating prodigies<br />
(<strong>of</strong>ten referred to as idiot savants) and people trained in<br />
mental calculation either for use in their work or as stage<br />
performers. The latter part <strong>of</strong> the book contains various<br />
algorithms used by those trained in the art.<br />
106<br />
Illustrations available:<br />
Title page<br />
B 92<br />
Barlow, Peter (1776–1862)<br />
An elementary investigation <strong>of</strong> the theory <strong>of</strong> numbers,<br />
with its application to the indeterminate and<br />
Diophantine analysis, the analytical and geometrical<br />
division <strong>of</strong> the circle, and several other curious<br />
algebraical and arithmetical problems.<br />
Year: 1811<br />
Place: London<br />
Publisher: J. Johnson and Co.<br />
Edition: 1st<br />
Language: English<br />
Binding: modern leather half bound over marbled boards<br />
Pagination: pp. xvi, 507, [3]<br />
Collation: A–2I 8 2K 7<br />
Size: 217x133 mm<br />
Erwin Tomash Library<br />
Barlow, Peter Barnard, Francis Pierrepont<br />
B 92<br />
Barlow was a mathematician at the Royal Military<br />
Academy in England. He was self-educated and initially<br />
made his reputation through an essay concerned with<br />
timber stresses based on research he had done at the<br />
Woolwich arsenal. He is best know today for his<br />
association with a specific type <strong>of</strong> telescope eyepiece<br />
(the Barlow lens), which he designed in the late 1820s,<br />
and for his mathematical tables (Barlow’s Tables) which<br />
remained in print until after World War II.<br />
This volume is highly technical work on number theory.<br />
It begins with a discussion <strong>of</strong> the number philosophy <strong>of</strong><br />
Pythagoras and proceeds to discuss primes, continued<br />
fractions, quadratic equations and other topics, <strong>of</strong>ten in<br />
relation to problems or theories first developed by the<br />
Greeks.<br />
Illustrations available:<br />
Title page<br />
B 93<br />
Barlow, Peter (1776–1862)<br />
A treatise on the manufactures and machinery <strong>of</strong> Great<br />
Britain … To which is prefaced, an introductory view<br />
<strong>of</strong> the principles <strong>of</strong> manufactures by <strong>Charles</strong> <strong>Babbage</strong>.<br />
Forming a portion <strong>of</strong> the Encyclopaedia Metropolitana.<br />
3 vols.<br />
Year: 1836<br />
Place: London<br />
Publisher: Baldwin and Braddock<br />
Edition: 2nd<br />
Language: English<br />
Figures: 87 engraved plates bound at end <strong>of</strong> v.3<br />
Binding: contemporary leather<br />
Pagination: v.1, pp. iii–viii, 412; v.2, pp. 413–828; v.3, pp.<br />
829–834<br />
Collation: v.1, π 3 B–L 4 M 2 N–3G 4 ; v.2, 3H–5N 4 ; v.3, 5O 3<br />
Size: 274x208 mm<br />
See <strong>Babbage</strong>, <strong>Charles</strong>; An introductory view <strong>of</strong> the<br />
principles <strong>of</strong> manufactures, 1836<br />
Illustrations available:<br />
None<br />
B 94<br />
Barnard, Francis Pierrepont (1854–1931)<br />
The casting-counter and the counting board. A <strong>chapter</strong><br />
in the history <strong>of</strong> numismatics and early arithmetic.<br />
Year: 1916<br />
Place: Oxford<br />
Publisher: Clarendon Press<br />
Edition: 1st<br />
Language: English<br />
Figures: 64 plates (numbered 1–46, 47a, 47b, 48–63)
Erwin Tomash Library<br />
Barnard, Francis Pierrepont Barozzi, Francesco<br />
B 94<br />
Binding: original cloth boards; gilt-stamped spine and front<br />
cover<br />
Pagination: pp. 358, [2]<br />
Collation: A–2Y 4<br />
Size: 283x219 mm<br />
Reference: Pul HA, p. 116<br />
Barnard was pr<strong>of</strong>essor <strong>of</strong> medieval archaeology at the<br />
<strong>University</strong> <strong>of</strong> Liverpool. At the time he began this work,<br />
there was little interest in casting counters or jettons, as<br />
they are also commonly known—from the French jeter,<br />
to throw. Jettons are the counters that are used on the<br />
European table abacus. Counters used on a counting<br />
board were the principal mechanical aid to calculation<br />
used in Europe during the Middle Ages. Terms such as<br />
borrow one, carry two, lay a wager and over the counter<br />
originated with the use <strong>of</strong> jettons and the counting board.<br />
Counters were known as gettoni in Italy, casting counters<br />
in England and rechenpfennig in Germany.<br />
In early times the counters were simply small pebbles<br />
or similar items. About the year 1200 they began to be<br />
minted in a coin-like format, the production <strong>of</strong> which was<br />
a major industry in Nuremberg from 1525 to 1700. Jettons<br />
came in a nest (usually a cylindrical metal case), which<br />
was <strong>of</strong>ten considered a suitable New Year’s gift. The<br />
Typical jetton, B 94<br />
image stamped into the jetton varied greatly but usually<br />
included a bust <strong>of</strong> the ruler on one side and some device<br />
(<strong>of</strong>ten a cross or other simple symbol on early versions)<br />
on the other (see illustration). Jettons were used up to the<br />
late 1700s, and many highly decorative examples exist<br />
for special areas or purposes—for example, the French<br />
minted special jettons for use in their North American<br />
colonies in the middle 1700s.<br />
This work is divided into three parts. The first discusses<br />
the jetton itself and catalogs many <strong>of</strong> them by decoration<br />
and inscription. The second section deals with counting<br />
tables and cloths. The last part is concerned with the<br />
methods used for performing arithmetic (casting) as<br />
described by various authors.<br />
This is considered the standard reference book on jettons<br />
and their use. Fox publishers reprinted it in 1981.<br />
Illustrations available:<br />
Title page<br />
Plate 2 <strong>of</strong> jettons<br />
Reckoning cloth<br />
B 95<br />
Barozzi, Francesco (1537–1604)<br />
Nest <strong>of</strong> jettons, B 94<br />
Il nobilissimo et antiquissimo giuoco Pythagoreo<br />
nominato rythmomachia, cioè battaglia di consonantie<br />
de numeri, in lingua volgare a modo di parafresi<br />
composto.<br />
Year: 1572<br />
Place: Venice<br />
Publisher: Gratioso Perchacino<br />
Edition: 1st<br />
Language: Italian<br />
Binding: modern paper boards<br />
Pagination: ff. [2], 24<br />
Collation: A–F 4 G 2<br />
Size: 196x130 mm<br />
Reference: Rcdi BMI, Vol. I, p. 83; Soth/Zeit BCM, Vol. III,<br />
#875–#498, p. 38<br />
107
Francesco Barozzi (also known as Franciscus Barocius<br />
or Barociusi) was a native <strong>of</strong> Crete who was a member <strong>of</strong><br />
a patrician Venetian family. He studied at Padua and also<br />
lectured there c.1559. He published works on astronomy<br />
and mathematics and is known to have produced a<br />
number <strong>of</strong> translations <strong>of</strong> Greek and Latin mathematical<br />
texts, among them Proclus’ commentary on the first<br />
book <strong>of</strong> Euclid. In 1587, he was charged with sorcery<br />
and brought before the Inquisition.<br />
This volume is essentially a translation <strong>of</strong> Claude de<br />
Boissière’s description <strong>of</strong> the number ratio game known<br />
as Rithmomachia from the Greek rhythmos (number)<br />
and machia (combat). In the title, the game is attributed<br />
to Pythagoras; however, the attribution is suspect as no<br />
known reference predates the eleventh century.<br />
As Smith (History <strong>of</strong> Mathematics) notes, the game is<br />
difficult to describe. It is based on the Greek number<br />
philosophy <strong>of</strong> Nicomachus and played on an elongated<br />
chess board with 8x16 squares. It uses variously shaped<br />
counters to represent numerical ratios. The object was<br />
to move the counters so as to get four numbers in a row<br />
that were related to arithmetic, geometric and harmonic<br />
progressions—there are apparently only six winning<br />
combinations <strong>of</strong> pieces.<br />
An introduction to the game can be found in Smith, D.<br />
E. and C. C. Eaton; “Rithmomachia, the great medieval<br />
number game,” The American Mathematical Monthly,<br />
April 1911, pp. 73–80. For a more complete historical<br />
and bibliographical discussion, see Folkerts, Menso;<br />
Essays on medieval mathematics, Aldershot, Ashgate<br />
108<br />
Erwin Tomash Library<br />
Barozzi, Francesco Barreme, François Bertrand de<br />
B 95<br />
Variorum, 2003. Chapter XI is titled Rithmomachia, a<br />
mathematical game from the middle ages.<br />
Folkerts points out that Rhythmos means not number<br />
but numerical relationship and that accordingly,<br />
Rithmomachia is a game that deals not with numbers but<br />
with the ratios <strong>of</strong> numbers.<br />
Illustrations available:<br />
Title page<br />
Game board<br />
Rithmomachia game board, B 95<br />
B 96<br />
Barreme, François Bertrand de (1640–1704)<br />
La geometrie servant a l’arpentage. Ouvrage si<br />
facile & si commode que par la seule addition on<br />
peut mesurer toute sorte de terres, bois, & batimens;<br />
et generalement toute figures & superficies pour<br />
irregulieres qu’elles puissent estre.<br />
Year: 1672<br />
Place: Paris<br />
Publisher: Barreme<br />
Edition: 1st<br />
Language: French<br />
Figures: engraved title page; 1 engraved plate<br />
Binding: contemporary calf; gilt spine<br />
Pagination: pp. [17], 5, [1], 7–17 (misnumbered 7 as 6, 8 as 6,<br />
9 as 7, 10 as 7, 11 as 8, 12 as 8, 13 as 8, 14 as 8, 15 as<br />
10, 16 as 11, 17 as 12), [2], ff. 13-30, pp. [72], [36], [36]<br />
Collation: a 6 * 12 C–E 6 * 6 R–X 6 g–3g 6 *-3* 6<br />
Size: 142x82 mm<br />
François Barreme was a native <strong>of</strong> Lyons who founded a<br />
private commercial mathematics school in Paris. He was
Erwin Tomash Library<br />
Barreme, François Bertrand de Barreme, François Bertrand de<br />
B 96<br />
Survey instruments, B 96<br />
responsible for the publication <strong>of</strong> many different types<br />
<strong>of</strong> tables and ready-reckoners during his lifetime. The<br />
tradition was continued by his son Nicolas. The tables<br />
became so popular that their name became a synonym<br />
for ready-reckoners and numerical tables, which are<br />
known by the name Barème in France today. While they<br />
were both popular and produced long after Barreme died,<br />
editions predating 1700 are rare.<br />
This first edition illustrates the beginning <strong>of</strong> the genre.<br />
The tables are difficult to use and waste space (see<br />
illustration <strong>of</strong> one page <strong>of</strong> the multiplication table).<br />
Indeed, examination <strong>of</strong> various editions <strong>of</strong> Barreme<br />
may be considered a short course in table design and<br />
typography.<br />
This work begins with a description <strong>of</strong> some elementary<br />
survey instruments and the mathematics needed to find<br />
the areas <strong>of</strong> simple geometric figures. The remainder <strong>of</strong><br />
the volume is composed <strong>of</strong> tables <strong>of</strong> use in surveying and<br />
commercial arithmetic.<br />
Illustrations available:<br />
Title page<br />
Formulae for triangles<br />
Survey instruments<br />
Multiplication table<br />
B 97<br />
Barreme, François Bertrand de (1640–1704)<br />
Le livre des aides, domaine, et finances. Tres -utile à<br />
toute sorte de personnes; …<br />
Year: 1685<br />
Place: Paris<br />
Publisher: Denys Thierry<br />
Edition: 1st<br />
Language: French<br />
Figures: engraved title frontispiece<br />
Binding: contemporary leather; rebacked, original gilt spine<br />
laid down; dentelle edges<br />
Pagination: pp. [4], 64 (misnumbered 62 as 60), [4], 65–68,<br />
[120], xv, [9]<br />
Collation: π 2 A–F 6 6 –5 6 §–7§ 6<br />
Size: 160x85 mm<br />
This volume consists <strong>of</strong> commercial tables. Typically<br />
the tables give multiples <strong>of</strong> various monetary units or<br />
exchange rates. These are supplemented by various<br />
tables <strong>of</strong> tariffs for moving quantities <strong>of</strong> wine and other<br />
goods by both land and water transport.<br />
Illustrations available:<br />
Title page<br />
Frontispiece<br />
Page <strong>of</strong> wine tables<br />
B 97<br />
109
110<br />
Erwin Tomash Library<br />
Barreme, François Bertrand de Barreme, François Bertrand de<br />
B 97<br />
B 98<br />
Barreme, François Bertrand de (1640–1704)<br />
Le livre des comptes faits.<br />
Year: 1673<br />
Place: Paris<br />
Publisher: Barreme<br />
Edition: 1st<br />
Language: French<br />
Figures: 2 engraved plates (portrait & anagram <strong>of</strong> Colbert)<br />
Binding: contemporary leather<br />
Pagination: ff. [95]<br />
Collation: π 8 A–H 6 * 6 R–X 6 Y 3<br />
Size: 151x82 mm<br />
Reference: Kress CL, 1326<br />
The title page states third edition, but no earlier one has<br />
been located. It is known that Barreme had published<br />
earlier sets <strong>of</strong> tables, and he might be simply defining<br />
these previous tables as his earlier editions. See<br />
advertisement on folio 1 in the illustrations.<br />
This volume <strong>of</strong> tables is limited to commercial<br />
applications, in particular for finding multiples <strong>of</strong> various<br />
denominations <strong>of</strong> the French currency.<br />
Illustrations available:<br />
Title page and advertisement<br />
Dedication portrait<br />
Currency table page<br />
B 98
Erwin Tomash Library<br />
Barreme, François Bertrand de Barreme, François Bertrand de<br />
B 99<br />
Barreme, François Bertrand de (1640–1704)<br />
Le livre facile pour aprendre l’arithmetique de soy<br />
mesme et sans maistre par des mèthodes si courtes, si<br />
claires et si bien ordonnées qu’il ne s’en est point veu<br />
de pareilles.<br />
Year: 1672<br />
Place: Paris<br />
Publisher: Barreme<br />
Edition: 1st<br />
Language: French<br />
Binding: contemporary calf; gilt spine<br />
Pagination: pp. [36], 199, [9]<br />
Collation: π 3 (-4) 11 (-12)* 4 A-Q 6*8<br />
Size: 160x86 mm<br />
Unlike most <strong>of</strong> Barreme’s publications, this one volume<br />
contains only a few tables. As the title indicates, this<br />
work concentrates on teaching the basics <strong>of</strong> arithmetic<br />
with examples <strong>of</strong> all four operations. The tables included<br />
are intended to aid in the basic instruction, but there are<br />
also a few dealing with currency conversions.<br />
Illustrations available:<br />
Title page and advertisement<br />
Galley division<br />
Multiplication table<br />
Currency conversion<br />
Dedication portrait, B 98<br />
Division examples, B 99<br />
B 99<br />
111
B 100<br />
Barreme, François Bertrand de (1640–1704)<br />
Le livre necessaire a toute sorte de conditions. Inventé<br />
de nouveau pour tirer tout d’un coup les Interets de<br />
plusieurs années, de plusieurs mois, de plusieurs jours<br />
en un moment et en un méme endroit, ce qu’on n’avoit<br />
jamais veu. On y voit aussi des tarifs bien comodes: ou<br />
sans avoir apris la division on y peut diviser jusqu’a<br />
trente mil livres. La reduction des monnoyes y’est d’une<br />
maniere particuliere. Le pr<strong>of</strong>it des marchands y est.<br />
Les changes y sont aussy, et les escontes a tant por<br />
cent. On y fait par la seule addition, les contributions,<br />
impositions et despartements. au sol la livre.<br />
112<br />
Year: 1671<br />
Place: Paris<br />
Publisher: Barreme<br />
Edition: 1st<br />
Language: French<br />
Binding: contemporary calf; gilt spine<br />
Pagination: pp. [66], 88, [102], 199–240 (mis#199 as 200, 200<br />
as 201), 373–396 (mis# 396 as 406), xii, 37–48<br />
Collation: π 4 A–B 610 * 7 (-*8)2A–2B 6 C–F 6 G 8 A–I 6 L–N 6 2H–2I 6 a 12<br />
Size: 163x85 mm<br />
Reference: Kress CL, 1280<br />
This volume is a standard set <strong>of</strong> commercial tables,<br />
the majority <strong>of</strong> which are oriented towards currency<br />
conversion, but with a few dealing with the number <strong>of</strong><br />
days between various dates.<br />
Illustrations available:<br />
Title page and advertisement<br />
Erwin Tomash Library<br />
Barreme, François Bertrand de Barreme, François Bertrand de<br />
B 100<br />
B 101<br />
Barreme, François Bertrand de (1640–1704)<br />
Le livre necessaire a toute sorte de conditions. Inventé<br />
de nouveau pour tirer tout d’un coup les Interets de<br />
plusieurs années, de plusieurs mois, de plusieurs jours<br />
en un moment et en un méme endroit, ce qu’on n’avoit<br />
jamais veu. On y voit aussi des tarifs bien comodes: ou<br />
sans avoir apris la division on y peut diviser jusqu’a<br />
trente mil livres. La reduction des monnoyes y’est d’une<br />
maniere particuliere. Le pr<strong>of</strong>it des marchands y est.<br />
Les changes y sont aussy, et les escontes a tant por<br />
cent. On y fait par la seule addition, les contributions,<br />
impositions et déspartements au sol la livre.<br />
Year: 1671<br />
Place: Paris<br />
Publisher: Barreme<br />
Edition: 1st (2nd issue)<br />
Language: French<br />
Binding: contemporary calf; gilt spine<br />
Pagination: pp. [32], 88, [102], 200–205, 217–240; xii<br />
Collation: π 7 * 4 * 5 2A–2B 6 C–F 6 G 8 A–I 6 M–N 6 a 6<br />
Size: 159x85 mm<br />
This second issue appears identical to the first except for<br />
the small changes on the title page and advertisement.<br />
The dedication and dedication ode to Monseigneur de la<br />
Reynie have also been removed. Perhaps the hoped-for<br />
patronage did not materialize.<br />
Illustrations available:<br />
Title page and advertisement<br />
B 102<br />
Barreme, François Bertrand de (1640–1704)<br />
Le livre necessaire à toute sorte de conditions. Inventé<br />
de nouveau pour tirer tout d’un coup les Intérêts de<br />
plusieurs années, de plusieurs mois, & de plusieurs<br />
jours en un moment et en un méme endroit, ce qu’on<br />
n’avoit jamais veu. On y voit aussi des tarifs bien<br />
comodes: ou sans avoir apres la division on y peut<br />
diviser jusqu’a trente mil livres. La réduction des<br />
monnoyes y’est d’une maniere particuliere. Le pr<strong>of</strong>it<br />
des marchands y est. Les changes y sont aussy, et les<br />
escontes à tant por cent. On y fait par la seule addition,<br />
les contributions, impositions et départements. Au sol<br />
la livre. (engraved title page similar to 1671 edition<br />
without date)<br />
(Second title) Le livre necessaire pour les comptables,<br />
avocats, notaires, procureurs, negotians, &<br />
generalement à toute sorte de conditions, inventé de<br />
nouveau, pour tirer tout d’un coup les Interests ou le<br />
produit de plusieurs années, de plusieurs mois, & de<br />
plusieurs jours …
Erwin Tomash Library<br />
Barreme, François Bertrand de Barreme, François Bertrand de<br />
Year: 1694<br />
Place: Paris<br />
Publisher: Denys Thierry<br />
Edition: 2nd<br />
Language: French<br />
Figures: engraved title frontispiece<br />
Binding: contemporary leather; dentelle edges<br />
Pagination: pp. [14], 296<br />
Collation: ä 7 A 8 B 4 –Z 8 2A 4 2B 4<br />
Size: 170x94 mm<br />
This is another <strong>of</strong> Barreme’s publications, containing the<br />
same types <strong>of</strong> commercial tables as in earlier editions.<br />
Some <strong>of</strong> the tables are identical with those from earlier<br />
editions while others are different, though similar. In the<br />
year <strong>of</strong> this publication, Barreme was appointed auditor<br />
to the Parisian Chambre des Comptes (Treasury).<br />
Illustrations available:<br />
Frontispiece<br />
Title page<br />
Frontispiece and title page, B 101<br />
B 103<br />
Barreme, François Bertrand de (1640–1704)<br />
Les tarifs et comptes fait du grand commerce ou<br />
l’on y fait les changes d’Angleterre, d’Hollande, de<br />
Flandres, d’Allemagne, de Suisse &c. Pourveu qu’on<br />
sache l’addition et en quel estat que le change soit. Les<br />
mesures et les poids des principales villes de l’Europe<br />
sont reduis aux mesures et poids des villes de France.<br />
Le pair des monnoyes y est. Les escontes y sont tous<br />
faits. Les instructions pour faire par regle les susdits<br />
changes y sont expliquées brievement.<br />
Year: 1670<br />
Place: Paris<br />
Publisher: Barreme<br />
Edition: 1st<br />
Language: French<br />
Binding: contemporary calf; gilt spine<br />
Pagination: pp. [24], 62, [2], ff. lxii–lxvii, pp. [2], 63–80, [8],<br />
81–96, 117–300, 361–395, 408–420<br />
113
114<br />
Collation: π 2 à 6 é 4 A–E 6 F 2 F 10 G–H 6 I 8 L–Z 6 & 6 2A 6 2G–2K 6<br />
Size: 157x84 mm<br />
This set <strong>of</strong> Barreme’s tables is devoted mainly to the<br />
conversion <strong>of</strong> weights and measures between various<br />
French regions and surrounding geographic areas.<br />
Illustrations available:<br />
Title page and advertisement<br />
Tables for Rouen<br />
B 104<br />
[Barreme, François Bertrand de (1640–1704)]<br />
– Nicholas Barreme<br />
Traité des parties doubles ou methode aisée pour<br />
apprendre à tenir en parties doubles les livres du<br />
commerce & des finances. Avec in traité de finance …<br />
Ce livre peut estre utile aux négocians, aux banquiers,<br />
aux financiers, & même aux magistrats.<br />
Year: 1721<br />
Place: Paris<br />
Publisher: Jean-Ge<strong>of</strong>roy Nyon<br />
Edition: 1st<br />
Language: French<br />
Binding: contemporary leather; red leather label<br />
Pagination: pp. [8], 302<br />
Collation: π 4 A–2O 4 2P 3<br />
Size: 206x133 mm<br />
Reference: Hist. HAL, p. 158; Kress CL, 3360<br />
Erwin Tomash Library<br />
Barreme, François Bertrand de Barreme, Gabriel<br />
B 104<br />
This is not another book <strong>of</strong> tables, but rather a volume<br />
describing double-entry bookkeeping and associated<br />
journals for commercial use. Issued in 1721, it must have<br />
been in preparation for some time because the examples<br />
are for the year 1719 with a few additions for 1720.<br />
Illustrations available:<br />
Title page<br />
B 105<br />
Barreme, Gabriel (1663–1711)<br />
B 105<br />
Livre d’arithmetique de Monsieur G.D. Moreau<br />
secretaire de Monsieur Voisin cons.r du Roy …. par<br />
Moy G. Barreme arithmeticien ordinaire du Roy.<br />
Year: 1688<br />
Place: Paris<br />
Edition: manuscript<br />
Language: French<br />
Binding: contemporary leather; gilt spine and covers<br />
Pagination: ff. 91<br />
Size: 375x244 mm<br />
Gabriel Barreme was the first son <strong>of</strong> François Bertrand<br />
Barreme. While the second son, Nicholas, continued<br />
his father’s publishing enterprise, Gabriel became the<br />
Arithmetician to the King.<br />
This large and elegant manuscript covers much <strong>of</strong> the<br />
same material as his father’s books, i.e., the four basic<br />
operations, the rule <strong>of</strong> three, fractions, problems involving
Erwin Tomash Library<br />
Barreme, Nicholas Barrow, John<br />
the calculation <strong>of</strong> interest, etc. It assumes knowledge <strong>of</strong><br />
simple addition and begins with mixed radix addition <strong>of</strong><br />
a column <strong>of</strong> French currency, which was then similar to<br />
the more familiar British sterling system.<br />
Illustrations available:<br />
Title page<br />
Addition example<br />
Division example<br />
Addition example, B 105<br />
B 106<br />
[Barreme, François Bertrand de (1640–1704)]<br />
– Nicholas Barreme<br />
L’ arithmetique du Sr Barreme ou le livre facile pour<br />
apprendre l’arithmetique de soi-même, & sans maître.<br />
Ouvrage tres necessaire a toute sorte de personnes: aux<br />
unes, pour apprendre l’arithmétique, & à ceux qui la<br />
sçavent, pour les aider à rappeler dans leur mémoire<br />
quantitié de regles qui s’oublient facilement, faute de<br />
pratique. Nouvelle edition, augmentée de plus 190<br />
pages, ou regles differentes, de la géométrie, servant au<br />
mesurage & à l’arpentage, & du traité d’arithmétique<br />
nécessaire à l’arpentage & au toisé.<br />
Year: 1736<br />
Place: Paris<br />
Publisher: Nyon, David, David, Didot<br />
Edition: 3rd<br />
Language: French<br />
Figures: engraved frontispiece and book notice<br />
Binding: contemporary leather; spine gilt<br />
Pagination: pp. [4], [12], 492, [80]<br />
Collation: π 2 A 6 A–3A 6 3B 4<br />
Size: 167x93 mm<br />
After François Barreme died in 1704, his son Nicholas<br />
continued his father’s business <strong>of</strong> publishing books <strong>of</strong><br />
tables. This is the same work as Le livre facile pour<br />
aprendre l’arithmetique de soy mesme et sans maistre<br />
par des methodes si courtes, si claires et si bien<br />
ordonnées qu’il ne s’en est point veu de pareilles, 1672.<br />
Nicholas appears to have made his first additions to his<br />
father’s work in 1706 but left the majority <strong>of</strong> the content<br />
unchanged (compare, for example, the illustration <strong>of</strong><br />
the division example in the father’s publication and this<br />
one).<br />
Illustrations available:<br />
Title page<br />
Division example<br />
B 106<br />
Barreme, Nicholas, editor<br />
See Barreme, François Bertrand de; Traité des<br />
parties doubles ou méthode aisée pour apprendre à<br />
tenir en parties doubles les livres du commerce &<br />
des finances.<br />
B 107<br />
Barrow, John (1764–1848)<br />
A description <strong>of</strong> pocket and magazine cases <strong>of</strong><br />
mathematical drawing instruments; in which is<br />
explained the use <strong>of</strong> each instrument, and particularly<br />
<strong>of</strong> the sector and plain scale, in the solution <strong>of</strong> a variety<br />
115
<strong>of</strong> problems; likewise, the description, construction, and<br />
use, <strong>of</strong> Gunter’s scale.<br />
116<br />
Year: 1794<br />
Place: London<br />
Publisher: J. and W. Watkins<br />
Edition: 1st<br />
Language: English<br />
Figures: 4 engraved folding plates<br />
Binding: modern boards<br />
Pagination: pp. viii, 128<br />
Collation: A 4 B–I 8<br />
Size: 216x131 mm<br />
Reference: Pogg Vol. I, p. 106; Hamb, DI, p. 47<br />
Barrow is identified on the title page as a private teacher<br />
<strong>of</strong> mathematics in London, a notation that has led to E.<br />
G. R. Taylor (Mathematical practitioners) to ascribe<br />
the book to John Barrow (1700–c.1772), a mathematics<br />
teacher. In fact, the book was written by John Barrow,<br />
later Second Secretary <strong>of</strong> the Admiralty, who was from<br />
a poor family and was mainly self-educated. He is<br />
known to have repeated Benjamin Franklin’s electrical<br />
experiments with a kite, and it is recorded that he gave<br />
a nasty electrical shock to a woman from the town who<br />
had come to see what he was doing. He was the first to<br />
ascend in a balloon in England, later travelling widely on<br />
expeditions to Greenland, China and South Africa.<br />
This book was sponsored, as were many like it, by a<br />
commercial instrument maker to explain the elementary<br />
uses <strong>of</strong> mathematical instruments. The publisher, J. &<br />
W. Watkins, sold instruments, and the descriptions <strong>of</strong><br />
many contain a phrase such as On the Calipers made<br />
by Messrs. Watkins are contained the following Lines,<br />
Table, etc. This book was his first publication, the likely<br />
result <strong>of</strong> his having used such instruments in his early<br />
surveying jobs.<br />
The instruments described and pictured in engravings<br />
include the plane and proportional compass, protractor<br />
and plane scale, Gunter’s line <strong>of</strong> numbers, the sector,<br />
Gunner’s compass, etc. The engravings are very detailed<br />
except for the Gunner’s compass, which, while showing<br />
a fine outline <strong>of</strong> the device, shows no detail <strong>of</strong> either the<br />
scales or the tables usually engraved on the arms.<br />
Illustrations available:<br />
Title page<br />
Plate with plane scale, sector, gunner’s compass etc.<br />
Barsotti, Guiseppe, translator<br />
See [Leibniz, Gottfried Wilhelm von] - M.<br />
Lamprecht [Guiseppe Barsotti, translator]; Vita<br />
del Sig. Barone G<strong>of</strong>fredo Guglielmo di Leibnitz<br />
data in luce dal Signor Lamprecht in lingua<br />
Tedesca, e tradotta in lingua Italiana …, 1787.<br />
Erwin Tomash Library<br />
Barsotti, Guiseppe Bartoli, Cosimo<br />
B 108<br />
Barstow, D.<br />
A secular diary for ascertaining any day <strong>of</strong> the week or<br />
month, in either the old or new style, commencing 1601,<br />
and continued up to the year 1900.<br />
Year: 1836<br />
Place: n/p<br />
Publisher: Barstow<br />
Edition: 1st<br />
Language: English<br />
Binding: original paper boards<br />
Pagination: broadside<br />
Size: 360x265 mm<br />
This is a single sheet, folded into small covers 127x80<br />
mm, giving tables to determine the day <strong>of</strong> the week or<br />
month for any given date from 1601 to 1900.<br />
Illustrations available:<br />
Sheet (2)<br />
B 109<br />
Bartoli, Cosimo (1503–1572)<br />
B 107<br />
Del modo di misurare le distantie, le superficie, i corpi,<br />
le piante, le provincie, le prospettive & tutte le altre<br />
cose terrene, che possono occorrere a gli huomini …
Year: 1564<br />
Place: Venice<br />
Publisher: Francesco di Franceschi<br />
Edition: 1st<br />
Language: Italian<br />
Figures: two double-page figures plus many woodcuts in the<br />
text<br />
Binding: contemporary vellum; with ties renewed<br />
Pagination: ff. [4], 48, 45–48, 49–141, [3]<br />
Collation: A4A–M4M4N–2N4 Cosimo Bartoli, B 109<br />
(Signature M repeated)<br />
Size: 226x170 mm<br />
Reference: Ricdi BMI I, p. 90<br />
Cosimo Bartoli was an exponent <strong>of</strong> using Italian,<br />
rather than Latin, for technical writing. In this book<br />
on surveying, he essentially translates the earlier Latin<br />
works <strong>of</strong> others (e.g., Oronce Fine, Alberti, Dürer and<br />
Gemma Frisius), making them available to the average<br />
literate Italian. The border <strong>of</strong> the title page is copied from<br />
Erwin Tomash Library<br />
Bartoli, Cosimo Bartoli, Cosimo<br />
B 109<br />
Quadrant, B 109<br />
Jacob’s staff, B 109<br />
Circumferentor, B 109<br />
his 1550 translation <strong>of</strong> Alberti’s De Re Aedificatoria (not<br />
in this collection), but his portrait was done specifically<br />
for this one. The title page, portrait and all the woodcut<br />
illustrations were used for subsequent editions <strong>of</strong> this<br />
work.<br />
This well-known volume actually comprises six books,<br />
covering everything a surveyor should know about a<br />
variety <strong>of</strong> instruments. It begins with simple illustrations<br />
<strong>of</strong> the use <strong>of</strong> Jacob’s Staff and a quadrant with shadow<br />
scales and progresses to the use <strong>of</strong> more complex<br />
instruments in a wide variety <strong>of</strong> applications. The second<br />
and third books cover practical applications <strong>of</strong> plane<br />
and solid geometry such as finding areas and volumes<br />
<strong>of</strong> irregular figures. Book 4 deals with cartography<br />
and is notable for a description <strong>of</strong> the use <strong>of</strong> the device<br />
called a circumferentor—an instrument combining a<br />
117
compass and a sighting device for determining angles <strong>of</strong><br />
elevation. Book 5 contains various pro<strong>of</strong>s <strong>of</strong> geometric<br />
propositions that might be <strong>of</strong> use to a surveyor. The final<br />
book is a discussion <strong>of</strong> how to find square roots and a<br />
table <strong>of</strong> squares for all integers from 1 to 661.<br />
The publisher is <strong>of</strong>ten known as Francesco Franseschi<br />
Sanese because he came from Siena. He is <strong>of</strong>ficially<br />
referred to as Francesco di Franseschi to differentiate<br />
him from Francesco Franceschi (without the di), who is<br />
Lucchese, from Lucca.<br />
118<br />
Illustrations available:<br />
Title page<br />
Portrait<br />
Colophon<br />
Quadrant with shadow scales<br />
Jacob’s Staff<br />
Astrolabe with shadow scales<br />
Quadrant showing origins <strong>of</strong> shadow scales<br />
Tables, page 1<br />
Circumferentor<br />
Erwin Tomash Library<br />
Bartoli, Cosimo Barton, William J.<br />
B 110<br />
Bartoli, Cosimo (1503–1572)<br />
Astrolabe, B 109<br />
Del modo di misurare le distantie, le superficie, i corpi,<br />
le piante, le provincie, le prospettive & tutte le altre<br />
cose terrene, che possono occorrere a gli huomini.<br />
Year: 1589<br />
Place: Venice<br />
Publisher: Francesco di Franceschi<br />
Edition: 2nd<br />
Language: Italian<br />
Figures: 2 folding plates plus many woodcuts in the text<br />
Binding: later vellum<br />
Pagination: ff. 145, [3]<br />
Collation: A–S 8 T 4<br />
Size: 214x153 mm<br />
Reference: Rcdi BMI, Vol. I, p. 90<br />
The second edition <strong>of</strong> this early Italian work on<br />
surveying is, essentially, identical to the first edition <strong>of</strong><br />
1564. Two <strong>of</strong> the large folding plates appear to have been<br />
reengraved, but other illustrations are carried over from<br />
the first edition.<br />
Illustrations available:<br />
Title page<br />
Colophon<br />
B 111<br />
Barton, William J.<br />
B 110<br />
Arithmeticke abreviated. Teaching the art <strong>of</strong> tennes or<br />
decimals to worke all questions in fractions as whole<br />
numbers, without reduction: An easier and plainer way<br />
than the vulgar. Shewing the use also <strong>of</strong> Napiers bones,<br />
by which multiplication and division is performed<br />
without charging the memory at all to those that will<br />
make use <strong>of</strong> them. As also the extracting <strong>of</strong> the square<br />
and cube roots, with divers applications there<strong>of</strong>.<br />
Year: 1634<br />
Place: London<br />
Publisher: James Boler and William Luggard<br />
Edition: 1st<br />
Language: English<br />
Binding: later half morocco over marbled paper boards<br />
Pagination: pp. [8], 140, [2]<br />
Collation: A 4 B–K 8 (- K8 blank)<br />
Size: 140x90 mm<br />
This, published less than twenty years after Napier’s<br />
Rhabdologia (1617), is one <strong>of</strong> the first arithmetics to<br />
explain the use <strong>of</strong> Napier’s rods as a method for facilitating<br />
multiplication, division and extraction <strong>of</strong> roots. Although<br />
translations <strong>of</strong> Napier’s work had quickly appeared in<br />
German (1618), Italian (1623) and Dutch (1626), with<br />
the exception <strong>of</strong> a brief mention in an English almanac <strong>of</strong><br />
1618, the bones had only been described in English once<br />
before in J. Dansie’s A Mathematicall manuel, London,<br />
1627. Barton provides samples <strong>of</strong> Napier’s bones and<br />
instructs his readers to either cut them out or make their
Erwin Tomash Library<br />
Bass, Michael T. Baudusson, M.<br />
own. He indicates: if you make them in paste-board, you<br />
cannot have less than 15; that is, 3 set.<br />
After describing the use <strong>of</strong> the bones, Barton continues<br />
with <strong>chapter</strong>s on business topics such as calculating<br />
pr<strong>of</strong>it, loss and interest as well as how to calculate the<br />
value <strong>of</strong> a barter trade deal for each side. The final<br />
sections deal with simple estimates <strong>of</strong> the tonnage <strong>of</strong><br />
a ship, the volume <strong>of</strong> a cask, measuring timber and an<br />
introduction to square and cube roots.<br />
Illustrations available:<br />
Title page<br />
Pages describing Napier’s bones<br />
B 112<br />
Bass, Michael T. (1799–1884)<br />
Street music in the metropolis.<br />
B 111<br />
Year: 1864<br />
Place: London<br />
Publisher: John Murray<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards; spine and front cover gilt<br />
Pagination: pp. viii, 120<br />
Collation: A 4 B–H 8 I 4<br />
Size: 186x116 mm<br />
Bass was head <strong>of</strong> Bass & Co., a brewery in Burton-on-<br />
Trent and a Member <strong>of</strong> Parliament from 1848 to his<br />
retirement in 1873. He seldom rose to speak but was<br />
evidently very active and involved in other aspects <strong>of</strong><br />
the job.<br />
As <strong>Charles</strong> <strong>Babbage</strong> makes clear in his autobiography<br />
(<strong>Babbage</strong>, Passages from the life <strong>of</strong> a philosopher,<br />
1864), he had little regard for street musicians. Michael<br />
Bass was the Member <strong>of</strong> Parliament who introduced a<br />
bill limiting this nuisance that was never adopted. This<br />
small volume is an attempt to rally support for the cause<br />
and details, among others, an incident in which <strong>Babbage</strong><br />
was forced to bring one street musician to court.<br />
Illustrations available:<br />
Title page<br />
Bassentin, Jacques<br />
See Jacquinot, Dominique; L’usage de l’astrolabe,<br />
avec un petit traicté de la sphere … Plus est<br />
adiousté une amplification de l’usage de<br />
l’astrolabe, par Jacques Bassentin Escossis, 1573<br />
B 113<br />
Baudusson, M.<br />
Le rapporteur exact, ou tables des cordes de chaque<br />
angle, depuis une minute jusqu’a cent quatre-vingts<br />
degrés pour un rayon de mille parties égales.<br />
Year: 1842<br />
Place: Paris<br />
B 112<br />
119
120<br />
Publisher: Bachelier<br />
Edition: 3rd<br />
Language: French<br />
Figures: 1 engraved folding plate<br />
Binding: contemporary leather; black leather label<br />
Pagination: pp. xviii, 156, 6<br />
Collation: 1–15 6<br />
Size: 136x81 mm<br />
There are two works bound into this volume. The first, by<br />
Baudusson, is a trigonometric table based on the metric<br />
division <strong>of</strong> the circle—a new system that never found<br />
acceptance. The second table (from 1834) by M. P. Le<br />
Terrier is based on the old 360-degree division. Both<br />
men were evidently associated with the great Cadastre<br />
table project headed by de Prony.<br />
Illustrations available:<br />
Title page <strong>of</strong> Baudusson<br />
Title page <strong>of</strong> Le Terrier<br />
Sample page from Baudusson<br />
Sample page from Le Terrier<br />
Erwin Tomash Library<br />
Baudusson, M. Bauschinger, Julius<br />
Baudusson title, B 113<br />
Le Terrier title, B 113<br />
B 114<br />
Baum, Frank George (1870–)<br />
An alternating current calculating device. For the use<br />
<strong>of</strong> electrical engineers.<br />
Year: 1902<br />
Place: Stanford, CA<br />
Publisher: Author<br />
Edition: 1st<br />
Language: English<br />
Figures: with calculating device and advertising flyer<br />
Binding: original paper wrappers; front cover lacking<br />
Pagination: pp. 22<br />
Size: 173x130 mm<br />
Rather than being a calculating device using alternating<br />
current, this is a nomogram with a plastic overlay for<br />
performing calculation on data involving alternating<br />
currents.<br />
Illustrations available:<br />
Title page<br />
Nomogram (color)<br />
B 114<br />
B 115<br />
Bauschinger, Julius (1860–1934) and Johann Theodor<br />
Peters (1869–1941)<br />
Logarithmisch-trigonometrische Tafeln mit acht<br />
dezimalstellen enthaltend die Logarithmen aller<br />
Zahlen von 1 bis 200000 und die Logarithmen<br />
der trigonometrischen Funktionen für jede<br />
Sexagesimalsekunde des Quadranten.<br />
Year: 1910–1911<br />
Place: Leipzig<br />
Publisher: Wilhelm Engelmann
Erwin Tomash Library<br />
Bauschinger, Julius Bauschinger, Julius<br />
Edition: 1st<br />
Language: German<br />
Figures: v.1. 1 photographic plate<br />
Binding: three-quarter red leather boards; gilt spine<br />
Pagination: 2 vols. v.1. pp. xx, 368; v.2. pp. 952<br />
Collation: v.1. π 10 1–23 8 ; v.2. 1–59 8 60 4<br />
Size: 279x195 mm<br />
Reference: Hend BTM, #197.0, p. 153; Zin GBAL, p. 87<br />
At the time <strong>of</strong> this project, Julius Bauschinger had<br />
just left his position as Director <strong>of</strong> the Astronomical<br />
Research <strong>Institute</strong> in Berlin and had become Director<br />
<strong>of</strong> the Imperial Observatory at Strassburg. An important<br />
German astronomer, he appreciated the usefulness <strong>of</strong><br />
logarithms to all branches <strong>of</strong> science. Johann Peters, a<br />
pr<strong>of</strong>essor in the Royal Astronomical Calculating <strong>Institute</strong><br />
in Berlin and an expert on methods <strong>of</strong> table production,<br />
was described by Archibald (see entry for Archibald,<br />
Mathematical Table Makers) as perhaps the greatest<br />
mathematical table maker <strong>of</strong> all time. Simultaneously<br />
with the start <strong>of</strong> hand calculation, they asked the engineer<br />
Hamann about the possibility <strong>of</strong> constructing a difference<br />
engine to help with the work. The resulting machine is<br />
illustrated in the frontispiece, and a description <strong>of</strong> its<br />
workings can be found in the first volume’s preface.<br />
These well-regarded tables were some <strong>of</strong> the first to be<br />
completely recalculated—most previously published<br />
tables having been based on those produced in the early<br />
1600s by Henry Briggs and Adriaan Vlacq. The Royal<br />
Prussian Academy <strong>of</strong> Sciences and the Imperial Academy<br />
<strong>of</strong> Science <strong>of</strong> Vienna sponsored the work.<br />
The work was published in two volumes—the first,<br />
containing logarithms <strong>of</strong> numbers, in 1910 and the<br />
second, logarithms <strong>of</strong> trigonometric functions, in 1911.<br />
The second volume, unlike the first, contains two title<br />
Volume two title page, B 115<br />
pages, one in German and one in English. The English<br />
title page was added to Volume 2 no doubt in order<br />
to capitalize upon the favorable reception <strong>of</strong> the first<br />
volume by extending its distribution to the British and<br />
American markets.<br />
As can be seen in the illustrations <strong>of</strong> the tables, the authors<br />
used a typographical device similar to that <strong>of</strong> Bagay to<br />
indicate where the most significant digits <strong>of</strong> the logarithm<br />
changed. The mark is a small asterisk in Volume 1 but<br />
was changed to a larger one in the second volume. The<br />
change was made because the authors felt the smaller<br />
mark was not sufficiently visible (see illustrations <strong>of</strong><br />
Difference calculating machine, B 115<br />
121
oth the sample logarithm and trigonometric pages and<br />
compare this mark to the easily visible marks used by<br />
Bagay).<br />
122<br />
Illustrations available:<br />
Title page<br />
Calculating machine<br />
Sample logarithm page<br />
Sample trigonometric page<br />
English title page in volume II<br />
B 116<br />
Baxandall, David (1874–1938)<br />
Calculating machines and instruments. Catalogue<br />
<strong>of</strong> the collections in the Science Museum South<br />
Kensington with descriptive and historical notes and<br />
illustrations.<br />
Year: 1926<br />
Place: London<br />
Publisher: H. M. S. O.<br />
Edition: 1st<br />
Language: English<br />
Figures: 13 photographic plates on 11 leaves<br />
Binding: original printed paper wrappers<br />
Pagination: pp. 85, [1]<br />
Size: 245x154 mm<br />
Reference: Ran ODC, p. 406; Bax CMI, pp. 85<br />
This is a catalog <strong>of</strong> the calculating machines and<br />
instruments in the London Science Museum. It covers<br />
everything from the abacus and exchequer tallies to<br />
harmonic analyzers. There is a small description <strong>of</strong> each<br />
machine and usually an indication <strong>of</strong> any significant<br />
improvements over earlier machines designed to perform<br />
the same process. The catalog was reprinted, with some<br />
minor changes to correct errors and slightly larger<br />
photographs, by the Science Museum in 1975.<br />
Illustrations available:<br />
Title page<br />
B 117<br />
Baxter, James Phinney (1893–1975)<br />
Scientists against time.<br />
Year: 1946<br />
Place: Boston<br />
Publisher: Little, Brown<br />
Edition: 1st<br />
Language: English<br />
Figures: 76 photolith plates<br />
Binding: original cloth boards; with dust jacket<br />
Pagination: pp.xvi,473, [1]<br />
Size: 213x138 mm<br />
In 1943 Vannevar Bush, who wrote a foreword to this<br />
book, had asked Dr. James Baxter, president <strong>of</strong> Williams<br />
College (but the wartime deputy director <strong>of</strong> the Office<br />
Erwin Tomash Library<br />
Baxandall, David Beaulieu, Jean de<br />
<strong>of</strong> Strategic Services) to write a history <strong>of</strong> the scientific<br />
accomplishments <strong>of</strong> the wartime scientists. This book is<br />
the result. The dust jacket describes this as<br />
The revealing history <strong>of</strong> American scientists<br />
at war and the story <strong>of</strong> the death-dealing and<br />
lifesaving devices which they contributed to<br />
victory in World War II.<br />
It covers everything from antibacterial drugs to guided<br />
bombs and the atomic bomb. Very little is said about<br />
calculation and, <strong>of</strong> course, nothing about code breaking.<br />
Illustrations available:<br />
Title page<br />
B 118<br />
Beaulieu, Jean de<br />
B 118<br />
Nouvelle invention d’arithmetique dont l’usage tres<br />
facile sera connu à la premiere lecture de l’instruction,<br />
& sera tout ce que l’aritmetique vulgaire peut executer,<br />
soit multiplications, divisions, reductions de monnoye,<br />
changes universels, regles de trois, extractions de<br />
racines carrées, toisez, & autres calculs: avec laquelle<br />
l’on peut faire en une heure de temps un calcul<br />
seroit impossible de faire en une journée entiere par<br />
l’arithmetique ordinaire. Necessaire à tous Officiers<br />
d’armées, tresoriers, payeurs, financiers, marchands, &<br />
à toutes sortes d’ouvriers; bref, à toutes personnes.<br />
Year: 1677<br />
Place: Paris<br />
Publisher: Chez l’Auteur
Erwin Tomash Library<br />
Beausard, Pierre Becmann, Gustav Bernhard<br />
Edition: 1st<br />
Language: French<br />
Figures: 7 double-page engraved tables<br />
Binding: contemporary marbled paper wrappers<br />
Pagination: pp. 8<br />
Collation: A 4<br />
Size: 251x190 mm<br />
Reference: H&J AM, Vol. II, B 13.4, p. 60<br />
Jean de Beaulieu held the position <strong>of</strong> Ingénieur<br />
géographe du Roi at La Rochelle. This is a multiplication<br />
table, in several sheets, <strong>of</strong> all numbers up to 210 x 100.<br />
A final sheet gives the decimal equivalent <strong>of</strong> fractions.<br />
It is interesting that despite the fact the decimal point<br />
had been in use since the early 1600s, this decimal table<br />
still relies on the old form <strong>of</strong> notation with accents (5’<br />
corresponds to 0.5; 25’’ to 0.25; 6666 4 to 0.6666, etc.)<br />
Illustrations available:<br />
Title page<br />
First page <strong>of</strong> multiplication table (portion)<br />
Decimal fraction table (portion)<br />
B 119<br />
Beausard, Pierre (1536–1577) et al.<br />
Decimal fraction table, B 118<br />
Annuli astronomici, instrumenti cum certissimi, tùm<br />
commodissimi, usus, ex variis authoribus, Petro<br />
Beausardo, Gemma Frisio, Joãne Dryandro, Boneto<br />
Hebraeo, Burchardo Mythobio, Orontio Finaeo, una<br />
cum meteoroscopio per Joãné Regiomontanum, &<br />
annulo non universali M.T. authore.<br />
Year: 1558<br />
Place: Paris<br />
Publisher: G. Cavellat<br />
Edition: 1st (Collected, 2nd issue)<br />
Language: Latin<br />
Binding: modern vellum<br />
Pagination: ff. 8, 159, [1] (i.e. ff. 103v–117)<br />
Collation: A 8 a–v 8<br />
Size: 162x106 mm<br />
Reference: H&L, #2589, p. 588; Cro CL, #62, p. 76<br />
Beausard, the editor <strong>of</strong> this work, was a pr<strong>of</strong>essor <strong>of</strong><br />
medicine and mathematics at the <strong>University</strong> <strong>of</strong> Louvain.<br />
The introduction describes elementary notions <strong>of</strong><br />
astronomy and the shadow scales on an astrolabe. This<br />
is followed by seven different works on the annulus,<br />
also known as the astronomical ring. The instruments<br />
are mainly ring sundials, but some are also elementary<br />
survey instruments. Detailed descriptions <strong>of</strong> the contents<br />
<strong>of</strong> each work are given in the individual entries. Many<br />
<strong>of</strong> these items were previously published in a work by<br />
Dryander.<br />
See<br />
1. Boneto, Hebræo, or Bonetus, de Latus; Annuli<br />
astronomici utilitatu[m] liber ad Alexandrum<br />
sextu[m] Po[n]tifice[m]) maximum, 1558, Paris.<br />
2. Dryander, Johann; Annulorum trium diversi<br />
generis instrumentorum astronomicoru[m] co[m]pone[n]di<br />
ratio usus, atque cu[m] quibusda aliis<br />
lectu iucu[m]dissimis, quoru[m] catalogum mox<br />
versa pagella indicabit, 1558, Paris.<br />
3. Fine, Oronce; Compendiaria tractatio de fabrica<br />
& usu annuli astronomici, 1558, Paris.<br />
4. Gemma Frisius, Reiner; Usus annuli astronomici,<br />
1558, Paris.<br />
5. M. T.; Compositio alterius annuli astronomici non<br />
universalis, sed add certam polarem elevationem<br />
instructi authore, 1558, Paris.<br />
6. Mithob, Burchard; Structura et usus annuli<br />
sphærici, 1558, Paris.<br />
7. Regiomontanus, Johannes; Ad Bessarionem<br />
Cardinalem Nicenum ad Patriarcham Constantinopolitanum:<br />
De compositione meteoroscopi,<br />
1558, Paris.<br />
B 120<br />
Becmann, Gustav Bernhard (1720–1783) and David<br />
Heinrich Becmann<br />
Fratrum Becmannorum. Tractatio mathematicojuridica<br />
de interusurio …<br />
Year: 1784<br />
Place: Goettingen<br />
Publisher: Io. Christian Dieterich<br />
Edition: 1st<br />
Language: Latin<br />
Binding: modern paper boards<br />
Pagination: pp. [4], 108<br />
Collation: )( 2 A–N 4 O 2<br />
Size: 211x160 mm<br />
Gustav Becmann was a pr<strong>of</strong>essor at Göttingen and was<br />
known for his writings on legal and financial concerns in<br />
tax and legacies. This work appeared a year after he died.<br />
123
The final process <strong>of</strong> seeing it through the press was done<br />
by his younger brother.<br />
While Becmann and his brother are known to have<br />
published other works on law, this book on the calculation<br />
and legal aspects <strong>of</strong> interest is not known in any other<br />
collection. It includes a discussion <strong>of</strong> both simple and<br />
compound interest as well as tables and formulas for<br />
calculating and the use <strong>of</strong> logarithms.<br />
124<br />
Illustrations available:<br />
Title page<br />
Interest table<br />
B 121<br />
Bede Venerabilis (672/3–735)<br />
De computo per gestum digitorum. Idem de loquela.<br />
Idem de ratione unciarum.<br />
b/w: Probus, Marcus Valerius; De notis Romanor[um]<br />
ex codice manuscripto castigatior, auctiorque,<br />
quam unquam antea, factus.<br />
b/w: Petrus, Deacon; De eadem re ad conradum<br />
primum imp. Ro[manorum].<br />
b/w: Alabaldus, Demetrius; De minutiis. Idem de<br />
ponderibus. Idem de mensuris.<br />
b/w: Leges XII tabularum, leges pontificiæ<br />
Ro[manorum]. Variæ verborum conceptiones,<br />
quibus antiqui cuz in rebus sacris, tum prophanis<br />
uterentur, sub titulo de Ritibus Romanorum<br />
collectæ. Phlegontis Trallani epistola de moribus<br />
Ægytiorum. Aureliani Cæsaris epistola de <strong>of</strong>ficio<br />
tribuni militum. Iscriptiones antiquæ variis in<br />
locis repertæ, atq[ue] aliæ, q[uam] quae in<br />
Erwin Tomash Library<br />
Bede Venerabilis Bede Venerabilis<br />
B 120<br />
Romano codice continentur. Hæc omnia nunc<br />
primum edita.<br />
Year: 1525<br />
Place: Venice<br />
Publisher: Joh. Tacuino<br />
Edition: 1st<br />
Language: Latin<br />
Figures: main title in red and black<br />
Binding: stamped vellum over wooden boards<br />
Pagination: ff. [4], XXIIII<br />
Collation: a 4 A–C 8<br />
Size: 218x149 mm<br />
Reference: Ada CBCE, P2122; Smi Rara, p. 140<br />
The Venerable Bede (Beda) was an English monk who<br />
spent his entire life (from the age <strong>of</strong> 7) in a monastery<br />
near what is now Newcastle upon Tyne. Although he<br />
never traveled more than fifty miles from his base, he<br />
became one <strong>of</strong> the great scholars <strong>of</strong> his day and wrote<br />
extensively on every major subject, even writing a tourist<br />
guide to sites in the Holy Land and other places. Bede’s<br />
monastery seems to have been the gathering place for<br />
many. It attracted people from around Europe, Ireland<br />
and even North Africa, all <strong>of</strong> whom added to the rich<br />
resources available to Bede.<br />
Volume title page, B 121<br />
Colophon, B 121
Erwin Tomash Library<br />
Bede Venerabilis Bede Venerabilis<br />
Bede documented the medieval form <strong>of</strong> hand gestures<br />
known as finger numerals, and his is the first printed<br />
record we have <strong>of</strong> them. Bede’s description is short and<br />
contains no diagrams. It simply lists the finger positions<br />
used to represent integers from 1–9,999 and adds a very<br />
short remark on the Greek alphabetic number system.<br />
The work is bound with different works by Bede and<br />
others (see the title page).<br />
For a succinct discussion <strong>of</strong> Bede finger reckoning, see<br />
Sachiko Kusukawa, A manual computer for reckoning<br />
time, In Claire Richter Sherman, Writing on hands.<br />
Memory and knowledge in early modern Europe.<br />
<strong>University</strong> <strong>of</strong> Washington Press, Seattle, 2000, pp. 28–<br />
34.<br />
Illustrations available:<br />
Title page <strong>of</strong> the entire volume<br />
Title page <strong>of</strong> the computo<br />
Four pages <strong>of</strong> text <strong>of</strong> the computo (in three images)<br />
Colophon<br />
B 122<br />
Bede Venerabilis (672/3–735)<br />
De natura rerum et temporum rationes. Libri duo. Nunc<br />
recens inventi, & in lucem editi.<br />
Year: 1529<br />
Place: Basel<br />
Publisher: Henricus Petrus<br />
Edition: 1st (two texts together)<br />
Language: Latin<br />
Figures: 16 plates<br />
Computo title page, B 121<br />
Binding: later quarter vellum heavy paper boards<br />
Pagination: ff. [16], 74<br />
Collation: å 6 ß 6 ð 4 a–l 6 m 8<br />
Size: 279x194 mm<br />
Reference: Smi Rara, p. 159; Sart Vol. I, pp. 510–11; DSB I,<br />
pp. 564–66; Smi HM II, p. 200; Zin GBAL, #1374<br />
This volume, like the 1525 work mentioned above,<br />
is composed <strong>of</strong> a number <strong>of</strong> different works. Bede’s<br />
De computu digitorum is the same, very short, work<br />
previously described. The one obvious difference is that<br />
a more complete list <strong>of</strong> the Greek alphabetic number<br />
symbols is given.<br />
Illustrations available:<br />
Main title page<br />
Title page <strong>of</strong> Bede’s De natura rerum<br />
Complete text (in two images) <strong>of</strong> Computu digitorum<br />
Colophon<br />
B 123<br />
Bede Venerabilis (672/3–735)<br />
Bede first page, B 122<br />
Colophon, B 122<br />
Opuscula cumplura de temporum ratione diligenter<br />
castigata: atque illustrata veteribus quibusdam<br />
annotationibus una cum scholiis in obscuriores aliquot<br />
locos, authore Johanne Noviomago.<br />
125
w: Anselm, In omnes Pauli …<br />
126<br />
Year: 1537<br />
Place: Cologne<br />
Publisher: Johannes Prael for P. Quentel<br />
Edition: 1st (collected)<br />
Language: Latin<br />
Binding: Flemish blindstamped over wooden boards, rolls <strong>of</strong><br />
medallion heads and foliage forming a double panel;<br />
clasps and catches; corner bosses<br />
Pagination: ff. [14], 18, [6], 30 (misnumbered 19 as 21, 24 as<br />
20), XXXI–CXXVI (misnumbered 35 as 25, 37 as 27,<br />
38 as 138, 45 as 46, 53 as 46, 54 as 49, 60 as 54, 78<br />
as76), [4]<br />
Collation: A 4 B 6 C 4 D–G 6 a–x 6 y 4<br />
Size: 310x200 mm<br />
Reference: Ada CBCE, #A1174; Zin GBAL, #1657; Smi Rara,<br />
p. 159; Ada CBCE, #B448<br />
This edition <strong>of</strong> Bede’s work on finger numerals (De<br />
computu) is identical to that appearing in the 1529 edition.<br />
After this very short section, the rest <strong>of</strong> the volume<br />
contains works by Bede on arithmetic, astronomy, the<br />
calendar and chronology.<br />
Illustrations available:<br />
Title page for the volume (Anselm title page)<br />
Title page for Bede’s work<br />
Complete text <strong>of</strong> De computu in two images<br />
Colophon <strong>of</strong> Bede’s work<br />
Bede Venerabilis (672/3–735)<br />
See Artabasda, Nicolaus <strong>of</strong> Smyrna; Græci<br />
Mathematici ΕΚΦΡΑΣΙC numerorum notationis per<br />
gestum digitorum, 1614.<br />
Erwin Tomash Library<br />
Bede Venerabilis Bedwell, William<br />
B 123<br />
B 124<br />
Bedwell, William (1561–1632), translator and editor<br />
De numeris geometricis. Of the nature and proprieties<br />
<strong>of</strong> geometricall numbers. First written by Lazarus<br />
Schonerus, and now Englished, enlarged and illustrated<br />
with divers and sundry tables and observations<br />
concerning the measuring <strong>of</strong> plaines and solids; all<br />
teaching the fabricke, demonstration and use <strong>of</strong> a<br />
singular instrument, or rular, long since invented and<br />
perfitted by Thomas Bedwell Esquire.<br />
b/w: Digges, Leonard; Tectonicon: briefly shewing<br />
the exact measuring, and speedy reckoning all<br />
manner <strong>of</strong> land, squares, timber, stone, steeples,<br />
pillers, globes, &c.<br />
Year: 1614<br />
Place: London<br />
Publisher: Richard Field<br />
Edition: 1st<br />
Language: English<br />
Figures: 1 large letterpress folding table<br />
Binding: modern vellum<br />
Pagination: pp. [viii], 82<br />
Collation: A–L 4 M 1<br />
Size: 179x131 mm<br />
Bede title page, B 123<br />
Often considered the first English translation <strong>of</strong> Lazarus<br />
Schoner’s treatise on the Greek theory <strong>of</strong> numbers (first<br />
published as an appendix to his edition <strong>of</strong> Peter Ramus,<br />
Arithmetices libri duo, Frankfurt, 1586), in fact it is an<br />
enlarged, and rewritten, version <strong>of</strong> this material rather than<br />
a translation. Bedwell’s motive was to provide a basis for<br />
the explanation <strong>of</strong> the use <strong>of</strong> the trigonicum, which was<br />
a ruler invented by his uncle, Thomas Bedwell, about<br />
forty years earlier. This ruler was similar to instruments
Erwin Tomash Library<br />
Bedwell, William Beghin, Auguste<br />
described by Digges in the other work bound in this<br />
volume. The first <strong>chapter</strong> considers geometrical numbers<br />
in general (he makes a point <strong>of</strong> not calling them figurate<br />
or cossick numbers, which would have been the more<br />
common terminology) and <strong>chapter</strong>s 2 and 4 deal with<br />
square and cubic numbers. Chapters 3 and 5 are the<br />
practical application <strong>of</strong> these ideas in the measurement<br />
<strong>of</strong> cloth, painting, wainscoting, timber, etc.<br />
In the preface Bedwell indicates that he would publish<br />
more on his uncle’s ruler, a promise he kept with his<br />
Mesolabium architectonicum <strong>of</strong> 1631 (see Addenda).<br />
Illustrations available:<br />
Title page<br />
B 125<br />
Beebe, Levi N.<br />
B 124<br />
First steps among figures. A drill book in the<br />
fundamental rules <strong>of</strong> arithmetic. Teachers’ edition.<br />
b/w: Beebe, Levi N.; First steps among figures. A<br />
drill book in the fundamental rules <strong>of</strong> arithmetic.<br />
Pupils’ edition.<br />
Year: 1883<br />
Place: Syracuse, NY<br />
Publisher: C. W. Bardeen<br />
Edition: 6th<br />
Language: English<br />
Binding: original cloth boards; stamped in black ink on spine<br />
and front cover; rear cover blind stamped and water<br />
stained<br />
Pagination: pp. 192, 140<br />
Size: 162x110 mm<br />
These two works illustrate the teaching <strong>of</strong> arithmetic in<br />
the United States during the last portion <strong>of</strong> the nineteenth<br />
century. The teacher’s edition gives detailed instructions<br />
as to exactly what should be taught and suggestions (e.g.,<br />
“Teach in counting that the second <strong>of</strong> two things is not<br />
itself two, but one”) as to where misunderstandings might<br />
occur. The work is full <strong>of</strong> drill exercises and arithmetical<br />
word problems. The teacher’s edition contains the<br />
answers to all the drill problems in the pupil’s edition.<br />
Illustrations available:<br />
Title page<br />
B 126<br />
Beghin, Auguste<br />
B 125<br />
Règle a calculs. Instruction - application numériques<br />
- tables et formules.<br />
Year: 1904<br />
Place: Paris<br />
Publisher: Chez Béranger and Tavernier-Gravet<br />
Edition: 3rd<br />
Language: French<br />
Figures: 135 in text<br />
Binding: original paper wrappers<br />
Pagination: pp. xi, [1], 127, [1]<br />
Collation: π 6 1–8 8<br />
Size: 254x168 mm<br />
Beghin is known as the person who first designed a slide<br />
rule with a displaced scale—where the indices are not<br />
127
at the ends <strong>of</strong> the scale but near the middle, a situation<br />
that lessens the amount the slide has to move in many<br />
calculations.<br />
This is a large work on the use <strong>of</strong> a special slide rule<br />
created by Auguste Beghin in 1898. The instructions are<br />
illustrated with seventy-four problems and 135 figures.<br />
128<br />
Illustrations available:<br />
Title page<br />
Erwin Tomash Library<br />
Beghin, Auguste Bell, Eric Temple<br />
B 127<br />
Beghin, Auguste<br />
B 127<br />
Règle à calculs. Instruction - application numériques.<br />
100 problèmes pratiques et industriels. Tables et<br />
formules.<br />
Year: 1912<br />
Place: Paris<br />
Publisher: Chez Béranger and Tavernier-Gravet<br />
Edition: 5th<br />
Language: French<br />
Figures: 190 in text<br />
Binding: original paper wrappers; unopened<br />
Pagination: pp. x, 185, [5]<br />
Collation: π 5 1–11 8 12 7<br />
Size: 255x166 mm<br />
An expanded edition <strong>of</strong> the instructional manual by<br />
Beghin on the use <strong>of</strong> his slide rule—this edition claims<br />
to have 190 figures, almost all <strong>of</strong> which are simple line<br />
drawings.<br />
Illustrations available:<br />
Title page<br />
B 128<br />
Bell, Eric Temple (1883–1960)<br />
The development <strong>of</strong> mathematics.<br />
Year: 1945<br />
Place: New York<br />
Publisher: McGraw-Hill<br />
Edition: 2nd<br />
Language: English<br />
Binding: original cloth boards; with dust jacket<br />
Pagination: pp. xii, 638<br />
Size: 228x150 mm<br />
A native <strong>of</strong> Aberdeen, Scotland, Eric Temple Bell first<br />
attended the <strong>University</strong> <strong>of</strong> London before moving to the<br />
United States, where he earned his A.B. degree in 1904<br />
at Stanford <strong>University</strong>. He later received an A.M. degree<br />
at Washington <strong>University</strong> and a Ph.D. at Columbia. After<br />
beginning as an instructor in the mathematics department<br />
at Washington, he rose to become a full pr<strong>of</strong>essor and then<br />
left to take a pr<strong>of</strong>essorship at the California <strong>Institute</strong> <strong>of</strong><br />
Technology. He was extensively involved with scientific<br />
associations, serving as president <strong>of</strong> the Mathematical<br />
Association <strong>of</strong> America and vice president <strong>of</strong> the<br />
American Association for the Advancement <strong>of</strong> Science.<br />
Well known as a writer <strong>of</strong> technical mathematical papers,<br />
he was also a successful popularizer through his writings<br />
on historical aspects <strong>of</strong> mathematics. While accessible to<br />
the interested amateur, his historical writings remain a<br />
significant source for the pr<strong>of</strong>essional historian.<br />
Organized by subject rather than by time, this history<br />
<strong>of</strong> mathematics begins with the concept <strong>of</strong> pro<strong>of</strong> and its<br />
place in mathematics and ends with the development <strong>of</strong><br />
statistics.<br />
Illustrations available:<br />
Title page<br />
B 129<br />
Bell, Eric Temple (1883–1960)<br />
The magic <strong>of</strong> numbers.<br />
Year: 1946<br />
Place: New York<br />
Publisher: McGraw-Hill<br />
Edition: 1st<br />
Language: English<br />
Figures: photograph frontispiece<br />
Binding: original cloth boards; with dust jacket<br />
Pagination: pp. viii, [2], 418<br />
Size: 202x137 mm<br />
This volume covers the development <strong>of</strong> the concepts <strong>of</strong><br />
numbers. Bell starts from Pythagoras and leads up to the<br />
realm <strong>of</strong> physics via set theory and other branches <strong>of</strong><br />
mathematics.
Illustrations available:<br />
Title page<br />
B 130<br />
Bell, Eric Temple (1883–1960)<br />
Mathematics. Queen and servant <strong>of</strong> science.<br />
Year: 1952<br />
Place: London<br />
Publisher: Bell<br />
Edition: 1st (English)<br />
Language: English<br />
Binding: original cloth boards; with dust Jacket<br />
Pagination: pp. xx, [2], 437, [1]<br />
Size: 202x138<br />
A history <strong>of</strong> pure and applied mathematics.<br />
Illustrations available:<br />
Title page<br />
B 131<br />
Bell, Eric Temple (1883–1960)<br />
Men <strong>of</strong> mathematics.<br />
Year: 1937<br />
Place: New York<br />
Publisher: Simon and Schuster<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards; with dust jacket<br />
Pagination: pp. xviii, 3–592, [2]<br />
Size: 231x151 mm<br />
Erwin Tomash Library<br />
Bell, Eric Temple Bell, T. F.<br />
B 129 B 131<br />
This volume describes the lives <strong>of</strong> the great<br />
mathematicians. Organized chronologically, Bell begins<br />
with Zeno and ends with Cantor.<br />
Illustrations available:<br />
Title page<br />
B 132<br />
Bell, John Fred (1898–)<br />
A history <strong>of</strong> economic thought.<br />
Year: 1953<br />
Place: New York<br />
Publisher: Ronald<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards; with dust jacket<br />
Pagination: pp. x, 696<br />
Size: 228x145<br />
A history <strong>of</strong> economics from ancient times to the early<br />
twentieth century.<br />
Illustrations available:<br />
Title page<br />
B 133<br />
Bell, T. F.<br />
Jacquard weaving and designing.<br />
Year: 1895<br />
Place: London<br />
129
130<br />
Publisher: Longmans, Green and Co.<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards<br />
Pagination: pp. viii, 303, [1]<br />
Collation: A 4 B–U 8<br />
Size: 213x136 mm<br />
The design and operations <strong>of</strong> the Jacquard loom and its<br />
variants are described herein, as well as the manner in<br />
which they are set up to produce weavings <strong>of</strong> various<br />
kinds.<br />
Joseph Marie Jacquard (1752–1834) was a mechanic in<br />
Lyons who had invented a machine for weaving fishing<br />
nets. He appears to have begun experiments on improving<br />
ordinary weaving looms about 1790—a model <strong>of</strong> a<br />
machine <strong>of</strong> this date is in the Conservatoire des Arts et<br />
Métier in Paris, but it is not a Jacquard loom as we know<br />
it today. About 1804, he was brought to Paris to repair<br />
Vaucanson’s loom (an earlier punched tape version <strong>of</strong><br />
the automatic loom), and it seems that his attention was<br />
drawn to the potential <strong>of</strong> this technology at that time.<br />
Jacquard’s birth name was Joseph Marie <strong>Charles</strong>—the<br />
extended family had nicknames for each branch, and he<br />
adopted the nickname Jacquard as his formal surname.<br />
Illustrations available:<br />
Title page<br />
B 134<br />
Belli, Silvio Vicentin (–1575)<br />
Libro del misurar con la vista …. Nel quale<br />
s’insegna, senza trauagliar con numeri, a misurar<br />
facilissimamente le distantie, l’altezze, e le pr<strong>of</strong>ondità<br />
con il quadrato geometrico, e con altri stromenti, de’<br />
Erwin Tomash Library<br />
Belli, Silvio Vicentin Belli, Silvio Vicentin<br />
B 133<br />
quali in ogni luogo quasi in un subito si puo prouedere.<br />
Si mostra ancora una bellissima uia di ritrouare<br />
la pr<strong>of</strong>ondità di qual si uoglia mare; & un modo<br />
industrioso di misurar il circuito di tutta la terra.<br />
Year: 1565<br />
Place: Venice<br />
Publisher: Giordano Ziletti<br />
Edition: 1st<br />
Language: Italian<br />
Figures: 54 woodcut diagrams in text<br />
Binding: 18th-century Italian paper boards<br />
Pagination: pp. [8], 108<br />
Collation: * 4 A–N 4 O 2<br />
Size: 194x140 mm<br />
Reference: Rcdi BMI Vol. I, p. 107; Kie SI, p. 116<br />
B 134<br />
Belli taught mathematics in Vicenza and was a founding<br />
member <strong>of</strong> the Accademia Olimpica in 1555. He later<br />
became an architect, practicing in Ferrara, Modena,<br />
Rome and Venice.<br />
His work on surveying was very popular and had at least<br />
six editions in the sixteenth century. It was later combined<br />
with another <strong>of</strong> Belli’s works (Della Proportione, 1573)<br />
and published as Quattro libri giometici in 1595.<br />
In this book Belli deals mainly with simple survey<br />
problems for which rough estimates <strong>of</strong> distances and<br />
heights suffice and describes the use <strong>of</strong> a geometrical<br />
square with a sighting vane. He gives many examples<br />
<strong>of</strong> estimating the solution to a problem by creating<br />
scale drawings on drumheads (essentially using them<br />
as a plane table), improvising survey instruments from<br />
a pair <strong>of</strong> sticks and even estimating distances using the
Erwin Tomash Library<br />
Beman, Wooster Woodruff Benese, Richard<br />
peak <strong>of</strong> the surveyor’s cap, all methods that would have<br />
been quite useful in military campaigns or emergency<br />
situations.<br />
The final <strong>chapter</strong>s discuss means for measuring the<br />
depths <strong>of</strong> the oceans and finding the circumference <strong>of</strong><br />
the earth.<br />
Illustrations available:<br />
Title page<br />
Geometric square and sight<br />
Estimating using the peak <strong>of</strong> a cap<br />
Drumhead surveying<br />
Drumhead and geometric square surveying<br />
Drumhead surveying, B 134<br />
Drumhead surveying, B 134<br />
Beman, Wooster Woodruff (1850–1922) and David<br />
Eugene Smith (1860–1944)<br />
See Fink, Karl; A brief history <strong>of</strong> mathematics, 1910<br />
B 135<br />
Benese, Richard de (fl.1537–1547)<br />
The boke <strong>of</strong> measurying <strong>of</strong> lande as well <strong>of</strong> woodland as<br />
plowland, & pasture in the feelde; & to compt the true<br />
nombre <strong>of</strong> acres <strong>of</strong> the same …<br />
Year: ca.1565<br />
Place: London<br />
Publisher: Thomas Colwell<br />
Edition: 4th<br />
Language: English<br />
Binding: Straight grained green morocco by W. Pratt for F. S.<br />
Ellis; marbled end papers; gilt edges; gilt tooled spine<br />
Pagination: ff. [56]<br />
Collation: A–G 8<br />
Size: 140x92 mm<br />
Reference: Win ESTC, 1876; Hymn AC, #277; Ken, #1457<br />
B 135<br />
Benese (sometimes de Benese) was the author <strong>of</strong> the<br />
first book on surveying in English. He was Canon <strong>of</strong><br />
the Augustinian priory <strong>of</strong> Merton and was forced to<br />
surrender it to Henry VIII upon the dissolution <strong>of</strong> the<br />
monasteries in 1538. Nevertheless, his career prospered,<br />
for his expertise led to his appointment as Surveyor <strong>of</strong><br />
Works at Hampton Court and Chaplain to Henry VIII.<br />
This very simple book on surveying practices was first<br />
published around 1537. It remained the standard work<br />
on the subject in the English language for almost forty<br />
years, this fourth edition being the last. The demise<br />
<strong>of</strong> serfdom in England, and the rise <strong>of</strong> individual land<br />
ownership, spurred interest in and the development <strong>of</strong><br />
surveying techniques. This little work was timely and<br />
popular in its day because survey techniques were little<br />
known, and unscrupulous sellers would <strong>of</strong>ten overstate<br />
the amount <strong>of</strong> land being sold.<br />
Earlier editions <strong>of</strong> this book contain tables (evidently the<br />
first ever printed in English) relating lengths in perches<br />
<strong>of</strong> the sides <strong>of</strong> rectangular fields to the area they contain<br />
in acres. This edition contains a table that relates money<br />
to area, as Benese explains:<br />
By cause in coumptyng <strong>of</strong> money it is not muche<br />
used to compte anye summes in markes, but<br />
most comomlye in poudes. Thefore because<br />
Marks do sygnyfye acres in comptynge the<br />
measures <strong>of</strong> lande, & poundes be no lyghtly<br />
turned into Markes by them that bee not experte<br />
in reakenynge, and castyng <strong>of</strong> a compt. Therefore<br />
in these sumes folowyine ye shall se pence turned<br />
131
132<br />
into perches grotes turned into dayeworkes. xl.d<br />
into a roode, a noble into di. acre, a Royal into .iii.<br />
roodes: a marke into an acre, & poundes turned<br />
into Markes, the which there be name acres.<br />
A short section at the end discusses how To measure<br />
Tymber or Stone, in length, breadth and depthe by the<br />
foote square.<br />
Like many other books <strong>of</strong> this era, for example, the<br />
illustration <strong>of</strong> Ptolemy in Gregor Reisch’s Margarita<br />
philosophica (<strong>of</strong> which the woodcut in this volume is<br />
only a crude copy), this work continues the suggestion<br />
that Ptolemy was the inventor <strong>of</strong> the quadrant (see<br />
illustration <strong>of</strong> the goddess <strong>of</strong> astronomy showing Ptolemy<br />
how to use a crude quadrant). It also continues the error<br />
that Ptolemy was a king <strong>of</strong> Egypt (note the crown and<br />
royal robes). The old typeface and random spelling make<br />
this a quite interesting book.<br />
Illustrations available:<br />
Title page<br />
Ptolemy<br />
Table<br />
Erwin Tomash Library<br />
Bennett, Wendell Clark Berkeley, Edmund Callis<br />
B 136<br />
Bennett, Wendell Clark (1905–1953)<br />
Ptolemy, B 135<br />
Numbers, measures, weights and calendars.<br />
Year: 1949<br />
Place: Washington, D.C.<br />
Publisher: Smithsonian Institution U.S.G.P.O.<br />
Edition: Extract<br />
Language: English<br />
Binding: original printed paper wrappers<br />
Pagination: pp. [2], 601–610<br />
Size: 242x154 mm<br />
weights and measures, and calendar systems <strong>of</strong> major<br />
native groups in South America.<br />
Illustrations available:<br />
Title page<br />
B 137<br />
Berkeley, Edmund Callis (1909–1988)<br />
Circuit algebra - introduction.<br />
Year: 1952<br />
Place: New York<br />
Publisher: Edmund C. Berkeley Associates<br />
Edition: 1st<br />
Language: English<br />
Figures: 24 figures in text<br />
Binding: original paper wrappers<br />
Pagination: pp. [1], i, 34<br />
Size: 280x216 mm<br />
Berkeley, a native <strong>of</strong> New York, graduated with an A.B.<br />
summa cum laude in mathematics from Harvard in 1930,<br />
entered the computer field in 1938 as an actuary using<br />
punched card machines for the Prudential Insurance<br />
Company <strong>of</strong> America, and worked with Howard Aiken<br />
during the war as an active-duty naval reserve <strong>of</strong>ficer.<br />
After the war, he returned briefly to Prudential, where<br />
he participated in studies that led to the purchase <strong>of</strong> a<br />
UNIVAC I. In 1947, a meeting to which he invited seven<br />
friends resulted in the establishment <strong>of</strong> the Association<br />
for Computing Machinery, better known as the ACM.<br />
Berkeley was the first member and acted as secretary<br />
until 1953. He went into business for himself as Edmund<br />
C. Berkeley and Associates in 1948 (later Berkeley<br />
Enterprises), started a publication known as Computers<br />
and Automation in 1951, consulted for industry, and<br />
This small extract was originally published in the<br />
Smithsonian Institution, Bureau <strong>of</strong> American Ethnology,<br />
Bulletin 143, Handbook <strong>of</strong> South American Indians Vol.<br />
5, pp. 601–610. It briefly describes number systems, B 137
Erwin Tomash Library<br />
Berkeley, Edmund Callis Berkeley, Edmund Callis<br />
devised and sold several relay computers and small<br />
robots (Simon, Squee, Relay Moe, etc.) as educational<br />
projects in kit form.<br />
This work covers Boolean algebra and how it can be<br />
used to describe circuits composed <strong>of</strong> tubes, relays, delay<br />
lines and other devices.<br />
Illustrations available:<br />
Title page<br />
B 138<br />
[Berkeley, Edmund Callis (1909–1988)]<br />
Geniacs: Simple electronic brain machines, and how<br />
to make them. Also: manual for Geniac electric brain<br />
construction kit No. 1.<br />
Year: 1955<br />
Place: New Haven<br />
Publisher: Oliver Garfield<br />
Edition: 1st<br />
Language: English<br />
Binding: original paper wrappers<br />
Pagination: pp. 64<br />
Size: 215x140 mm<br />
In 1950, Berkeley Associates produced a small<br />
educational computer known as Simon intended to teach<br />
the basic principles <strong>of</strong> switching circuits. Because the<br />
parts for Simon cost $300, it was decided to market it as<br />
a kit. This report is the manual for the resulting Geniac<br />
kit, which by 1955 sold for only $20. With it you could<br />
produce a number <strong>of</strong> ultra-simple devices ranging from<br />
a doorbell to a machine for converting from binary to<br />
decimal. The introduction states that<br />
We have had great help from several outstanding<br />
computer men in the design <strong>of</strong> about one third<br />
<strong>of</strong> the Geniac circuits … and regret that they feel<br />
they have to remain anonymous.<br />
Illustrations available:<br />
Cover page<br />
B 139<br />
Berkeley, Edmund Callis (1909–1988)<br />
Giant brains or machines that think.<br />
Year: 1949<br />
Place: New York<br />
Publisher: John Wiley<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards; with dust jacket<br />
Pagination: pp. xvi, 270<br />
Size: 212x138 mm<br />
Reference: Ran ODC, p. 407<br />
B 138<br />
This volume was one <strong>of</strong> the first to popularize computers<br />
and was a major reason for the association <strong>of</strong> brain with<br />
computer. It covers all the major machines <strong>of</strong> those years<br />
(differential analyzers, punched card machines, Aiken’s<br />
machines, Bell Labs machines, ENIAC, etc.) and<br />
speculates on what the future would bring. The book was<br />
overly optimistic as to exactly what computers would<br />
shortly be able to accomplish, but Berkeley insisted all<br />
his life that he was correct and that it just would take<br />
a little longer. He published fourteen other books and<br />
continued to publish his Computers and Automation<br />
(later renamed Computers and People) until his death.<br />
In later life Berkeley became more interested in people<br />
and anti-nuclear causes. Portents <strong>of</strong> this shift in interests<br />
can be seen from the fact that the last <strong>chapter</strong>s <strong>of</strong> this<br />
book are devoted to social issues. In 1972, ACM honored<br />
Berkeley as its founder at its 25th Anniversary Dinner.<br />
His acceptance speech was a direct denunciation <strong>of</strong> those<br />
in computing who worked on the killing devices used in<br />
the Vietnam war, <strong>of</strong> computing companies that built such<br />
horrors, and <strong>of</strong> ACM for ignoring this immorality. He<br />
said that it was a gross neglect <strong>of</strong> responsibility that ACM<br />
was not investigating whether computer applications<br />
were good or evil and how computers could be used to<br />
increase the good <strong>of</strong> society. Several prominent ACM<br />
members, employees <strong>of</strong> the firms and government<br />
agencies that Berkeley had identified, ostentatiously<br />
walked out <strong>of</strong> the banquet room while he was speaking.<br />
133
The leaders <strong>of</strong> ACM were embarrassed by their honoree,<br />
and the ACM never publicly referred to the incident in<br />
any way.<br />
This copy is inscribed by the author to Erwin Tomash. A<br />
second copy <strong>of</strong> this work is available in the collection.<br />
134<br />
Illustrations available:<br />
Title page<br />
Inscription<br />
Erwin Tomash Library<br />
Bernard, Edward Bernard, Edward<br />
B 140<br />
Bernard, Edward (1638–1696)<br />
B 139<br />
Inscription, B 139<br />
De mensuris et ponderibus antiquis libri tres. Editio<br />
altera, purior et duplo locupletior.<br />
Year: 1688<br />
Place: Oxford<br />
Publisher: Sheldonian Theatre<br />
Edition: 1st<br />
Language: Latin<br />
Figures: 3 folding plates<br />
Binding: 18th-century olive morocco; gilt spine and edges<br />
B 140<br />
Numerals, B 140
Erwin Tomash Library<br />
Bernard, Edward Bernegger, Matthias<br />
Pagination: pp. [16], 261, [83]<br />
Collation: § 4 §§ 4 A–Z 4 2A–2U 4<br />
Size: 180x110 mm<br />
Bernard was a Fellow <strong>of</strong> St. John’s College Oxford,<br />
where he had earlier been a scholarship student and an<br />
expert in weights and measures. He is known to have<br />
created star tables that were published in Hooke’s<br />
Philosophical Collections in 1684 and was well enough<br />
thought <strong>of</strong> to be appointed as Christopher Wren’s<br />
successor to the Savilian chair <strong>of</strong> astronomy in 1673. He<br />
was a keen collector <strong>of</strong> ancient manuscripts and spoke<br />
many oriental languages.<br />
This work is an enlarged and amended version <strong>of</strong> a letter<br />
prefixed to Dr. Pocock’s Commentary on Hosea, 1685.<br />
It discusses the numerical systems <strong>of</strong> several different<br />
civilizations, both ancient and <strong>of</strong> his own day, and it<br />
incorporates material from European, Far Eastern,<br />
Middle Eastern and African sources. The typesetting<br />
must have been problematic because <strong>of</strong> the numerous<br />
instances <strong>of</strong> Hebrew, Arabic, Greek and other alphabets.<br />
Illustrations available:<br />
Title page<br />
System <strong>of</strong> numerals<br />
Chinese table<br />
B 141<br />
B 141<br />
Bernecker, C. (1760–a.1778)<br />
The Birmingham ready calculator; shewing in twenty<br />
tables, the sums necessary, from one shilling to fifty<br />
pounds, to produce real pr<strong>of</strong>its, from 2½ to 50 per cent.<br />
on prime cost; after allowing discounts from 2½ to 50<br />
per cent. on the selling prices.<br />
Year: 1778<br />
Place: Birmingham<br />
Publisher: Printed by Pearson and Rollason; and sold by R.<br />
Baldwin<br />
Edition: 1st<br />
Language: English<br />
Binding: contemporary marbled boards; rebacked<br />
Pagination: pp. iv, 140<br />
Collation: A 2 B–S 4 T 2<br />
Size: 209x125 mm<br />
This is a ready reckoner for financial affairs. Little seems<br />
to be known about the author.<br />
Illustrations available:<br />
Title page<br />
Page from the tables<br />
B 142<br />
Bernegger, Matthias (1582–1640)<br />
Manuale Mathematicum, darinn begriffen. Die<br />
Tabulae Sinuum, Tangentium, Secantium: sowol<br />
die Quadrat- und Cubictafel; sambt gründlichem<br />
unterricht wie solche nützlich zugebrauchen. Allen Baw<br />
un[d] Kriegsverständigen, Feldmessern und andern<br />
Kunstliebenden hiebevor in Teutsche Sprach an tag<br />
geben, An jetzo aber wider ubersehe[n], und auffs New<br />
in truck gegeben …<br />
Year: 1619<br />
Place: Strasbourg<br />
Publisher: Anton Bertram for Paul Ledertz<br />
Edition: 1st (German)<br />
Language: German<br />
Binding: contemporary vellum; title cropped at bottom with<br />
no loss<br />
Pagination: pp. [8], 64, [184], [94], [26]<br />
Collation: )( 4 A–D 8 A–L 8 M 4 N–T 8 V 4<br />
Size: 156x94 mm<br />
Reference: Pogg Vol. I, p. 155<br />
Matthias Bernegger was a pr<strong>of</strong>essor <strong>of</strong> mathematics<br />
and rhetoric at the <strong>University</strong> <strong>of</strong> Strasbourg. He is<br />
best known for his unauthorized 1612 translation <strong>of</strong><br />
Galileo’s work on the sector (see entry for Galilei,<br />
Galileo [Bernegger, Matthias, translator]; Tractatus de<br />
proportionum instrumento, quod merito compendium<br />
universæ geometriæ dixeris, 1635), to which he added a<br />
set <strong>of</strong> notes that almost doubled the size <strong>of</strong> the text. The<br />
notes are a description <strong>of</strong> the construction <strong>of</strong> the sector,<br />
135
(the lines inscribed, not the physical construction <strong>of</strong> the<br />
mechanism) and many added examples <strong>of</strong> its use.<br />
This present volume is a set <strong>of</strong> trigonometric tables<br />
designed for use in surveying and other similar tasks.<br />
It begins with a description <strong>of</strong> elementary geometry<br />
and trigonometry, followed by a quadrant with the<br />
calculations for finding heights <strong>of</strong> towers. The majority<br />
<strong>of</strong> the work is taken up by a table <strong>of</strong> sines, tangents and<br />
secants, all done to a radius (see the sector essay) <strong>of</strong><br />
10,000,000. The last two sections <strong>of</strong> the work contain<br />
tables for squares and cubes <strong>of</strong> numbers.<br />
136<br />
Illustrations available:<br />
Title page<br />
Title page <strong>of</strong> trigonometric table<br />
Title page <strong>of</strong> squares table<br />
Title page <strong>of</strong> cubes table<br />
Sample page from trigonometric table<br />
Erwin Tomash Library<br />
Bernegger, Matthias Bernoulli, Jacob<br />
B 142<br />
B 143<br />
Bernoulli, Jacob (1654–1705)<br />
Ars conjectandi, opus posthumum, Accedit tractatus de<br />
seriebus infinitis, et epistola Gallicè scripta de Ludo<br />
Pilæ Reticularis.<br />
Year: 1713<br />
Place: Basel<br />
Publisher: Thurneisen Brothers<br />
Edition: 1st<br />
Language: Latin<br />
Figures: 2 engraved folding charts (p. 24 & p. 172), 1 engraved<br />
folding plate (p. 306)<br />
Binding: original semi-stiff boards; uncut<br />
Pagination: pp. [4], 306, [2], 36<br />
Collation: π 2 A–2P 4 2Q 2 a–d 4 e 2<br />
Size: 212x174 mm<br />
Reference: Horb 100, #12<br />
Jacob Bernoulli was the first <strong>of</strong> what became a large<br />
and important family <strong>of</strong> mathematicians. The eldest<br />
<strong>of</strong> three brothers, Jacob originally studied philosophy<br />
and theology then, against his father’s advice, also<br />
took up mathematics and astronomy. His youngest<br />
brother, Johann (from whom the majority <strong>of</strong> the family<br />
mathematicians are descended), was also advised against<br />
the sciences, but under Jacob’s tutelage, he too became<br />
a mathematician. Despite their early collaboration,<br />
continued work on similar problems led to bitterness<br />
and a lifelong rivalry. Jacob traveled extensively and<br />
met with scientists in France, Germany, Britain and the<br />
Netherlands. He occupied the prestigious position <strong>of</strong><br />
pr<strong>of</strong>essor <strong>of</strong> mathematics at Basel.<br />
Bernegger, Matthias (1582–1640)<br />
See entries for [Galilei, Galileo] - Matthias<br />
Bernegger, De proportionum instrumento, 1612<br />
and Tractatus de proportionum instrumento, 1635. B 143
Erwin Tomash Library<br />
Bernoulli, John III Beutel, Tobias<br />
While making contributions in many areas <strong>of</strong> mathematics<br />
and mechanics, this volume contains Jacob’s most<br />
famous work. It is considered as the foundation <strong>of</strong> the<br />
mathematical theory <strong>of</strong> probability and, indeed, has<br />
been termed the foundation <strong>of</strong> the field <strong>of</strong> mathematical<br />
statistics. The editing <strong>of</strong> the manuscript was incomplete<br />
when Jacob died and his nephew Nicolas (the son <strong>of</strong><br />
Jacob’s brother <strong>of</strong> the same name) saw it through the<br />
press. This work, whose title means casting, as in the<br />
casting <strong>of</strong> dice (not counters), is divided into four parts.<br />
The first is a discussion <strong>of</strong> Huygens’ De ratiociniis in<br />
alae ludo, and the second deals with permutations in<br />
which Bernoulli derives a number <strong>of</strong> fundamental notions<br />
about series. The third applies the theory developed in<br />
Part II to twenty-four examples <strong>of</strong> games <strong>of</strong> chance for<br />
which Bernoulli calculates the odds. The final section<br />
is more philosophical in nature and makes reference to<br />
moral as opposed to mathematical expectation and the<br />
law <strong>of</strong> large numbers (the fundamental underpinning <strong>of</strong><br />
most simulations). This last section also contains some<br />
comments on jeu de paume—a game similar to modern<br />
tennis having little to do with the major topic <strong>of</strong> the<br />
work. This is Jacob’s thinly disguised satirical response<br />
to some caustic criticisms made earlier <strong>of</strong> his views on<br />
scholarly logic.<br />
Illustrations available:<br />
Title page<br />
B 144<br />
Bernoulli, John III (1744–1807)<br />
A sexcentenary table; exhibiting at sight, the result <strong>of</strong><br />
any proportion, where the terms do not exceed 600<br />
seconds or 10 minutes with precepts and examples.<br />
b/w: Taylor, Michael S.; A sexagesimal table …, 1780<br />
Year: 1779<br />
Place: London<br />
Publisher: William Richardson<br />
Edition: 1st<br />
Language: English<br />
Binding: contemporary half-bound leather, marbled boards;<br />
rebacked; red leather label<br />
Pagination: pp. viii, 165, [1]<br />
Collation: a–b 2 A–2S 2 T 1<br />
Size: 284x229 mm<br />
See the entry for Taylor, Michael S.A.; A sexagesimal<br />
table…,1780.<br />
John (Johann) Bernoulli, a member <strong>of</strong> the famous Swiss<br />
mathematical family—the grandson <strong>of</strong> Johann and<br />
grandnephew <strong>of</strong> Jacob Bernoulli, was a child prodigy,<br />
obtaining a master <strong>of</strong> jurisprudence degree at age<br />
fourteen. By the age <strong>of</strong> twenty, he was asked by Frederick<br />
II to reorganize the observatory in Berlin. While his<br />
mathematical works are not <strong>of</strong> great importance today,<br />
he wrote many papers on diverse subjects and eventually<br />
became the trustee <strong>of</strong> the family documents.<br />
Illustrations available:<br />
Title page<br />
B 145<br />
Beutel, Tobias<br />
B 144<br />
Neu auffgelegte Arithmetica, Oder sehr nützliche<br />
und schöne Rechen-Kunst mit kurtzen Regulen und<br />
Exemplis, Nach der Practica, welche ausführlich<br />
hierinnen beschriben ist, nebenst der Coss oder<br />
Algebra.<br />
Year: 1670<br />
Place: Leipzig<br />
Publisher: Printed by Johann Wittigau for Philip Fuhrman<br />
Edition: 4th<br />
Language: German<br />
Figures: engraved frontispiece; title in red and black<br />
Binding: Contemporary vellum; with ties<br />
Pagination: pp. [24], 502, [2] (interleaved from p. 1 to p. 475)<br />
Collation: ):( 12 A–X 12<br />
Size: 127x75 mm<br />
Reference: Pogg Vol. I, p. 181<br />
This copy is interleaved with contemporary inscriptions<br />
in finely penned handwriting in brown ink.<br />
This arithmetic book begins with numeration (including<br />
an example <strong>of</strong> Roman numerals using some <strong>of</strong> the<br />
alternate forms for “M”) and continues with the four<br />
basic operations and rule <strong>of</strong> three, multiplication being<br />
illustrated with an unusual triangular table. The same<br />
material is repeated in the next section, this time dealing<br />
137
with fractions rather than integers. The latter sections<br />
contain a discussion <strong>of</strong> elementary algebra, and the final<br />
quarter <strong>of</strong> the book is devoted to tables dealing with<br />
money and similar practical matters.<br />
138<br />
Illustrations available:<br />
Title page (color)<br />
Frontispiece<br />
Roman numerals<br />
Multiplication table<br />
Handwritten gelosia multiplication<br />
Erwin Tomash Library<br />
Beutel, Tobias Bevan, Benjamin<br />
B 145<br />
Frontispiece, B 145<br />
B 146<br />
Bevan, Benjamin (fl.1804–1838)<br />
A practical treatise on the sliding rule. In two parts.<br />
Part the first being an introduction to the use <strong>of</strong> the rule<br />
generally as adapted for calculations that usually occur<br />
to persons in trade. Part the second containing formulæ<br />
for the use <strong>of</strong> surveyors, architects, civil engineers, and<br />
scientific gentlemen.<br />
Year: 1822<br />
Place: London<br />
Publisher: Author<br />
Edition: 1st<br />
Language: English<br />
Binding: original paper boards<br />
Pagination: pp. 101, [7]<br />
Collation: A–F 4 G 2 H–O 4<br />
Size: 227x138 mm<br />
Reference: Tay MP II, #1084<br />
Roman numeral forms, B 145<br />
Multiplication table, B 145<br />
Benjamin Bevan was an engineer and architect/surveyor<br />
who lived in Bushey Heath, England. Little is known<br />
about him, but he notes in the preface that he had spent<br />
eighteen years in very extensive public undertakings and<br />
had taught the use <strong>of</strong> the slide rule to a number <strong>of</strong> young<br />
persons. He developed his new slide rule, with divisions<br />
to three places <strong>of</strong> decimal, some time about 1813. He<br />
was obviously well connected because he was able to use<br />
Jesse Ramsden’s dividing machine for the markings. The<br />
rule was manufactured, beginning about the time <strong>of</strong> this<br />
publication, by William O. Carey (1789–1891), whose<br />
shop was on the Strand in London. Carey advertised the<br />
rule as being for accountants and surveyors.
Erwin Tomash Library<br />
Beveridge, William Beyer, Johann Hartmann<br />
After a brief introduction to the slide rule, the majority <strong>of</strong><br />
the work is taken up with examples from many different<br />
trades. Each example is shown with a clear diagram that<br />
illustrates how the slide rule should be set to accomplish<br />
the task (see illustration <strong>of</strong> simple interest calculations).<br />
Illustrations available:<br />
Title page<br />
Interest calculation<br />
B 147<br />
Beveridge, William (1637–1708)<br />
Institutionum chronologicarum libri II. Unà cum<br />
totidem arithmetices chronologicæ libellis.<br />
Year: 1669<br />
Place: London<br />
Publisher: Thomas Roycraft for Walter Kettilby<br />
Edition: 1st<br />
Language: Latin<br />
Binding: contemporary leather<br />
Pagination: pp. [8], 259, [5]<br />
Collation: A–2L 4<br />
Size: 185x142 mm<br />
Reference: Win ESTC, B.2095<br />
B 146<br />
William Beveridge was a scholar at St. John’s College<br />
Cambridge and an expert on oriental languages. He<br />
was ordained in 1660 and took up the post <strong>of</strong> Vicar <strong>of</strong><br />
Ehling, which position left him enough time to follow<br />
his scholarly interests. He stayed there twelve years, and<br />
it was during that period this book was written. In 1704,<br />
he was made Bishop <strong>of</strong> St. Asaph.<br />
This work, on ancient number systems and the calendar,<br />
is described by DeMorgan, Arithmetical books as<br />
learned, but not always judicious. It is <strong>of</strong> interest from<br />
both a typographical and historical standpoint for the<br />
many different fonts <strong>of</strong> exotic character sets used to print<br />
out the tables, ranging from Hebrew and Greek to various<br />
Middle Eastern languages, including Arabic, Samaritan<br />
and Syriac. The complexity <strong>of</strong> the problem facing the<br />
printer may be seen from the table illustrated.<br />
Illustrations available:<br />
Title page<br />
Numerical systems table (3)<br />
B 148<br />
Beyer, Johann Hartmann (1563–1625)<br />
B 147<br />
Ein newe und schöne Art der Vollkommenen Visier<br />
- Kunst: Derengleichen hiebevor niemaln in keiner<br />
Spraach gesehen worden. Wie man nemlich vierlerlen<br />
unterschiedne Visierstäbe zurichten auch mit den<br />
selbigen allerhand regulierte hole Cörper. Sie seyen<br />
so gross oder kleyn sie immer mögen als mancherley<br />
Särcke Röhrcästen Brunnen, Fass, Bütten, Eymer,<br />
Gläser, Kugeln, & visieren und deren inhallt gantz<br />
leichtich erfündigen soll.<br />
Year: 1603<br />
Place: Frankfurt<br />
Publisher: Palthenium for J. Rosen<br />
139
140<br />
Edition: 1st (German)<br />
Language: German<br />
Binding: later vellum over boards<br />
Pagination: pp. [12], 68, 192, [38]<br />
Collation: )( 4 )()( 2 2A–2H 4 2I 2 A–2A 4 2A–2D 4 2E 3<br />
Size: 196x155 mm<br />
Reference: Pogg Vol. I, p. 183<br />
Johann Beyer was not only a well-known Frankfurt<br />
physician and mathematician but was also a person <strong>of</strong><br />
civic eminence due to his position as Bürgermeister. His<br />
wide contact with the scientific community is illustrated<br />
by a letter he is known to have written to Kepler in 1616<br />
in which he used a combination <strong>of</strong> both the decimal<br />
point (actually a comma) and the old system <strong>of</strong> accents<br />
to represent decimal fractions. For example, Beyer wrote<br />
the number 314.15926 (100π) as 314,1’5’’9’’’2’’’’6’’’’’<br />
(using a comma as the decimal indicator but still using<br />
the accents as well) and claimed this system <strong>of</strong> notation<br />
as his invention. This may well have been true as far as<br />
Beyer was concerned; however, Simon Stevin had used<br />
the decimal point notation years earlier. The same system<br />
<strong>of</strong> notation, this time with multiple and inconsistent uses<br />
<strong>of</strong> the decimal point and Roman numerals for the accents,<br />
can be seen in this work.<br />
Erwin Tomash Library<br />
Beyer, Johann Hartmann Beyer, Johann Hartmann<br />
B 148<br />
Accents denoting decimal places, B 148<br />
This book is an early basic work on gauging, with<br />
emphasis on the calculation <strong>of</strong> the volume contained in<br />
various solid geometric figures. Beyer also discusses<br />
the extraction <strong>of</strong> cube roots, gives practical examples<br />
<strong>of</strong> gauging and includes tables for such things as the<br />
circumference and area <strong>of</strong> circles having diameters from<br />
0.1 to 108 units in steps <strong>of</strong> 0.1 unit. Unfortunately, the<br />
value <strong>of</strong> π Beyer used appears to be 3.14172 rather than<br />
3.14159, and this value limits their usefulness (accurate<br />
values for π had been calculated to 35 decimal places<br />
prior to the date <strong>of</strong> this publication).<br />
Illustrations available:<br />
Title page<br />
Decimal point example<br />
Table page<br />
B 149<br />
Beyer, Johann Hartmann (1563–1625)<br />
B 149<br />
Stereometriae inanium nova et facilis ratio, geometricis<br />
demonstrationibus confirmata & necessariis<br />
obscuriorum quorundam delineationibus illustrata:<br />
Qua corporum regularium omnium, tam rectilineorum<br />
quam curvilineorum capacitates promtissime<br />
explorantur.<br />
Year: 1603<br />
Place: Frankfurt<br />
Publisher: Zacharias Palthenius for Jonas Rhodius<br />
Edition: 1st (Latin)<br />
Language: Latin<br />
Figures: 67 woodcut text diagrams, numerous charts<br />
Binding: contemporary vellum over boards
Erwin Tomash Library<br />
Bianchini, Giovanni Bianchini, Giovanni<br />
Pagination: pp. [12], 268, [38]<br />
Collation: )( 4 2)( 2 A–2K 4 L 2 2A–2D 4 2E 3<br />
Size: 191x151 mm<br />
Reference: Pogg Vol. I, p. 183<br />
This is a Latin version <strong>of</strong> the work described above.<br />
While the works are similar, containing the same woodcut<br />
diagrams and tables, the examples <strong>of</strong> calculations <strong>of</strong>ten<br />
differ, and the accuracy <strong>of</strong> the tables suffers from the<br />
same problem as in the German version. See comments<br />
in Beyer, Johann Hartmann; Ein newe und schone Art<br />
der Vollkommenen Visier-Kunst, 1603.<br />
Illustrations available:<br />
Title page<br />
B 150<br />
Bianchini, Giovanni (ca.1410–1469)<br />
Tabulae celestium motuum eorumque canones.<br />
Year: 1460–1470<br />
Place: Italy<br />
Edition: manuscript<br />
Language: Latin<br />
Figures: Manuscript tables in red and black<br />
Binding: contemporary vellum over boards<br />
Pagination: ff. [b], [1], [2b], [16], 1–122, [2b], [4], [4b], [1],<br />
[2b]<br />
Size: 294x220 mm<br />
According to Thorndike’s History <strong>of</strong> magic and<br />
experimental science, Bianchini was probably the<br />
fifteenth century’s foremost astronomer. He lived and<br />
worked for many years in the service <strong>of</strong> three successive<br />
D’Este Dukes at Ferrara, where he was in contact with<br />
several <strong>of</strong> the greatest astronomers <strong>of</strong> the century. Georg<br />
Peuerbach (1423–61), the teacher <strong>of</strong> Regiomontanus<br />
(1436–76), lectured in Ferrara in 1450, and Rose states<br />
(Italian Renaissance <strong>of</strong> Mathematics, p. 14)<br />
Regiomontanus himself visited Ferrara in the<br />
1460’s, having perhaps been lured there by the<br />
prospect <strong>of</strong> meeting Bianchini with whom he<br />
initiated a scientific correspondence.<br />
At this time Bianchini would have been in his late<br />
forties or early fifties and as the leading figure <strong>of</strong> the last<br />
generation <strong>of</strong> astronomers would have been an impressive<br />
person to the young Peuerbach and his even younger<br />
student and collaborator, Regiomontanus. At an even<br />
earlier date than that cited by Rose, Regiomontanus<br />
and Peuerbach were both calculating ephemerides from<br />
Bianchini’s tables around 1456. Of their contemporaries<br />
(Regiomontanus’ &. Peuerbach’s), only Bianchini …<br />
possessed a comparable pr<strong>of</strong>iciency and originality.<br />
(DSB Vol. 15, pp. 474–475).<br />
B 150<br />
In this manuscript work, Bianchini set out to reconcile<br />
the Alfonsine tables—for two centuries the standard in<br />
Europe by the time he wrote—with those <strong>of</strong> Ptolemy.<br />
He was a great admirer <strong>of</strong> Ptolemy and critical <strong>of</strong> the<br />
corrupted Ptolemaic and Alfonsine texts then in current<br />
use. Thorndike observes that historically<br />
… many have erred by neglecting, because <strong>of</strong><br />
their difficulty, the Alfonsine Tables for longitude<br />
and the Ptolemaic for finding the latitude <strong>of</strong> the<br />
planets. Accordingly in his Tables Bianchini has<br />
combined the conclusions, roots and movements<br />
<strong>of</strong> the planets by longitude <strong>of</strong> the Alfonsine Tables<br />
with the Ptolemaic for latitude, and with the rules<br />
<strong>of</strong> Ptolemy which Alfonso too had employed.<br />
Bianchini’s Tables must have been useful and perhaps<br />
even popular since they went through three printed<br />
editions. The text was first published in 1495 at Venice.<br />
A second edition was printed in 1526, and another<br />
appeared in Basel in 1553.<br />
The manuscript is roughly divided into two parts: the<br />
first <strong>of</strong> fifteen leaves includes an introduction and the<br />
Canones, which explain how the tables were calculated<br />
and how to use them. The second comprises tables and<br />
occupy the balance <strong>of</strong> the work. Manuscript copies <strong>of</strong><br />
the tables alone are recorded in some European libraries,<br />
but here they appear together with the Canones. Of<br />
additional interest is a letter from the Venetian humanist<br />
and Senator Marco Sanuto (ca.1466–1533) starting on<br />
folio 10v and 11r, running onto the lower margin <strong>of</strong><br />
141
the latter, relating to certain astronomical problems,<br />
which suggests possible avenues <strong>of</strong> inquiry relating<br />
to provenance. Sanuto was the dedicatee <strong>of</strong> Pacioli’s<br />
Summa de arithmetica.<br />
There is a purchase inscription on the last leaf dated 1474<br />
that reads I bought these tables in 1474 (see illustration).<br />
Various watermarks—“R” similar to Briquet 897-0-71,<br />
scissors-Briquet 3668, crossed arrows-Briquet 6269, four<br />
flowers similar to Briquet 6689 & 6690—all indicate<br />
Italy mid-fifteenth century.<br />
A fifteenth-century coat <strong>of</strong> arms with a rampant lion<br />
watercolor flanked by the initials B and L on the first<br />
page <strong>of</strong> the introduction is similar to the lion found<br />
in Rietstap’s Armorial General Illustre, vol. 4, for<br />
the Loredano family <strong>of</strong> Venice (see illustration). The<br />
Loredano family provided Venice with several Doges,<br />
beginning with Leonardo Loredano (1438–1521);<br />
however, we have not been able to attach the initials<br />
B.L. to any <strong>of</strong> the descendants. The inner front cover<br />
<strong>of</strong> the binding bears the large bookplate <strong>of</strong> the sixteenth<br />
century collector Ferdinand H<strong>of</strong>fman (1540–1607)<br />
(see illustration). This copy was dispersed along with<br />
other books from H<strong>of</strong>fman’s library in the Gilh<strong>of</strong>er &<br />
Ranschburg sale <strong>of</strong> the Bibliothek Alexander Fürst<br />
Dietrichstein, November, 1933.<br />
According to C. U. Faye and W.H. Bond, Supplement to<br />
the Census <strong>of</strong> Medieval and Renaissance Manuscripts in<br />
the United States and Canada, 1962, only one manuscript<br />
copy <strong>of</strong> the Tabulae was recorded in the United States,<br />
that being the Honeyman copy, which was subsequently<br />
sold when the library was dispersed in 1979.<br />
The above material was adapted from that supplied by<br />
New York City bookseller Richard Lan <strong>of</strong> Martayan<br />
Lan.<br />
The manuscript shows a late transition phase between<br />
the Arabic forms <strong>of</strong> the numerals and the European forms<br />
after they were frozen at the invention <strong>of</strong> printing—note,<br />
in particular, the form <strong>of</strong> the figure “5.”<br />
142<br />
Illustrations available:<br />
Book plate <strong>of</strong> Ferdinand H<strong>of</strong>fman<br />
Purchase inscription <strong>of</strong> 1474<br />
First page <strong>of</strong> introduction with crest (color)<br />
First page <strong>of</strong> tables (color)<br />
Second last page <strong>of</strong> tables (color)<br />
Table <strong>of</strong> days <strong>of</strong> the year (color)<br />
Erwin Tomash Library<br />
Bianchini, Giovanni Biler, Johann Matthes<br />
Purchase inscription 1474, B 150<br />
B 151<br />
Biermann, L.<br />
Die Gottinger entwicklungen elektronischer<br />
Rechenautomaten In Probleme der Entwicklung<br />
programmgesteuerter Rechengerate und<br />
Integrieranlagen.<br />
b/w: Cremer, Hubert (editor); Probleme der<br />
Entwicklung programmgesteuerter Rechengerate<br />
und Integrieranlagen, 1953<br />
Year: 1953<br />
Place: Aachen<br />
Publisher: Rhein-Westf. Technische Hochschule<br />
Edition: 1st<br />
Language: German<br />
Binding: cloth boards original paper wrappers bound in<br />
Pagination: pp. [2], XIV, 75, [1], 10<br />
Size: 207x145 mm<br />
See entry for Cremer; Probleme der Entwicklung<br />
programmgesteuerter Rechengerate, 1953, where more<br />
information and illustrations may be found.<br />
Illustrations available:<br />
None<br />
B 152<br />
Biler, Johann Matthes<br />
H<strong>of</strong>fman bookplate, B 150<br />
(Gebrauch) Zweyer Neuen Mathematischen<br />
Instrumenten. Dass Erste von Herrn Ozanam, Math:<br />
Pr<strong>of</strong>s. zu Paris 1688. Und das Andere von Hn. Joh:<br />
Matth. Bilern J.V.D. und Käyszl. Post-Meistern in
Erwin Tomash Library<br />
Biler, Johann Matthes Biler, Johann Matthes<br />
Jena erfunden. Mit welchen Ersten, man geschwinde<br />
und accurat alle Auffgaben, so zur Feldmes-Kunst<br />
gehören, ohn einiges Ausrechnen, gar leichtlich<br />
auf lösen kan. Und vermittelst des Zweyten, alle<br />
Proportiones in der Mathesi ohne Circul, Lineal und<br />
ohne Rechnung, bloss mit einen Seidenen schwartzen<br />
Faden oder Haar, so wohl in Arithmetica, Geometria,<br />
Altimetria, Trigonometria, als Stereometria,<br />
Fortificatio, Astronomia und Astrologia mit ungemeiner<br />
Geschwindigkeit und sonderbahren Vergnügen des<br />
Liebhabers können gefunden werden. Sonderlich aber<br />
denen Ingenieuren und welche auf Academien diese<br />
Disciplinen, lernen wollen, zu mercklichen Vortheil und<br />
besten, verfertiget und ans Tages Licht gebracht.<br />
Year: 1705<br />
Place: Jena<br />
Publisher: Henrich Christoph Cröker<br />
Edition: 2nd<br />
Language: German<br />
Figures: 5 engraved folding plates<br />
Binding: later boards<br />
Pagination: pp. 87, [1]<br />
Collation: A–E 8 F 4<br />
Size: 198x152 mm<br />
B 152<br />
In 1691, Jacques Ozanam published his Dictionaire<br />
mathématique, which contained a section on practical<br />
geometry (surveying). The first part <strong>of</strong> this work is<br />
actually Ozanam’s surveying section. The instrument<br />
(a plane table) described here was given a full-page<br />
illustration by Ozanam. The original Ozanam illustration<br />
was augmented by adding a pole stand, but it is otherwise<br />
identical. The text is a short description <strong>of</strong> its use in<br />
elementary surveying.<br />
Bound at the end <strong>of</strong> this short Ozanam work is the one by<br />
Biler that illustrates the use <strong>of</strong> a half-circular instrument.<br />
This is identical with one that he published in 1696 (Biler,<br />
Neu erfundenes instrumentum, 1696). Leaving out some<br />
examples has shortened the text, and the illustrations are,<br />
for the most part, pasted in where they were included<br />
with the text in the earlier version. A large foldout plate,<br />
identical to that from the 1696 version except for an<br />
inscription, illustrates the instrument.<br />
Illustrations available:<br />
Title page<br />
Instrument<br />
Surveying example.<br />
B 153<br />
Biler, Johann Matthes<br />
Plane table, B 152<br />
Surveying example, B 152<br />
Neu erfundenes instrumentum mathematicum universale<br />
vermittelst dessen alle proportiones in der Mathesi<br />
ohne Circul, Lineal und ohne Rechnung, bloss mit<br />
einen Seidenen schwartzen Faden oder Haar so wohl in<br />
Arithmetica, Geometria, Altimetria, Trigonometria, alss<br />
Stereometria, Fortificatio, Astronomia und Astrologia<br />
mit ungemeiner Geschwindigkeit und sonderbahren<br />
Vergnügen des Leibhabers können gesuchet und<br />
gefunden werden. Allen und jeden so hohen alss<br />
143
niedrigen Stands-Personen so denen Mathematischen<br />
Wissenschafften beygethan, und der Rechen Kunst nicht<br />
wohlerfahren. Sonderlich aber denen Ingenieuren und<br />
welche auf Academien diese Disciplinen, lernen wollen,<br />
zu mercklichen Vortheil und besten, verfertiget und ans<br />
Tages Licht gebracht.<br />
144<br />
Year: 1696<br />
Place: Jena<br />
Publisher: Henrich Christoph Cröker<br />
Edition: 1st<br />
Language: German<br />
Figures: 1 folding plate<br />
Binding: modern heavy paper wrappers<br />
Pagination: ff. [18]<br />
Collation: π 4 B–D 4 E 2<br />
Size: 198x152 mm<br />
See entry for Biler, (Gebrauch) Zwyer Neuen<br />
Mathematischen Instrumenten, 1705.<br />
This is a short work on elementary surveying techniques.<br />
It describes a half-circular sighting instrument and<br />
illustrates its use with a few simple problems involving<br />
triangles.<br />
Illustrations available:<br />
Title page<br />
Instrument<br />
Erwin Tomash Library<br />
Biler, Johann Matthes Binet, Alfred<br />
B 153<br />
Biler’s instrument, B 153<br />
BINAC<br />
See Eckert-Mauchly Computer Corporation; Binac<br />
demonstrated. New electronic brain<br />
B 154<br />
Binet, Alfred (1857–1911)<br />
Psychologie des grands calculateurs et joueurs<br />
d’échecs.<br />
Year: 1894<br />
Place: Paris<br />
Publisher: Librairie Hachette et Cie.<br />
Edition: 1st<br />
Language: French<br />
Binding: original printed paper wrappers; uncut<br />
Pagination: pp. viii, 364, 8<br />
Collation: π 4 1–22 8 23 6 c 4<br />
Size: 187x122 mm<br />
Binet was the famous French psychologist after whom<br />
the Binet scale <strong>of</strong> the mental age <strong>of</strong> a child is named.<br />
He was director <strong>of</strong> the Laboratory <strong>of</strong> Physiological<br />
Psychology in Paris. In the mid 1880s, he began a long<br />
series <strong>of</strong> studies into intelligence and thought processes<br />
that culminated in his 1903 publication <strong>of</strong> Étude<br />
experimentale de l’intelligence, in which he reported on<br />
an in-depth study <strong>of</strong> the intellectual development <strong>of</strong> his<br />
two daughters.<br />
This volume was part <strong>of</strong> his studies in mental processes.<br />
It examines the calculating prodigies, particularly one<br />
called Jacques Inaudi, an Italian shepherd boy who<br />
progressed to giving stage performances, and several<br />
champion chess players.<br />
Illustrations available:<br />
Title page<br />
B 154
B 155<br />
Bion, Nicholas (ca.1652–1733)<br />
Traité de la construction et des principaux usages des<br />
instrumens de mathématique.<br />
Year: 1709<br />
Place: Paris<br />
Publisher: Chez La Veuve de Jean Boudot<br />
Edition: 1st<br />
Language: French<br />
Figures: 28 engraved plates (1 folding)<br />
Binding: contemporary leather rebacked<br />
Pagination: pp. [8], 352<br />
Collation: a 4 A–Y 8<br />
Size: 208x137 mm<br />
Reference: Soth/Zeit BCM, Vol III, #875–#508, p. 39<br />
Nicholas Bion was the king’s engineer for mathematical<br />
instruments. It is surprising how little is known about<br />
his life beyond the fact his workshops were in Paris. His<br />
name is very well known, but it is difficult to determine if<br />
his fame rests on the quality <strong>of</strong> his instruments or on this<br />
respected work. Only a few <strong>of</strong> his original instruments<br />
appear to have survived.<br />
Erwin Tomash Library<br />
Bion, Nicholas Bion, Nicholas<br />
Sector measurements, B 155<br />
B 155<br />
Bion’s sector, B 155<br />
The work is encyclopedic and gives descriptions <strong>of</strong> the<br />
mathematical instruments commonly available at the<br />
beginning <strong>of</strong> the eighteenth century. Bion interpreted<br />
mathematical broadly, for the work contains information<br />
on devices used in a variety <strong>of</strong> scientific and engineering<br />
fields. It is composed <strong>of</strong> a preface giving definitions <strong>of</strong><br />
mathematical terms, followed by eight separate books:<br />
1. rulers and protractors<br />
2. the sector: containing a line <strong>of</strong> equal parts (“B” in<br />
his figure 1), line <strong>of</strong> planes (“C”), line <strong>of</strong> polygons<br />
(“D”), line <strong>of</strong> chords (“F”), line <strong>of</strong> solids (“H”)<br />
and line <strong>of</strong> metals (“G”).<br />
3. the compass (including both proportional compass<br />
and beam compass)<br />
4. surveying devices (quadrants, chords, chains and<br />
sighting devices)<br />
5. water levels and gunner’s instruments (gunner’s<br />
compass and quadrant)<br />
6. astronomical instruments (large quadrants and<br />
micrometers for measuring)<br />
7. navigational instruments, including, for example,<br />
the Jacob’s staff and the mariner’s quadrant, which<br />
were, by then, no longer in use<br />
8. sundials <strong>of</strong> all forms at all orientations, the<br />
nocturnal and a water clock<br />
Folding sundial, B 155<br />
145
The volume was intended for the instrument user<br />
rather than the instrument maker. The descriptions <strong>of</strong><br />
several devices (optical and micrometer instruments in<br />
particular) are lacking in detail that might indicate that<br />
Bion was not familiar with them or, perhaps more likely,<br />
that he did not wish his rivals to be able to reproduce his<br />
instruments.<br />
146<br />
Illustrations available:<br />
Title page<br />
The sector<br />
Usage <strong>of</strong> the line <strong>of</strong> lines in the sector<br />
Gauging rods<br />
Usage <strong>of</strong> the line <strong>of</strong> chords in the sector<br />
The artillery instruments<br />
A device showing sundials on various surfaces<br />
Colophon<br />
Erwin Tomash Library<br />
Bion, Nicholas Bion, Nicholas<br />
Artillery instruments, B 155<br />
Gauging rods, B 155<br />
Colophon, B 155<br />
B 156<br />
Bion, Nicholas (ca.1652–1733)<br />
Traité de la construction et des principaux usages des<br />
instrumens de mathematique.<br />
Year: 1716<br />
Place: Paris<br />
Publisher: La Veuve Boudot; et al.<br />
Edition: 2nd<br />
Language: French<br />
Figures: 30 engraved plates (1 folding)<br />
Binding: contemporary calf<br />
Pagination: pp. viii, 392<br />
Collation: a 4 A–2A 8 2B 4<br />
Size: 197x133 mm<br />
Reference: Soth/Zeit BCM, Vol. III, #875–#509, p. 39<br />
This second edition is not quite identical to the first <strong>of</strong><br />
1709. Bion added an extra <strong>chapter</strong> (the eighth) to Book<br />
Four on the subject <strong>of</strong> fortifications and another (the fifth)<br />
to Book Six on the construction <strong>of</strong> a pendulum clock for<br />
astronomical observations (see the entry for the third,<br />
1723, edition for illustrations from these sections).<br />
Illustrations available:<br />
Title page<br />
Colophon<br />
B 157<br />
Bion, Nicholas (ca.1652–1733)<br />
B 156<br />
Traité de la construction et des principaux usages des<br />
instrumens de mathématique.<br />
Year: 1723<br />
Place: The Hague<br />
Publisher: P. Husson, T. Johnson, P. Gosse et al.<br />
Edition: 3rd<br />
Language: French<br />
Figures: 30 folding engraved plates; engraved frontispiece; title<br />
in red and black
Erwin Tomash Library<br />
Bion, Nicholas Bion, Nicholas<br />
Binding: contemporary mottled calf<br />
Pagination: pp. [8], 392<br />
Collation: π 4 A–3C 4<br />
Size: 240x185 mm<br />
Reference: Bru MLAL I, p. 950; Pogg Vol. I, pp. 194–95; Dau<br />
HTI, 389; DSB II, pp. 132–133<br />
The text <strong>of</strong> this, the third edition, is identical to the second<br />
(1716), containing the same additional sections that Bion<br />
had included there. It has a new frontispiece illustrating<br />
the use <strong>of</strong> some <strong>of</strong> the simpler instruments.<br />
Illustrations available:<br />
Title page<br />
Frontispiece<br />
Artillery instruments<br />
Pendulum clock<br />
Fortifications<br />
B 158<br />
Bion, Nicholas (ca.1652–1733)<br />
B 157<br />
Traité de la construction et des principaux usages des<br />
instrumens de mathematique.<br />
Year: 1752<br />
Place: Paris<br />
Publisher: C.A. Jombert & Nion fils.<br />
Edition: 4th<br />
Language: French<br />
Figures: engraved frontispiece; engraved portrait; 37 engraved<br />
folding plates<br />
Binding: contemporary leather; gilt spine<br />
Pagination: pp. [8], 460<br />
Collation: π 4 A–3L 4 3M 2<br />
Size: 250x192 mm<br />
Frontispiece, B 157<br />
Fortifications, B 157<br />
This fourth edition was published after Bion’s death in<br />
1733, the printing being supervised by his son. It uses the<br />
same frontispiece as the second edition (1716) but also<br />
includes an idealized engraved portrait <strong>of</strong> Bion—done<br />
posthumously (c. 1740) by De Larmessin, the King’s<br />
engraver. The content <strong>of</strong> the second edition has been<br />
further augmented with an additional <strong>chapter</strong> to Book<br />
6 on octants and other astronomical instruments; two<br />
very small additions to Book 7 (dignified by being given<br />
their own <strong>chapter</strong>); and a completely new Book 9, which<br />
describes a miscellaneous collection <strong>of</strong> devices from<br />
water pumps to burning glasses.<br />
147
148<br />
Illustrations available:<br />
Title page<br />
Colophon<br />
Portrait<br />
Erwin Tomash Library<br />
Bion, Nicholas Bion, Nicholas<br />
B 158<br />
Nicholas Bion, B 158<br />
Colophon, B 158<br />
B 159<br />
Bion, Nicholas (ca.1652–1733) [Edmund Stone (1700–<br />
1768), translator]<br />
The construction and principal uses <strong>of</strong> mathematical<br />
instruments. Translated from the French <strong>of</strong> M. Bion,<br />
chief instrument-maker to the French King. To<br />
which are added, the construction and uses <strong>of</strong> such<br />
instruments as are omitted by M. Bion; particularly <strong>of</strong><br />
those invented or improved by the English.<br />
Year: 1723<br />
Place: London<br />
Publisher: Printed for H.W. by J.Senex and W. Taylor<br />
Edition: 1st (English)<br />
Language: English<br />
Figures: 26 engraved folding plates; title in red and black<br />
Binding: contemporary paneled leather; red leather label<br />
Pagination: pp. viii, 264<br />
Collation: π 2 A–3X 2<br />
Size: 342x221 mm<br />
Reference: DSB II, p. 133; Hamb DI, p. 37<br />
Edmund Stone, the translator <strong>of</strong> this work, was the son <strong>of</strong><br />
a gardener to the Scottish Duke <strong>of</strong> Argyle. At the age <strong>of</strong><br />
8, another servant taught him to read. Shortly thereafter<br />
he noticed an architect working on the duke’s house,<br />
using instruments and making calculations. Inquiring<br />
about these, he learned <strong>of</strong> the existence <strong>of</strong> arithmetic and<br />
geometry and purchased a book on the subject. When<br />
Stone was 18 and a gardener on the estate, the duke saw a<br />
copy <strong>of</strong> Newton’s Principia in the grass. Assuming it was<br />
from his library, the duke called a servant to return it and<br />
was very surprised when the young gardener intervened,<br />
claiming it was his own. The duke became his patron<br />
(this translation is dedicated to him) and provided him<br />
with employment that allowed time for Stone to study.<br />
Stone became a Fellow <strong>of</strong> the Royal Society in 1725.<br />
The patronage continued until the duke’s death in 1743.<br />
Thereafter, Stone lost his employment and was reduced<br />
to poverty (he had to resign his membership in the Royal<br />
Society because he could not afford to pay the dues) and<br />
eventually died a pauper.<br />
According to the translator’s preface (see the illustrations),<br />
Stone had wanted to produce a work on instruments<br />
and decided that Bion’s provided the best model<br />
available. Rather than writing one himself, he decided<br />
to translate the French work and add to it those English<br />
instruments that Bion had overlooked. An example <strong>of</strong><br />
such an addition—the inclusion <strong>of</strong> the English gunner’s<br />
calipers—can be seen by comparing the plate showing<br />
artillery instruments in the first (1709) edition <strong>of</strong> Bion<br />
with the present volume.<br />
Stone also added, as an example <strong>of</strong> the power <strong>of</strong> the<br />
instruments, a short section on The Use <strong>of</strong> the Sector in
Erwin Tomash Library<br />
Bion, Nicholas Bion, Nicholas<br />
the Construction <strong>of</strong> Solar Eclipses, in which he details<br />
the path, across Europe, <strong>of</strong> the Moon’s shadow for the<br />
eclipse <strong>of</strong> May 11, 1724—the year after the publication<br />
<strong>of</strong> this translation.<br />
This work is translated from the second (1716) edition <strong>of</strong><br />
Bion and includes the additional <strong>chapter</strong>s on fortification<br />
and the pendulum clock from that edition. It appeared at<br />
the same time as Bion’s third French edition.<br />
Illustrations available:<br />
Title page (color)<br />
Plate <strong>of</strong> artillery instruments<br />
Translator’s preface (pages v, vi, vii)<br />
B 159<br />
Artillery instruments, B 159<br />
B 160<br />
Bion, Nicholas (ca.1652–1733) [Edmund Stone (1700–<br />
1768), translator]<br />
The construction and principal uses <strong>of</strong> mathematical<br />
instruments. Translated from the French <strong>of</strong> M. Bion,<br />
chief instrument-maker to the French King. To<br />
which are added, the construction and uses <strong>of</strong> such<br />
instruments as are omitted by M. Bion; particularly <strong>of</strong><br />
those invented or improved by the English…<br />
Year: 1758<br />
Place: London<br />
Publisher: Printed for J. Richardson<br />
Edition: 2nd (English)<br />
Language: English<br />
Figures: 30 engraved plates<br />
Binding: contemporary leather; rebacked<br />
Pagination: pp. viii, 264; [4] 265–326<br />
Collation: π 2 A–4N 2 O 3<br />
Size: 349x225 mm<br />
Reference: DSB II. p. 133; Hambly, DI, p. 37<br />
Stone, as he indicates in the advertisement to the<br />
supplement to this addition, was prevailed upon by<br />
the publishers to produce a second printing <strong>of</strong> the<br />
1723 edition, enlarged by the addition <strong>of</strong> material on a<br />
number <strong>of</strong> new and improved instruments. While this is<br />
undoubtedly true, by this date Stone had lost his patron<br />
and being forced to live on his own resources must have<br />
contributed to his decision to produce the supplementary<br />
material. Hence the allusion to several motives in his<br />
explanation.<br />
The text is identical to the first edition, and the<br />
supplement, while it may have increased sales, contains<br />
little that adds to the work (see Taylor, E. G. R.;<br />
Mathematical practitioners <strong>of</strong> Hanoverian England, pp.<br />
25–30, for a detailed list <strong>of</strong> the contents and other relevant<br />
information). The supplement contains information<br />
on both reflecting and refracting telescopes and on the<br />
camera obscura. Most <strong>of</strong> the improvements noted in the<br />
supplement come from the Philosophical Transactions<br />
<strong>of</strong> the Royal Society, which are referenced frequently.<br />
Illustrations available:<br />
Title page<br />
B 161<br />
Bion, Nicholas (ca.1652–1733) [Johann Gabriel<br />
Doppelmayr (1671–1750), translator]<br />
Neu eröffnete Mathematische Werkschule, oder<br />
Gründliche Anweisung, wie die Mathematische<br />
Instrumenten<br />
Year: 1712<br />
Place: Frankfurt and Leipzig<br />
Publisher: H<strong>of</strong>mannischen Buchladen<br />
149
150<br />
Edition: 1st (German)<br />
Language: German<br />
Figures: engraved frontispiece; title in red and black; 28<br />
engraved folding plates<br />
Binding: contemporary vellum<br />
Pagination: pp. [8], 48, 176<br />
Collation: )( 3 )()( 3 A–3C 4 D 1<br />
Size: 214x158 mm<br />
This German edition <strong>of</strong> Bion’s work is a translation <strong>of</strong><br />
the first (1709) French edition. It does not contain the<br />
sections Bion added to his second French edition (1716).<br />
The frontispiece resembles (but is not identical to) that<br />
Erwin Tomash Library<br />
Bion, Nicholas Bion, Nicholas<br />
B 161<br />
<strong>of</strong> the later 1723 French edition, perhaps because they<br />
were both printed outside <strong>of</strong> France.<br />
Johann Gabriel Doppelmayr, the translator, studied<br />
law at Nuremberg, Altdorf and Halle, but then decided<br />
to switch to physics and mathematics. After traveling<br />
in Germany, Holland, and England, he returned to<br />
Nuremberg and was appointed pr<strong>of</strong>essor <strong>of</strong> mathematics<br />
in 1704, a post he retained for the rest <strong>of</strong> his life. As<br />
early as 1705, he is known to have published a number<br />
<strong>of</strong> other translations as well as his own works on an<br />
eclipse, the globes and an atlas. None <strong>of</strong> his writings<br />
show much originality but were useful in transmitting<br />
scientific findings from England, France and Holland to<br />
Germany.<br />
Illustrations available:<br />
Title page<br />
Frontispiece<br />
B 162<br />
Bion, Nicholas (ca.1652–1733) [Johann Gabriel<br />
Doppelmayr (1671–1750)]<br />
Weitere Eröffnung der neuen Mathematische Werk-<br />
Schule, Nicolai Bion.<br />
Year: 1717<br />
Place: Nuremberg.<br />
Publisher: Peter Conrad Monath<br />
Edition: 1st (German)<br />
Language: German<br />
Figures: title in red and black; 12 engraved folding plates<br />
Binding: contemporary vellum<br />
Frontispiece, B 161 B 162
Erwin Tomash Library<br />
Bion, Nicholas Bion, Nicholas<br />
Pagination: pp. [8], 48<br />
Collation: π 4 A–F 4<br />
Size: 214x158 mm<br />
This short work is bound with the 1712 German<br />
translation <strong>of</strong> Bion. Despite the display <strong>of</strong> Bion’s name on<br />
the title page, it is written by the translator Doppelmayr<br />
and illustrates a number <strong>of</strong> instruments, which, although<br />
claiming to be from Bion’s workshop, do not appear in<br />
any <strong>of</strong> Bion’s French editions. The most inventive are<br />
optical—binocular and reflecting telescopes (some with<br />
multiple internal reflections in order to reduce the length<br />
<strong>of</strong> the tube), a camera obscura and a lantern projector.<br />
The copper engraved plates are similar in style to those<br />
used in Bion’s works.<br />
Illustrations available:<br />
Title page<br />
Telescopes and binoculars<br />
Camera obscura<br />
Lantern projector<br />
B 163<br />
Bion, Nicholas (ca.1652–1733)<br />
Telescopes and Binoculars, B 162<br />
L’ usage des astrolabes, tant universels que particuliers.<br />
Accompagné d’un traité, qui en explique la construction<br />
par des manieres simples & faciles, avec les figures<br />
necessaires pour l’intelligence de ce traité.<br />
Year: 1702<br />
Place: Paris<br />
Publisher: Chez Laurent d’Houry & Jean Boudot<br />
B 163<br />
Edition: 1st<br />
Language: French<br />
Binding: contemporary leather; spine gilt decorated<br />
Collation: a 5 A–K 12 L 2<br />
Size: 162x95 mm<br />
Reference: Bud IOS, p. 32–36<br />
Nicholas Bion was famous for books on mathematical<br />
and astronomical instruments. This comprehensive text<br />
on astrolabes is not as well known as his later, more<br />
ambitious work on the construction and use <strong>of</strong> all types<br />
<strong>of</strong> instruments. This is the last book entirely about<br />
astrolabes to be published in the French language.<br />
The planispheric astrolabe was a relatively welldocumented<br />
device when Bion wrote this treatise. It is<br />
essentially a map <strong>of</strong> the heavens superimposed on a map<br />
<strong>of</strong> the earth (or at least significant features <strong>of</strong> the earth<br />
such as the observer’s horizon, zenith, tropics, equator,<br />
etc.) with a movable rete representing the position <strong>of</strong> the<br />
stars and sun. Its major shortcoming is that it is limited<br />
to use at only one latitude. To overcome this handicap,<br />
larger astrolabes <strong>of</strong>ten were fitted with exchangeable<br />
plates for different latitudes.<br />
By the time Bion composed this work, a large number <strong>of</strong><br />
variations and modifications had been made, resulting in<br />
a so-called universal astrolabe. See the Appendix essay<br />
on the astrolabe for more information.<br />
The first <strong>chapter</strong> covers the commonly found planispheric<br />
astrolabe and describes the improvements due to Gemma<br />
151
Frisius and Juan de Rojas Sarmiento. The new form <strong>of</strong><br />
universal astrolabe due to Philippe de La Hire is then<br />
described. La Hire was a well-known astronomer and a<br />
pr<strong>of</strong>essor <strong>of</strong> mathematics who, perhaps not incidentally,<br />
wrote a one-page endorsement for this volume.<br />
152<br />
Illustrations available:<br />
Title page<br />
Colophon<br />
Rete diagram <strong>of</strong> astrolabe<br />
Erwin Tomash Library<br />
Bion, Nicholas Bion, Nicholas<br />
Astrolabe rete, B 163<br />
B 164<br />
Bion, [Nicholas] Nicolaus (ca.1652–1733) [Johann<br />
Gabriel Doppelmayr (1671–1750), translator]<br />
Zwote Eröfnung der neuen mathematischen Werkschule<br />
Nicolaus Bions in welcher sowohl die Zubereitung als<br />
der Gebrauch verschiedener anderer mathematischen<br />
absonderlich der zur Geometrie und Optik gehörigen<br />
Instrumenten die im besagten Autor nicht zu finden<br />
denen Liebhabern deutlich vor Augen geleget und<br />
erkläret werden<br />
Year: 1765<br />
Place: Nürnberg<br />
Publisher: George Peter Monath<br />
Edition: 2nd (German)<br />
Language: German<br />
Figures: 20 engraved folding plates<br />
Binding: contemporary three-quarter bound leather over boards<br />
Pagination: pp. [8], 48, [12], 176<br />
Collation: )(4A–F4)(4)()(2A–Y4<br />
Size: 209x166 mm<br />
Doppelmayr was the translator <strong>of</strong> the first edition <strong>of</strong><br />
Bion’s work on mathematical instruments into German<br />
(see the entry for Bion, Nicholas; Neu eröffnete<br />
Mathematische Werkschule, oder gründliche Anweisung,<br />
wie die Mathematische Instrumenten, 1712), and he also<br />
added several <strong>of</strong> his own descriptions to the translation.<br />
He continues that practice here, claiming the instruments<br />
to be from the workshop <strong>of</strong> Bion. No description <strong>of</strong> them<br />
is found in the French editions <strong>of</strong> Bion’s work, although<br />
some similar ones appear in an addenda to the second<br />
edition <strong>of</strong> the English translation (see the entry for Bion,<br />
Nicholas [Edmund Stone, translator]; The construction<br />
and principle uses <strong>of</strong> mathematical instruments, 1758,<br />
London).<br />
This posthumous edition is devoted to surveying (usually<br />
sighting devices) and also includes some <strong>of</strong> the optical<br />
instruments (telescopes and binoculars) that are found in<br />
his earlier work.<br />
Illustrations available:<br />
Title page<br />
B 164<br />
B 165<br />
Bion, [Nicholas] Nicolaus (ca.1652–1733) [Johann<br />
Gabriel Doppelmayr (1671–1750), translator]<br />
Dritte Eröfnung der neuen mathematischen Werkschule<br />
Nicolaus Bions in welcher die Zubereitung und der<br />
Gebrauch verschiedener astronomischen Instrumenten<br />
bescrieben wird<br />
b/w: Bion, Nicholas; Zwote Eröfnung der neuen<br />
mathematischen Werkschule Nicolaus Bions<br />
in welcher sowohl die Zubereitung als der<br />
Gebrauch verschiedener anderer mathematischen<br />
absonderlich der zur Geometrie und Optik<br />
gehörigen Instrumenten die im besagten Autor
Erwin Tomash Library<br />
Bion, Nicholas Bird, John<br />
nicht zu finden denen Liebhabern deutlich vor<br />
Augen geleget und erklaret werden<br />
Year: 1765<br />
Place: Nürnberg<br />
Publisher: George Peter Monath<br />
Edition: 2nd (German)<br />
Language: German<br />
Figures: 20 engraved folding plates<br />
Binding: contemporary bound three-quarter bound leather<br />
Pagination: pp. [8], 48, 176<br />
Collation: )( 4 A–F 4 )( 4 )()( 2 A–Y 4<br />
Size: 209x166 mm<br />
Reference: Bud IOS, pp. 32–36<br />
This posthumous edition, like the one bound with<br />
it, continues Doppelmayr’s practice <strong>of</strong> adding his<br />
own descriptions to the original work. He claims the<br />
instruments are from the workshop <strong>of</strong> Bion, however,<br />
with a few exceptions (such as the pendulum clock), no<br />
description <strong>of</strong> them is found in the French editions <strong>of</strong><br />
Bion. This edition is devoted to astronomical devices<br />
and draws on Doppelmayr’s early work on globes. It also<br />
illustrates devices such as large astronomical quadrants<br />
and transit sighting instruments.<br />
Illustrations available:<br />
Title page<br />
B 166<br />
Biot, Edouard Constant (1803–1850)<br />
B 165<br />
Table génerale d’un ouvrage Chinois intitulé [title in<br />
Chinese] souan-fa-tong-tsong ou collection des régles<br />
du calcul. Extract from Journal Asiatique. VIII, 1839.<br />
Year: 1839<br />
Place: Paris<br />
Publisher: Imprimerie Royale<br />
Edition: <strong>of</strong>fprint<br />
Language: French<br />
Binding: original paper wrappers<br />
Pagination: pp. 27, [1]<br />
Size: 220x140 mm<br />
Presentation copy: Offers à Monsieur Boner[?] de la par<br />
de l’auteur. E Biot<br />
This is a short note commenting on elementary Chinese<br />
mathematics that Biot found in a book from the Royal<br />
Library.<br />
Illustrations available:<br />
Title page<br />
B 166<br />
Biot, Edouard Constant, translator<br />
See <strong>Babbage</strong>, <strong>Charles</strong>; Traité sur l’économie des<br />
machines et des manufactures, 1833.<br />
B 167<br />
Bird, John (1709–1776)<br />
The method <strong>of</strong> constructing mural quadrants.<br />
Exemplified by a description <strong>of</strong> the brass mural<br />
quadrant in the Royal Observatory at Greenwich.<br />
Year: 1768<br />
Place: London<br />
Publisher: W. Richardson and S. Clark<br />
Edition: 1st<br />
Language: English<br />
Figures: 3 folding engraved plates separately housed in a cloth<br />
folder<br />
Binding: later paper wrappers<br />
153
154<br />
Pagination: pp. 28<br />
Collation: A–C 4 E 2<br />
Size: 258x201 mm<br />
Reference: Pogg Vol. I, p. 200; Gun AOW II, 319<br />
See also the entry for Bird, John; The method <strong>of</strong> dividing<br />
astronomical instruments, 1767, London.<br />
This volume is the second half <strong>of</strong> Bird’s commitment to<br />
produce a full description <strong>of</strong> how he created the 8-foot<br />
mural quadrant. It is interesting in that Bird describes<br />
not only the details <strong>of</strong> his successful construction <strong>of</strong><br />
the quadrant but also his failures (such as an attempt to<br />
create the telescope without bracing).<br />
Illustrations available:<br />
Title page<br />
B 168<br />
Bird, John (1709–1776)<br />
The method <strong>of</strong> dividing astronomical instruments.<br />
Year: 1767<br />
Place: London<br />
Publisher: J. Nourse; and Mess. Mount and Page<br />
Edition: 1st<br />
Language: English<br />
Figures: 1 large engraved folding plate<br />
Binding: later paper wrappers<br />
Pagination: pp. vi, 14<br />
Collation: A–E 2<br />
Size: 258x201 mm<br />
John Bird was a major instrument maker in London.<br />
He began his career as a weaver but soon developed a<br />
part-time business helping watch face makers. He later<br />
worked for an instrument maker named Graham before<br />
opening his own instrument shop. He was commissioned<br />
to construct a large (8-foot radius) mural quadrant at<br />
the Royal Observatory at Greenwich (completed in<br />
1749) when the earlier one done by Graham began to<br />
deform under its own weight. The Commissioners <strong>of</strong><br />
Longitude (and, in particular, the Astronomer Royal,<br />
Neville Maskelyne) were responsible for the quadrant’s<br />
construction and wanted to ensure that the methods used<br />
by Bird (then in business for some thirty-four years)<br />
would be available to his successors. In return for a sum<br />
<strong>of</strong> £500 (plus an additional £60 for engraved plates), Bird<br />
agreed to take an apprentice and instruct him for seven<br />
years and to present to the commissioners a full and<br />
complete description <strong>of</strong> how the quadrant scales were<br />
divided. This volume is the fulfillment <strong>of</strong> the written<br />
part <strong>of</strong> that commitment. The quadrant had actually been<br />
constructed seventeen years earlier, and one can presume<br />
that the commissioners were anxious to have all the plans<br />
and descriptions finished.<br />
Erwin Tomash Library<br />
Bird, John Birkh<strong>of</strong>f, Garrett<br />
Great care was obviously taken with the division <strong>of</strong> the<br />
scales. Bird describes how the brass quadrant scales and<br />
the pine beam compasses were left in a locked room over<br />
night so that they might stabilize to the same temperature.<br />
He also sketches out a method <strong>of</strong> dividing a scale by<br />
establishing a few elementary basic measurements and<br />
then using repeated bisections to create the other marks.<br />
The one diagram is marked Plate iv because it is the<br />
fourth plate from his engraved plates <strong>of</strong> the quadrant (see<br />
entry for Bird, John; The method <strong>of</strong> constructing mural<br />
quadrants. Exemplified by a description <strong>of</strong> the brass<br />
mural quadrant in the Royal Observatory at Greenwich,<br />
1768, for the other three).<br />
Illustrations available:<br />
Title page<br />
B 169<br />
Birkh<strong>of</strong>f, Garrett (1911–); K. O. Friedrichs and T. E.<br />
Sterne, editors<br />
Transactions <strong>of</strong> the symposium on fluid mechanics and<br />
computing held at New York <strong>University</strong>, April 23–24,<br />
1953. The first symposium on applied mathematics<br />
sponsored by the American Mathematical Society and<br />
Office <strong>of</strong> Ordnance Research, U. S. Army<br />
Year: 1954<br />
Place: New York<br />
Publisher: Interscience Publishers<br />
B 168
Erwin Tomash Library<br />
Bishop, Calvin Collier Blachman, Nelson Meri<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards<br />
Pagination: pp. [iv], 243, [1]<br />
Size: 253x171 mm<br />
Fluid flow is <strong>of</strong> interest to both the physics and military<br />
communities. In particular, the military applications are<br />
in the areas <strong>of</strong> airflow around planes and projectiles,<br />
through jet engines and in the behavior <strong>of</strong> explosives.<br />
Thus it was appropriate for both the academic and<br />
military groups to sponsor such a meeting.<br />
This volume includes the papers presented at the 1953<br />
meeting (with the exception <strong>of</strong> a talk given by John von<br />
Neumann on the Role <strong>of</strong> Computing Machines, but one<br />
can speculate that it was similar to a number <strong>of</strong> such talks<br />
he gave around this time in which fluid dynamics played<br />
a prominent role). The papers that are produced here deal<br />
with the theoretical aspects <strong>of</strong> problems, and there are<br />
few detailed references to any military applications.<br />
Illustrations available:<br />
Title page<br />
B 170<br />
Bishop, Calvin Collier (1882–)<br />
Practical use <strong>of</strong> the slide rule<br />
Year: 1944<br />
Place: New York<br />
B 170<br />
Publisher: Current Publishing<br />
Edition: 1st<br />
Language: English<br />
Binding: original printed paper wrappers<br />
Pagination: pp. 63<br />
Size: 212x132 mm<br />
Bishop was a teacher in the Technical High School in<br />
Buffalo, New York.<br />
This is a generic text on the use <strong>of</strong> the slide rule. It<br />
contains a series <strong>of</strong> problems for the student, with<br />
answers, at the end.<br />
Illustrations available:<br />
Title page<br />
B 171<br />
Bishop, Calvin Collier (1882–)<br />
[Slide rule]<br />
b/w: Keuffel & Esser Company; Elementary<br />
instructions for operating the slide rule.<br />
b/w: Harris, <strong>Charles</strong> O.; Slide rule<br />
Year: n/d<br />
Place: Tehran, Shāh’ Ābād<br />
Publisher: Kit-abfurūshī-i-Zavvār<br />
Edition: 1st<br />
Language: Farsi<br />
Binding: original printed paper wrappers<br />
Pagination: pp. [4], 106<br />
Size: 215x138 mm<br />
This is a Farsi edition <strong>of</strong> this classic work on the slide<br />
rule. First published as Practical use <strong>of</strong> the Slide rule,<br />
1944.<br />
Illustrations available:<br />
Title page<br />
B 172<br />
Blachman, Nelson Meri (1923–)<br />
A survey <strong>of</strong> automatic digital computers<br />
Year: 1953<br />
Place: Washington, D.C.<br />
Publisher: Office <strong>of</strong> Naval Research<br />
Edition: 1st<br />
Language: English<br />
Binding: original cardboard wrappers<br />
Pagination: pp. vi, 109, [1]<br />
Size: 267x184 mm<br />
Blachman worked for the Office <strong>of</strong> Naval Research in<br />
Washington, D.C. Earlier surveys <strong>of</strong> computers had<br />
been done, but the rapid development <strong>of</strong> the technology<br />
had made them out <strong>of</strong> date. Blachman, with help from<br />
the others acknowledged in the Preface, undertook to<br />
bring the survey up to date. The work is useful because<br />
155
it covers not only electronic stored program computers<br />
but also machines such as those constructed at Harvard<br />
by Aiken, relay computers built in Tokyo, British and<br />
European machines, and little-known projects such as<br />
the <strong>University</strong> <strong>of</strong> Toronto UTEC computer. No mention<br />
is made <strong>of</strong> the Zuse machines. Each entry gives technical<br />
details <strong>of</strong> the machine and short remarks that do not fit<br />
into any <strong>of</strong> the pre-assigned entry categories.<br />
156<br />
Illustrations available:<br />
Title page<br />
ERA 101 page<br />
Erwin Tomash Library<br />
Blackburn, John E. Blagrave, John<br />
B 173<br />
Blackburn, John E.<br />
Components handbook<br />
Year: 1949<br />
Place: New York<br />
Publisher: McGraw-Hill Book Company<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards<br />
Pagination: pp. xviii, 626<br />
Size: 230x145 mm<br />
B 172<br />
This is No. 17 in the Radiation Laboratory Series<br />
publications. It was intended as a reference work to<br />
accompany volumes 18–23 <strong>of</strong> the series. The volume was<br />
intended to be a broad survey <strong>of</strong> the field <strong>of</strong> electrical,<br />
mechanical and electronic components that were used<br />
by the Radiation Laboratory, but because <strong>of</strong> the decision<br />
to shut the Office <strong>of</strong> Publications, several <strong>chapter</strong>s were<br />
omitted. It represents a state-<strong>of</strong>-the-art survey <strong>of</strong> the<br />
technology in use at the time and includes everything<br />
from simple cables to elementary electronic devices,<br />
instrument motors, relays and vacuum tubes. It is heavily<br />
illustrated with photographs and diagrams <strong>of</strong> the devices<br />
as well as numerous tables giving characteristics and test<br />
results as determined by the Radiation Laboratory.<br />
Illustrations available:<br />
Title page<br />
B 174<br />
Blagrave, John (1558?–1612)<br />
B 173<br />
The mathematical jewel. Shewing the making, and most<br />
excellent use <strong>of</strong> a singuler instrument so called: in that<br />
it performeth with wonderfull dexteritie, whatsoever is<br />
to be done, either by quadrant, ship, circle, cylinder,<br />
ring, dyall, horoscope, astrolabe, sphere, globe, or any<br />
such like heret<strong>of</strong>ore devised: yea, or by most tables<br />
commonly extant: and that generally to all places from<br />
pole to pole.<br />
Year: 1585<br />
Place: London<br />
Publisher: Walter Venge<br />
Edition: 1st<br />
Language: English<br />
Figures: 3 engraved frontispiece plates; 2 engraved full-page<br />
tables<br />
Binding: contemporary limp vellum<br />
Pagination: pp. [16], 124<br />
Collation: 4 2 A–P 4 Q 2<br />
Size: 268x182 mm<br />
Blagrave was a mathematician, surveyor and instrument<br />
maker from Reading. Educated at St. John’s College,<br />
Oxford, he never took a degree but returned to Reading,<br />
where he lived <strong>of</strong>f the legacy <strong>of</strong> land left to him by his<br />
father. He left a legacy to the town <strong>of</strong> Reading (the sum<br />
<strong>of</strong> 20 nobles annually) to be competed for by three maid
Erwin Tomash Library<br />
Blagrave, John Blagrave, John<br />
servants selected by town parishes who were to cast lots<br />
for their prize money each Good Friday.<br />
The instrument described is a planispheric astrolabe that<br />
had a universal projection modified from the Catholicon<br />
<strong>of</strong> Gemma Frisius—a description <strong>of</strong> which can be<br />
found in the second booke. Blagrave added a movable<br />
rete (<strong>of</strong>ten found on standard astrolabes but not on the<br />
Catholicon), which simplified its use for astronomical<br />
calculations. This astrolabe was universal in the sense<br />
that it did not require a number <strong>of</strong> different plates or<br />
maters to be used at different latitudes. The instrument<br />
is illustrated in a number <strong>of</strong> full-page engravings serving<br />
as frontispieces to the work—engraved by the author<br />
according to the title page. This was an expensive<br />
instrument to build and consequently was not much<br />
used. While this is the only edition <strong>of</strong> this work, the<br />
Jewel was described ten years later in a work by Thomas<br />
Blundeville (Exercises, 1622), and instruction in its use<br />
was also <strong>of</strong>fered by Robert Hartwell, a London teacher<br />
<strong>of</strong> mathematics, in 1623 (see Waters, David Watkin; Art<br />
<strong>of</strong> navigation, 1958, p. 570).<br />
B 174<br />
Arc drawing instrument, B 174<br />
Mathematical jewel, B 174<br />
The work is divided into six bookes. The first deals with<br />
elementary concepts <strong>of</strong> astronomy; the second with<br />
the design and manufacturing <strong>of</strong> the jewel; the third<br />
with the use <strong>of</strong> the instrument for both navigation and<br />
astronomical calculations; the fourth considers the same<br />
material as the third, but the examples and methods <strong>of</strong><br />
working come from Blagrave’s own research; the fifth<br />
is a treatise on spherical triangles; and the last is a work<br />
on the use <strong>of</strong> the jewel in creating sundials <strong>of</strong> all types.<br />
For such a small volume, it is remarkably complete and<br />
would have made a very useful reference work even<br />
if one did not have a jewel to use. In the fourth book,<br />
Blagrave mentions that he had made a jewel two feet in<br />
diameter and that he had problems drawing all the arcs<br />
on it. He then illustrates a drawing instrument that would<br />
suffice in such a situation.<br />
Blagrave is known to have made other instruments,<br />
in particular a familiar staff, which may have been an<br />
instrument for artillerymen.<br />
The work contains a handwritten note which reads:<br />
Here stands Mr. Gray master <strong>of</strong> this house<br />
And his poor catt playing with a mouse.<br />
John Balgrave marred this Grayes widdow (She was a<br />
Hungerford) this John was symple had yssue by the widdowe<br />
1 Anthony who marryed Jane Borlafs. 2 John the author <strong>of</strong><br />
the booke. 3 Alexander the excellent chess player in England.<br />
Anthony had Sir John Blagrave knight who caused his teeth to<br />
be all drawn out and after had a sett <strong>of</strong> ivory teeth in agayne.<br />
157
158<br />
Illustrations available:<br />
Title page<br />
Instrument plate 1<br />
Instrument plate 2<br />
Instrument plate 3<br />
Arc drawing instrument<br />
Inscription<br />
B 175<br />
Blaine, Robert Gordon<br />
Quick and easy methods <strong>of</strong> calculating. A simple<br />
explanation <strong>of</strong> the theory and use <strong>of</strong> the slide rule,<br />
logarithms, &c. With numerous examples worked out.<br />
Year: 1898<br />
Place: London<br />
Publisher: E. & F.N. Spon<br />
Edition: 1st<br />
Language: English<br />
Figures: 1 folding plate<br />
Binding: original cloth boards<br />
Pagination: pp. xii, 144, 2<br />
Collation: A 6 B–K 8<br />
Size: 161x100 mm<br />
Blaine was lecturer at the City and Guilds’ Technical<br />
College in Finsbury.<br />
This is a work on the slide rule containing an introduction<br />
to logarithms and using examples from mechanical<br />
and hydraulic engineering. The explanations are rather<br />
pedantic with few illustrations.<br />
Illustrations available:<br />
Title page<br />
Erwin Tomash Library<br />
Blaine, Robert Gordon Blanquart de Sept-Fontaines, L. M.<br />
B 175<br />
B 176<br />
Blaine, Robert Gordon<br />
Some quick and easy methods <strong>of</strong> calculating. A simple<br />
explanation <strong>of</strong> the theory and use <strong>of</strong> the slide rule,<br />
logarithms, etc. With numerous examples worked out.<br />
Year: 1912<br />
Place: London<br />
Publisher: E. & F.N. Spon<br />
Edition: 4th<br />
Language: English<br />
Figures: 1 folding plate<br />
Binding: original cloth boards<br />
Pagination: pp. xii, 152<br />
Collation: A 6 B–K 8 L 4<br />
Size: 161x100 mm<br />
Note the addition <strong>of</strong> Some to the title between the first<br />
edition and the fourth <strong>of</strong> 1912.<br />
Illustrations available:<br />
Title page<br />
B 177<br />
Blanquart de Sept–Fontaines, L. M.<br />
Les intérêts des comptes courans tout calculés, quels<br />
qu’en soient et le taux et le capital, ou tables qui, pour<br />
le calcul de ces intérêts, soit qu’on les arrête une fois<br />
l’an seulemant, ou de six en six mois, soit encore qu’il<br />
s’agisse de négociations d’effets ou de prêt d’argent<br />
pour un nombre de jours quelqonque, n’exigent que la<br />
simple ouverture d’une page, et le secours de l’addition<br />
substituée aux longues opérations employées jusqu’à<br />
présent. Ces tables accommodées également aux deux<br />
styles francais et grégorien, le dernier en faveur des<br />
lieux où l’on suit l’ere ancienne.<br />
Year: 1802<br />
Place: Paris<br />
Publisher: Henri Agasse<br />
Edition: 1st<br />
Language: French<br />
Binding: contemporary leather, tree grained; spine gilt; red<br />
leather label<br />
Pagination: pp. xvi, 378<br />
Collation: a–b 4 A–3A 4 3B 1<br />
Size: 252x185 mm<br />
The most fascinating aspect <strong>of</strong> this work is that these<br />
interest tables were produced for use with both the old<br />
Gregorian and the new French calendar. The introduction<br />
states that Sept-Fontaines was attempting to produce a<br />
set <strong>of</strong> tables for commercial activity that would be as<br />
useful as those available to mathematicians.<br />
Illustrations available:<br />
Title page<br />
Page <strong>of</strong> tables
Erwin Tomash Library<br />
Blaschke, Ernst Blaschke, Ernst<br />
B 178<br />
Blaschke, Ernst (1856–1926)<br />
Vorlesungen über Mathematische Statistik. (Die lehre<br />
von den Statistischen Masszhalen)<br />
Year: 1906<br />
Place: Leipzig and Berlin<br />
Publisher: B. G. Teubner<br />
Edition: 1st<br />
Language: German<br />
Figures: 5 photographic plates<br />
Binding: original cloth boards<br />
Pagination: pp. viii, 268<br />
Collation: a 4 1–16 8 17 6<br />
Size: 223x151 mm<br />
Ernst Blaschke was a pr<strong>of</strong>essor at the Technischen<br />
Hochschule in Vienna.<br />
This volume is not directly concerned with calculating<br />
machinery until the last <strong>chapter</strong>, when the author<br />
describes some <strong>of</strong> the new punched card machinery. In<br />
particular, he briefly describes the Hollerith machines<br />
used for the U.S. census and also equipment developed<br />
specifically for the insurance industry by John K. Gore,<br />
an actuary at the Prudential Life Insurance Company.<br />
Gore’s little-known system is illustrated with his card<br />
punch and sorting machine.<br />
Illustrations available:<br />
Title page<br />
Gore’s card punch<br />
Gore’s sorting machine<br />
B 177<br />
Gore’s card sorter, B 178<br />
Gore’s card punch, B 178<br />
B 178<br />
159
Bloch, Richard Milton (1901–2000)<br />
See Mathematical tables and other aids to<br />
computation (MTAC)<br />
B 179<br />
Blom, Frans Ferdinand (1893–1963)<br />
Commerce, trade and monetary units <strong>of</strong> the Maya<br />
160<br />
Year: 1935<br />
Place: Washington, D.C.<br />
Publisher: Smithsonian<br />
Edition: Extract<br />
Language: English<br />
Binding: wrappers, uncut<br />
Pagination: pp. 423–440<br />
Size: 243x157 mm<br />
This is an extract from the Smithsonian report for 1934,<br />
pp. 423–440. It is uncut.<br />
Illustrations available:<br />
Title page<br />
Blount, Thomas (1857–1911)<br />
See Addenda entry: Estienne, Henri; The art <strong>of</strong> making<br />
devises: treating <strong>of</strong> hieroglyphicks, symbols,<br />
emblemes, ænigma’s, sentences, parables, reverses<br />
<strong>of</strong> medalls, armes, blazons, cimiers, cyphres and<br />
rebus. Fisrt written in French by Henry Estienne<br />
… Translated into English, and embelished with<br />
divers brasse figures by T[homas] B[lount].<br />
Whereunto is added, a catalogue <strong>of</strong> coronetdevises,<br />
both on the Kings and the Parliaments<br />
side, in the late warres. Paris, 1894.<br />
Erwin Tomash Library<br />
Bloch, Richard Milton Blundeville, Thomas<br />
B 180<br />
B 180<br />
Blundeville, Thomas (fl.1560–1602)<br />
His exercises, containing sixe treatises, the titles<br />
where<strong>of</strong> are set down in the next printed page: which<br />
treatises are verie necessarie to be read and learned<br />
<strong>of</strong> all yoong gentlemen that have not bene exercised<br />
in such disciplines, and yet are desirous to have<br />
knowledge as well in cosmographie, astronomie, and<br />
geographie, as also in the arte <strong>of</strong> navigation, in which<br />
arte it is impossible to pr<strong>of</strong>ite without the helpe <strong>of</strong> these,<br />
or such like instructions. To the furtherance <strong>of</strong> which<br />
arte <strong>of</strong> navigation, the said M. Blundevile speciallie<br />
wrote the said treatises and <strong>of</strong> meere good will doth<br />
dedicate the same to all young gentlemen <strong>of</strong> this realme.<br />
Year: 1594<br />
Place: London<br />
Publisher: John Windet<br />
Edition: 1st<br />
Language: English<br />
Figures: 4 woodcuts with volvelles (3 original moving parts,<br />
one replacement), 1 folding plate, 2 folding tables<br />
Binding: contemporary vellum<br />
Pagination: ff. [7], 350 (misnumbered ff. 151 as 149)<br />
Collation: A 7 B–2X 8 2Y 6<br />
Size: 197x147 mm<br />
Reference: Cro CL, #90<br />
Nocturnal, B 180<br />
Thomas Blundeville was educated at Cambridge, where<br />
he almost certainly met Edward Wright, who was to<br />
play a major role in the reform <strong>of</strong> navigation in England.<br />
After leaving Cambridge, he resided near Norwich,<br />
where he taught mathematics to the sons <strong>of</strong> the nobility.
Erwin Tomash Library<br />
Blundeville, Thomas Blundeville, Thomas<br />
He is known as the author <strong>of</strong> a number <strong>of</strong> works, mostly<br />
dealing with horsemanship; however, some were about<br />
maps, globes and the use <strong>of</strong> instruments in navigation.<br />
He was well connected to the scientific establishment<br />
<strong>of</strong> his day, for among his friends were such notables as<br />
Henry Briggs, Edward Wright, William Gilbert, etc.<br />
This is an important book in the history <strong>of</strong> navigation.<br />
Here for the first time the modern forms <strong>of</strong> the<br />
trigonometric functions <strong>of</strong> sine, tangent and secant<br />
were published in English (see essay on the sector for<br />
a description <strong>of</strong> the old forms based on a circle <strong>of</strong> given<br />
radius). These new tables, first suggested by Peuerbach<br />
and Regiomontanus about a hundred years earlier, had<br />
been long known to astronomers and mathematicians but<br />
had seldom been considered in the context <strong>of</strong> navigation.<br />
It is also the first description <strong>of</strong> navigation based on<br />
Mercator’s projection (as revised by Edward Wright)<br />
to be available in English and also included the latest<br />
navigational techniques <strong>of</strong> continental European authors.<br />
Blundeville occasionally added his own observations on<br />
minor points (such as noting that large astrolabes are<br />
more accurate, but they have a tendency to blow in the<br />
wind, and thus the smaller, heavier Spanish astrolabes<br />
are more practical for use on a ship).<br />
The work begins with the elements <strong>of</strong> arithmetic,<br />
including fractions and square roots. The necessity<br />
for knowing <strong>of</strong> square roots is justified by the strange<br />
example, occasionally seen in other works from this<br />
era, <strong>of</strong> a sergeant needing to arrange his men in square<br />
formation on the battlefield. The arithmetic proceeds<br />
with a discussion <strong>of</strong> sexagesimal numbers (degrees,<br />
minutes and seconds) and how they are manipulated<br />
and included is a large foldout multiplication table for<br />
sexagesimal numbers.<br />
The second major section contains the tables <strong>of</strong> sines,<br />
tangents and secants. In his introduction he credits<br />
Peuerbach and Regiomontanus with the concept and<br />
indicates that the tables he is reproducing were first done<br />
by Regiomontanus in folio and recently corrected by<br />
Clavius. The values given for sine range between 4 and<br />
7 places <strong>of</strong> decimals, depending on their position in the<br />
table. Tangent values range from 4 to 11 decimal digits<br />
while secants are between 8 and 11 digits.<br />
The third book describes spherical trigonometry and<br />
the calculations necessary for navigation. It presents a<br />
graphical process (using only a protractor and straight<br />
edge) for determining the distances between any two<br />
points when knowing only their longitude and latitude.<br />
A treatise on the use <strong>of</strong> the terrestrial and celestial globes<br />
then follows.<br />
The next section discusses the map, not shown, created<br />
by Petrus Plancius in 1592. Not only does Blundeville<br />
describe the areas shown on the map, but he also covers<br />
the people, rulers and climates <strong>of</strong> each location. The<br />
descriptions are <strong>of</strong>ten remarkably detailed. For example,<br />
the city <strong>of</strong> Catan (Canton?) in China is noted as being<br />
surrounded by walls that extend for twelve Italian miles<br />
and three hundred fifty paces and which is more than<br />
foure houres journey, not reckoning the suburbs, which<br />
are very large and full <strong>of</strong> people. He also mentions the<br />
Great Wall (which hath in length 400 Spanish Leagues)<br />
and explains why it was constructed. Some <strong>of</strong> these facts<br />
so impressed an earlier owner that they are pointed out<br />
in marginal inscriptions. The facts about the Great Wall<br />
have been recopied onto the blank first leaf.<br />
Pages 280 to 303 contain a description <strong>of</strong> the mathematical<br />
jewel or astrolabe <strong>of</strong> Blagrave. While the instrument is<br />
not illustrated, each <strong>of</strong> its component parts is described<br />
in some detail. Blundeville does not present Blagrave’s<br />
entire text but limits himself to the subject <strong>of</strong> navigation.<br />
For example, he does not describe, as did Blagrave, the<br />
use <strong>of</strong> the instrument in creating sundials. It seems clear<br />
that if a jewel were at hand, Blundeville’s text would be<br />
sufficient for use by a navigator.<br />
The last section <strong>of</strong> the book is entitled A new and<br />
necessaire Treatise <strong>of</strong> Navigation, a title that gives<br />
only a general indication <strong>of</strong> its wide-ranging content.<br />
The section begins with a description <strong>of</strong> the cross-staff<br />
(Jacob’s staff), the mariner’s astrolabe (mariner’s ring)<br />
and the magnetic compass. Notable is a description <strong>of</strong> a<br />
nocturnal or Rectifier <strong>of</strong> the North Star (one <strong>of</strong> the few<br />
instruments illustrated). There is also a section on calendar<br />
computation, in particular the calculation <strong>of</strong> Easter and<br />
other movable festivals. This latter can be considered an<br />
example <strong>of</strong> finger reckoning in that the calculation <strong>of</strong><br />
calendar items such as the Epact are accomplished by<br />
counting <strong>of</strong>f various spaces on the left thumb.<br />
It was in this last section on navigation that Blundeville<br />
(p. 326) indicates that (see illustration)<br />
… Mercator hath in his universal carde or Mappe<br />
made the spaces <strong>of</strong> the Parallels <strong>of</strong> latitude to be<br />
wider euveie one than other from the Equinoctiall<br />
towards either <strong>of</strong> the Poles, by what rule I knowe<br />
not, unlesse it be by such a Table, as my friend<br />
E. Wright <strong>of</strong> Cais colledge in Cambridge at my<br />
request sent me (I thanke him) not long since for<br />
that purpose…<br />
There was a second edition in 1597 and a seventh in<br />
1636.<br />
161
162<br />
Illustrations available:<br />
Title page<br />
Sexagesimal multiplication table<br />
Sine table<br />
Tangent table<br />
Secant table<br />
Nocturnal<br />
Wright’s table<br />
Erwin Tomash Library<br />
Blundeville, Thomas Boehn, Otto<br />
B 181<br />
Blundeville, Thomas (fl. 1560–1602)<br />
B 181<br />
His exercises, contayning eight treatises, the titles<br />
where<strong>of</strong> are set downe in the next printed page: which<br />
treatises are very necessary to be read and learned<br />
<strong>of</strong> all yong gentlemen that have not beene exercised<br />
in such disciplines, and yet are desirous to have<br />
knowledge as well in cosmographie, astronomie, and<br />
geographie, as also in the art <strong>of</strong> navigation, in which<br />
art it is impossible to pr<strong>of</strong>it without the helpe <strong>of</strong> these,<br />
or such like instructions. To the furtherance <strong>of</strong> which<br />
art <strong>of</strong> navigation, the sayd Master Blundevile specially<br />
wrote the said treatises, and <strong>of</strong> meere good will doth<br />
dedicate the same to all young gentlemen <strong>of</strong> this realme.<br />
Year: 1622<br />
Place: London<br />
Publisher: William Stansby for Richard Meighen<br />
Edition: 6th<br />
Language: English<br />
Figures: 2 folding plates [pp. 72, 695], 3 folding plates [pp.<br />
786 (2), 798]; 4 volvelles [pp. 315, 660, 720, 744]<br />
Binding: modern three-quarter bound morocco<br />
Pagination: pp. [16], 799, [1]<br />
Collation: A–3E 8<br />
Size: 200x143 mm<br />
Reference: Tay MP1, #27; Ken, #1499<br />
Although this edition is corrected and augmented<br />
according to the title page, it is substantially identical to<br />
the first edition. Included are Blagrave’s Mathematicall<br />
Jewel (1585), Molyneaux’s globes (1592), Hood’s crossstaff<br />
(1590) and Gemma Frisius’ quadratum nauticum<br />
and accounts <strong>of</strong> a number <strong>of</strong> explorations, including the<br />
voyages <strong>of</strong> Drake and Cavendish. The closing section<br />
entitled A brief description <strong>of</strong> universall maps and cards<br />
contains several references to America.<br />
Illustrations available:<br />
Title page<br />
B 182<br />
Boehn, Otto<br />
B 182<br />
Von geheimnisvollen Massen, Zahlen und Zeichen<br />
Year: 1929<br />
Place: Leipzig<br />
Publisher: Bernhard Sporn<br />
Edition: 1st<br />
Language: German<br />
Binding: original cloth boards<br />
Pagination: pp. 118<br />
Collation: 1–7 8 8 3<br />
Size: 187x123 mm<br />
This is a work describing mathematical ideas in<br />
architecture. The examples are drawn mainly from<br />
churches in Austria and Germany. It includes a short<br />
discussion <strong>of</strong> π and its calculation.<br />
Illustrations available:<br />
Title page
Erwin Tomash Library<br />
Boesel, Rudolf Boethius, Anicius Manlius Severinus<br />
B 183<br />
Boesel, Rudolf<br />
B 183<br />
Die Lochkarte im Fabrikbetrieb. Rationalisierung<br />
des industriellen Rechnungswesen mit Hilfe des<br />
Lochkartenverfahrens.<br />
Year: 1930<br />
Place: Berlin<br />
Publisher: Carl Heymann<br />
Edition: unknown, likely 1st<br />
Language: German<br />
Figures: 6 photographic plates<br />
Binding: original paper wrappers<br />
Pagination: pp. [2],100<br />
Collation: π 1 1–6 8 7 2<br />
Size: 296x201 mm<br />
This is a tutorial on the use <strong>of</strong> the Powers punched<br />
card tabulating equipment in industrial accounting. In<br />
Powers tabulating machine, B 183<br />
general, the Powers equipment is similar in function to<br />
the punched card tabulating equipment produced by IBM<br />
but differs in that while the IBM equipment transmits its<br />
signals via electrical connections, the Powers equipment<br />
performs the same job mechanically via moving wires.<br />
Illustrations available:<br />
Title page<br />
Powers tabulating machine<br />
B 184<br />
Boethius, Anicius Manlius Severinus (ca.480–524/525)<br />
Arithmetica Boetij<br />
Year: 1488<br />
Place: Augsburg<br />
Publisher: Erhard Ratdolt<br />
Edition: 1st<br />
Language: Latin<br />
Figures: 7 pp. <strong>of</strong> ms. notes and figures at end<br />
Binding: modern brown morocco<br />
Pagination: ff. 48<br />
Collation: a–f 8<br />
Size: 195x147 mm<br />
Reference: Smi Rara, p. 25; G<strong>of</strong>f IAL, B828; Rcrdi BMI I, p.<br />
139<br />
From a distinguished patrician family, Boethius has<br />
been described as the last Roman and the first scholastic<br />
philosopher. While little is known <strong>of</strong> his early life and<br />
how he obtained his formidable Greek education,<br />
it is speculated that he studied in either Athens or<br />
Alexandria. Boethius’s abilities secured him one <strong>of</strong> the<br />
highest positions in the Ostrogothic kingdom, but the<br />
Arian king Theodoric, apparently suspecting a plot with<br />
the Byzantine emperor Justin I, had him arrested and<br />
executed. While awaiting execution, he wrote his famous<br />
philosophical work Consolatione Philosophiae.<br />
First page, B 184<br />
163
This Arithmetic, dedicated to Boethius’s father-in-law,<br />
Aurelius Memmius Symmachus, was part <strong>of</strong> a project<br />
to produce a text for each <strong>of</strong> the four mathematically<br />
oriented disciplines: arithmetic, music, geometry<br />
and astronomy. He termed these four subjects the<br />
quadrivium, a term that was in use in European schools<br />
until well after the Middle Ages. There is no indication<br />
he ever managed to complete this project—as only his<br />
works on arithmetic and music survive. In this volume,<br />
Boethius adheres to the early Greek idea <strong>of</strong> arithmetic<br />
as something more akin to modern number theory than<br />
anything <strong>of</strong> a practical nature (the Greeks would have<br />
termed the process <strong>of</strong> doing arithmetical operations as<br />
logistic rather than arithmetic).<br />
This work is loosely based on the Greek Arithmetica<br />
Eisagoge <strong>of</strong> Nicomachus <strong>of</strong> Gerasa (fl.100AD). It<br />
contains little or nothing original to Boethius, but it<br />
was presented in Latin in such a way that it appealed<br />
to the medieval scholar and became the standard work<br />
from which such subjects were taught for almost 1,000<br />
years. The subject matter originated with Pythagoras (ca.<br />
540 BC) and his followers, who developed a philosophy<br />
based on numbers and their symbolism. Nicomachus<br />
was a Pythagorean, and we can easily trace the origins<br />
<strong>of</strong> most <strong>of</strong> this work back to Pythagoras himself (or at<br />
least to his era).<br />
The work is heavily concerned with sequences and ratios<br />
between values—something that stemmed from the<br />
Greek difficulty with fractions and fractional notation.<br />
A large, well-laid-out multiplication table is the same<br />
as in earlier manuscript copies with the exception that<br />
here, and in the rest <strong>of</strong> the text, the newer Hindu-Arabic<br />
164<br />
Erwin Tomash Library<br />
Boethius, Anicius Manlius Severinus Boethius, Anicius Manlius Severinus<br />
numerals are used rather than the original Roman variety.<br />
Another major topic, again stemming from Pythagoras,<br />
is figurative numbers (those that can be arranged into<br />
geometric shapes such as triangles, squares, cubes, etc).<br />
This copy ends with seven pages <strong>of</strong> early (contemporary?)<br />
manuscript notes and diagrams relating to the movements<br />
<strong>of</strong> Saturn, Jupiter, Mars, Venus, Mercury, the sun and the<br />
moon.<br />
Illustrations available:<br />
Diagram with sequences<br />
First page<br />
Multiplication table<br />
Page with triangular numbers<br />
Venus manuscript diagram and notes<br />
Colophon<br />
B 185<br />
Boethius, Anicius Manlius Severinus (ca.480–524/525)<br />
Arithmetica, duobus discreta libris; adiecto<br />
commentario, mysticam numerorum applicationem<br />
perstríngente, declarata.<br />
Year: 1521<br />
Place: Paris<br />
Publisher: Simon Colines [Colinaeus]<br />
Edition: 16th<br />
Language: Latin<br />
Binding: contemporary vellum<br />
Pagination: ff. 138<br />
Collation: a–s 6 t 8 v–x 6 y 10<br />
Size: 275x200 mm<br />
Reference: Rcrdi I, 140; DeMorgan, p. 13<br />
This is the first edition <strong>of</strong> Boethius’ Arithmetica with the<br />
addition <strong>of</strong> the commentary by Girardus Ruffus (Gérard<br />
Roussel). Smith (Rara) indicates that This commentary<br />
greatly exceeds the text in extent, and as to ponderosity<br />
it leaves little to be desired. As a piece <strong>of</strong> typography,<br />
however, this is one <strong>of</strong> the best editions <strong>of</strong> Boethius. To a<br />
great extent, the commentary by Ruffus seems to rely on<br />
the work <strong>of</strong> Nicolaus Cusanus. For what little is known<br />
<strong>of</strong> the commentator, see the listing in this catalog for<br />
Roussel, Gérard. The work includes several diagrams,<br />
which help in the explanation. In particular, there is a<br />
large circular diagram that relates the Greek alphabetical<br />
number system to the Hindu-Arabic (on the innermost<br />
circles <strong>of</strong> the illustration) and indicates some <strong>of</strong> the<br />
properties <strong>of</strong> each value.<br />
Triangular numbers, B 184 Colophon, B 185
Erwin Tomash Library<br />
Boethius, Anicius Manlius Severinus Boethius, Anicius Manlius Severinus<br />
Illustrations available:<br />
Title page<br />
Circular diagram relating numbers<br />
Page with figurative numbers<br />
Page with numerical sequences<br />
Colophon<br />
B 185<br />
B 186<br />
B 186<br />
Boethius, Anicius Manlius Severinus (CA.480–524);<br />
[Faber Stapulensis (1455–1536) and Clichtove, Josse<br />
(1472–1543), editors]<br />
In hoc libro contenta. Epitome compendiosaque<br />
introductio in libros arithmeticos divi Severini<br />
Boëtii: adjecto familiari commentario dilucidata.<br />
Praxis numerandi certis quibusdam regulis<br />
constricta. Introductio in geometriam breviusculis<br />
annotationibus explanata sex libris distincta. Primus<br />
de magnitudinibus et earum circumstantiis. Secundus<br />
de consequentibus contiguis & continuis. Tertius de<br />
punctis. Quartus de lineis. Quintus de superficiebus.<br />
Sextus de corporibus. Liber de quadratura circuli.<br />
Liber de cubicatione sphere. Perspectiva introductio.<br />
Insuper astronomicon.<br />
Year: 1503<br />
Place: Paris<br />
Publisher: Wolfgang Hopyl [Hopilius] & Henry Estienne<br />
[Stephens]<br />
Edition: 1st<br />
Language: Latin<br />
Binding: modern suede leather<br />
Pagination: ff. 112<br />
Collation: a–o 8<br />
Size: 263x190 mm.<br />
Reference: Smi Rara, pp. 29, 80–81; Ada CBCE, F17 Ren, p.<br />
1; Rcrdi BMI I, p. 142–143; DeM AB, p. 3<br />
Jodocus Clichtoveus was born Josse Clichtove in<br />
Nieuport, Belgium but spent most <strong>of</strong> his life in France<br />
editing early books in mathematics. See the entry for<br />
Jordanus, 1514, for remarks on Faber Stapulensis.<br />
As Smith (Rara, p. 30) points out, the various early<br />
editions <strong>of</strong> Boethius’ Arithmetic differ only in the<br />
combination <strong>of</strong> works they contain. In this edition<br />
Clichtoveus and Faber Stapulensis added material<br />
that would have fitted neatly into the curriculum <strong>of</strong> the<br />
quadrivium, namely works on the basic arithmetical<br />
operations, geometry and astronomy. The work on<br />
geometry is richly illustrated with marginal diagrams.<br />
Illustrations available:<br />
Title page<br />
Geometry page<br />
Astronomy colophon<br />
Astronomy colophon, B 186<br />
B 187<br />
[Boethius, Anicius Manlius Severinus (CA. 480–524)];<br />
Jacobus Faber Stapulensis (1455–1536) and Johann<br />
Jacobi Scheubel<br />
Fabri Stapulensis in arithmetica Boëthi epitome, unà<br />
cum difficiliorum locorum explicationibus & figuris<br />
(quibus antea carebat) nunc per Joannem Scheubelium<br />
adornatis & adjectis. Accessit Christierni Morsiani<br />
arithmetica practica, in quinqe partes digesta:<br />
quarum I. est de numeris integris. II. de fractionibus<br />
vulgaribus & physicis. III. de regulis quibusdam.<br />
165
IIII. de progressione & radicum extractione. V. de<br />
proportionibus.<br />
166<br />
Year: 1553<br />
Place: Basel<br />
Publisher: Henricus Petrus<br />
Edition: 10th<br />
Language: Latin<br />
Binding: paper wrappers<br />
Pagination: pp. 144<br />
Collation: A–I 8<br />
Size: 161x102 mm<br />
Reference: Smi Rara, p. 522; Rcrdi BMI II, p. 165<br />
This edition <strong>of</strong> Boethius’ Arithmetic, with comments by<br />
Faber Stapulensis, was produced by Johann Scheubel<br />
(1494–1570), who was a pr<strong>of</strong>essor <strong>of</strong> mathematics<br />
at Tubingen. See the entry for Jordanus, 1514, for<br />
comments on Faber Stapulensis.<br />
Illustrations available:<br />
Title page<br />
Colophon<br />
[Boethius, Anicius Manlius Severinus]<br />
See Jordanus de Nemore; In hoc opere contenta<br />
arithmetica decem libris demonstrata, 1514.<br />
B 188<br />
B<strong>of</strong>fito, Giuseppe (1869–1944)<br />
Gli strumenti della scienza e la scienza degli strumenti.<br />
Con l’illustrazione della tribuna di Galileo<br />
Year: 1929<br />
Place: Florence<br />
Publisher: Seeber<br />
Edition: 1st<br />
Language: Italian<br />
Figures: 136 lithograph plates<br />
Binding: original paper wrappers<br />
Pagination: pp. xvi, 217, [3]<br />
Collation: π 8 1–13 8 14 6<br />
Size: 250x177 mm<br />
Reference: Not in Rcdi BMI<br />
The prolific Barnabite priest and bibliographer B<strong>of</strong>fito, is<br />
noted not only for his exegesis <strong>of</strong> Dante’s Divine Comedy,<br />
but also for initiating the Bibliografia Galileiana.<br />
Erwin Tomash Library<br />
Boethius, Anicius Manlius Severinus Boisseau, Jean<br />
Galileo sector, B 188<br />
The present work, which discusses a collection <strong>of</strong><br />
scientific instruments, emphasizing those associated<br />
with Galileo, was issued in an edition <strong>of</strong> three hundred,<br />
only a hundred and eighty being <strong>of</strong>fered for sale. The<br />
others were apparently distributed to scholars—this<br />
is the copy owned by Henry Guerlac. The first part <strong>of</strong><br />
the text discusses the origins and evolution <strong>of</strong> scientific<br />
instruments, including other European and Arabic<br />
devices, and the second part discusses the origin <strong>of</strong><br />
museums devoted to them.<br />
The plates illustrate scientific instruments from all fields,<br />
mainly as shown in early printed books but occasionally<br />
as photographs. The plates also include a copy <strong>of</strong> the<br />
eleven-page manuscript <strong>of</strong> the first inventory <strong>of</strong> the<br />
Collezione Medicea agle Uffizi, 1654.<br />
Illustrations available:<br />
Front cover<br />
Title page<br />
Photo <strong>of</strong> Galileo sector<br />
B 189<br />
Boisseau, Jean (fl.1637–1658)<br />
Methode tres facile pour se servir de sinopse ou tableau<br />
circulaire tres utile et necessaire pour toutes sortes de<br />
personnes, & principalement ceux qui se plaisent à<br />
la science d’arithmetique avec une declaration de la<br />
valeur des poids & measures<br />
Year: 1637<br />
Place: Paris<br />
Publisher: Jean Boisseau<br />
Edition: Broadside<br />
Language: French<br />
Figures: broadside<br />
Binding: none<br />
Pagination: two sheets joined together.<br />
Size: 550x403 mm<br />
B 188
Erwin Tomash Library<br />
Boissière, Claude de Boissière, Claude de<br />
Jean Boisseau was a French geographer and genealogist<br />
who had an appointment as Enlumineur du Roi.<br />
This is a multiplication table in the form <strong>of</strong> a large<br />
circular volvelle (lacking the movable pointer). The<br />
device consists <strong>of</strong> thirty-seven concentric circles<br />
containing multiples <strong>of</strong> numbers found in the innermost<br />
circle. To multiply, one found the number (or one <strong>of</strong> its<br />
components, as after 10, only multiples <strong>of</strong> 10, 100, or<br />
1000 are shown) in the innermost circle, then moved<br />
the pointer (which evidently had the same markings as<br />
the sector with the multiples <strong>of</strong> 1 inscribed in it) to that<br />
sector. The product could be found by inspecting the<br />
value in the outer circle corresponding to the multiplier<br />
(or one <strong>of</strong> its components).<br />
The conversion table on the second sheet gives various<br />
systems <strong>of</strong> weights and measures for different goods:<br />
cloth <strong>of</strong> various kinds and origins, grains, wine, gold,<br />
time and distance, with the factors for converting them<br />
to the French systems.<br />
This device was known to Harsdörffer (see entry for<br />
Schwenter, Daniel and Harsdörffer, Georg Phillip;<br />
Deliciae physico-mathematicae, 1651), who reproduced<br />
a modified version. Leupold (Theatrum, 1727) also<br />
reproduced a version but had to rely on Schwenter’s<br />
example as he could not find an original. No other<br />
original example <strong>of</strong> this work is known.<br />
Illustrations available:<br />
Several scans, each showing a portion <strong>of</strong> the large instrument.<br />
B 190<br />
Boissière, Claude de (1554–1608)<br />
L’ art d’arythmetique contenant toute dimention, tres<br />
singulier et commode, tant pour l’art militaire, que<br />
autres calculations<br />
Year: 1554<br />
Place: Paris<br />
Publisher: Annet Briere<br />
Edition: 1st<br />
Language: French<br />
Binding: modern leather; covers gilt embossed; gilt spine<br />
Pagination: ff. 72<br />
Collation: A–I 8<br />
Size: 170x105 mm<br />
Reference: Smi Rara, pp 260–262<br />
Claude de Boissière was a philosopher, astronomer,<br />
mathematician and musician born near Grenoble.<br />
This arithmetic book is considered by some to have been<br />
written for students at the <strong>University</strong> <strong>of</strong> Paris. Smith<br />
(History <strong>of</strong> mathematics) prefers to classify Boissière as<br />
a dilettante <strong>of</strong> mathematics.<br />
The text is a combination <strong>of</strong> an elementary practical<br />
arithmetic and a discussion <strong>of</strong> theoretical aspects much<br />
like those treated by Boethius. It not only begins with<br />
simple numeration but carries this to the extreme. It<br />
mentions the usual orders such as units, tens, hundreds,<br />
etc. but also extends the system to Mille de Quintillions<br />
(thousands <strong>of</strong> quintillions). It is interesting that this<br />
section gives names for orders such as bimillions (a<br />
million million), trimillions (a million million million),<br />
quadrimillion, etc. but then indicates that it is suitable<br />
to shorten these names to billion or trillion to avoid<br />
confusion.<br />
B 190<br />
Pythagorean example, B 190<br />
After treating the four standard arithmetical operations<br />
(the only interesting variant is that he does subtraction<br />
very differently from the way it is done today—see<br />
illustration), he proceeds to a second book, in which he<br />
treats the more theoretical subjects. He considers not<br />
only the usual Boethian type <strong>of</strong> figurative numbers but<br />
167
also regular solids as well and some elementary survey<br />
problems illustrated with a diagram <strong>of</strong> the Pythagorean<br />
theorem. The work concludes with an interesting<br />
multiplication table that shows the names <strong>of</strong> relations<br />
between various numbers.<br />
168<br />
Illustrations available:<br />
Title page<br />
Subtraction<br />
Figures with regular faces<br />
Pythagorean example<br />
Multiplication table<br />
Colophon<br />
Erwin Tomash Library<br />
Boissière, Claude de Boissière, Claude de<br />
B 191<br />
Boissière, Claude de (1554–1608)<br />
Subtraction example, B 190<br />
L’ art d’arithmetique, contenant toute dimension: tres<br />
singulier & commode, tant pour l’art militaire, que<br />
pour la geometrie, & autres calculations … Reveu &<br />
augmenté par Lucas Tremblay …<br />
Year: 1563<br />
Place: Paris<br />
Publisher: Guillaume Cavellat<br />
Edition: 2nd<br />
Language: French<br />
Binding: contemporary vellum<br />
Pagination: ff. 72<br />
Collation: A–I 8<br />
Size: 170x105 mm<br />
Reference: Smi Rara, pp. 260–262<br />
This is the second edition <strong>of</strong> Nobilissimus et antiquissimus<br />
ludus Pythagoreus. Other than obvious typographic<br />
changes that have taken place (non now replaces nõ,<br />
etc.) the content <strong>of</strong> this edition is unchanged from that<br />
<strong>of</strong> the first.<br />
Illustrations available:<br />
Title page<br />
Gaming pieces, B 192<br />
B 192<br />
Boissière, Claude de (1554–1608)<br />
B 191<br />
B 192<br />
Nobilissimus et antiquissimus ludus Pythagoreus (qui<br />
Rythmomachia nominatur) in utilitatem & relaxationem<br />
studiosorum comparatus ad veram & facilem<br />
proprietatem & rationem numerorum assequendam …<br />
Year: 1556<br />
Place: Paris<br />
Publisher: Guillaume Cavellat<br />
Edition: 1st Latin<br />
Language: Latin<br />
Binding: contemporary blind stamped leather; vellum end<br />
papers<br />
Pagination: ff. 52<br />
Collation: A–F 8 G 4<br />
Size: 170x110 mm
Erwin Tomash Library<br />
Bolaffio, Jozé Vita Bonelli, Maria Luisa Righini<br />
Originally published in French in 1554, this Latin<br />
edition followed two years later. Boissière considered<br />
himself a mathematics teacher and used the game <strong>of</strong><br />
Rythmomachia as a vehicle for teaching arithmetic.<br />
Smith (History <strong>of</strong> Mathematics) indicates that Of the<br />
three standard treatises on the ancient number game<br />
<strong>of</strong> Rythmomachia … this is the clearest. All three are<br />
represented in this collection (see entries for Barozzi,<br />
1572, and Jordanus, 1514), and the other entries should<br />
be consulted for details. It is perhaps the clearest because<br />
it is, by far, the longest <strong>of</strong> the three and thus contains<br />
more detailed explanations <strong>of</strong> everything from the shape<br />
<strong>of</strong> the game board to the shapes <strong>of</strong> the pieces. According<br />
to Folkerts, Boissière’s history <strong>of</strong> the game is faulty.<br />
An English translation <strong>of</strong> this work is in J. F. C. Richards,<br />
“Boissière’s Pythagorean game,” Scripta Mathematica,<br />
vol. 12 (1946) pp. 177–217.<br />
Illustrations available:<br />
Title page<br />
Some <strong>of</strong> the gaming pieces<br />
B 193<br />
Bolaffio, Jozé Vita<br />
B 193<br />
Numeros certos para formar as combinaçoens de<br />
cambio entre a Praça de Lisboa e diversas outras<br />
Praças da Europa que tem cambio estabelecido com a<br />
mesma.<br />
Year: 1803<br />
Place: Vienna<br />
Publisher: Mathias André Schmidt<br />
Edition: 1st<br />
Language: Portuguese<br />
Figures: printed engraved table<br />
Binding: contemporary paper wrappers<br />
Pagination: pp. [14], [2]<br />
Size: 191x152 mm<br />
This set <strong>of</strong> tables relates the currency <strong>of</strong> Lisbon to that <strong>of</strong><br />
several major European trading centers.<br />
Illustrations available:<br />
Title page<br />
B 194<br />
Bolle, Georges, editor<br />
Conférence sur les applications des machines<br />
statistiques au P. -L.- M.<br />
Year: 1930<br />
Place: Nancy<br />
Publisher: Imprimerie Berger-Levrault<br />
Edition: 1st<br />
Language: French<br />
Figures: 2 photographic plates<br />
Binding: original paper wrappers<br />
Pagination: pp. 22, [10]<br />
Size: 270x180 mm<br />
These are the proceedings <strong>of</strong> a conference on punched<br />
card tabulating machines held in Paris. There is little<br />
technical detail, but several interesting photographs show<br />
the participants at the conference banquet or watching<br />
demonstrations <strong>of</strong> the equipment in use.<br />
Illustrations available:<br />
Front cover<br />
Bond, Henry (ca.1600–1678)<br />
See Phillippes, Henry; The sea-mans kalendar: or, an<br />
ephemerides <strong>of</strong> the sun, moon, and certain <strong>of</strong> the<br />
most notable fixed stars, 1674.<br />
B 195<br />
Bonelli, Maria Luisa Righini<br />
Catalogo degli strumenti del Museo di Storia della<br />
Scienza<br />
Year: 1954<br />
Place: Florence<br />
Publisher: Olschki<br />
Edition: 1st<br />
Language: Italian<br />
Figures: 16 photographic plates (1 folding)<br />
Binding: contemporary quarter leather boards; spine gilt<br />
Pagination: pp. viii, 394, [2]<br />
Size: 234x162 mm<br />
Reference: Not in Rcdi BMI<br />
This is a catalog <strong>of</strong> the scientific instruments in the<br />
collection housed in the Museo di Storia della Scienza<br />
in Florence. The section on mathematical instruments<br />
169
is significant as it contains an entry for and photograph<br />
<strong>of</strong> the mechanical geared sector invented by Samuel<br />
Morland.<br />
170<br />
Illustrations available:<br />
Title page<br />
Samuel Morland’s mechanical sector<br />
Catalogue entry for Morland’s mechanical sector<br />
Erwin Tomash Library<br />
Boneto, Hebræo Bonocchi, Giovanni Battista<br />
Morland’s sector, B 195<br />
B 196<br />
Bonet de Lates (Boneto, Hebræo) (? –1514 or 1515)<br />
Annuli astronomici utilitatu[m] liber ad Alexandrum<br />
sextu[m] Po[n]tifice[m] maximum<br />
Year: 1558<br />
Place: Paris<br />
B 196<br />
Publisher: G. Cavellat<br />
Edition: 1st (Collected, 2nd issue)<br />
Language: Latin<br />
Binding: modern vellum<br />
Pagination: ff. 8, 159, [1] (i.e. ff. 103v–117)<br />
Collation: A 8 a–v 8<br />
Size: 162x106 mm<br />
Reference: H&L, #2589, p. 588<br />
Bonetus Hebraeus, as he is sometimes known, was a<br />
physician and astrologer to Pope Alexander VI. This<br />
work deals with a design for an astrolabe that could be<br />
made into a ring for his Pope. The device is completely<br />
impractical because <strong>of</strong> its small size but would have<br />
made a very impressive bit <strong>of</strong> jewelry.<br />
Illustrations available:<br />
Title page with ring illustration<br />
Bonnycastle, John, editor<br />
See Bossut, <strong>Charles</strong>; A general history <strong>of</strong> mathematics<br />
from the earliest times, to the middle <strong>of</strong> the<br />
eighteenth century, 1803<br />
B 197<br />
Bonocchi, Giovanni Battista<br />
B 197<br />
Breve, et universale risolutione d’aritmetica, con la<br />
quale facilmente ogn’uno potrà rittouar, qual si voglia<br />
sorte di misura di terra all’uso del stato di Milano, & in<br />
ogni parte, doue si và à pertica.<br />
Year: 1617<br />
Place: Lodi<br />
Publisher: Paolo Bertoetti
Erwin Tomash Library<br />
Boole, George Boole, George<br />
Edition: 2nd<br />
Language: Italian<br />
Binding: original paper wrappers<br />
Pagination: pp. [4], 72<br />
Collation: * 2 A–I 4<br />
Size: 261x191 mm<br />
Reference: Smi Rara, p. 347; Rcdi BMI, Vol. I, p. 154<br />
This is a set <strong>of</strong> tables for converting units <strong>of</strong> measurement<br />
used in and around Milan. The first two pages provide a<br />
very short explanation, and the rest <strong>of</strong> the work is made<br />
up <strong>of</strong> the tables.<br />
Illustrations available:<br />
Title page<br />
Page <strong>of</strong> tables<br />
B 198<br />
Boole, George (1815–1864)<br />
An investigation <strong>of</strong> the laws <strong>of</strong> thought on which<br />
are founded the mathematical theories <strong>of</strong> logic and<br />
probabilities<br />
Year: 1854<br />
Place: London<br />
Publisher: Macmillan<br />
Edition: 1st<br />
Language: English<br />
Binding: modern leather; gilt spine; red leather label<br />
Pagination: pp. [12], 426, 6<br />
Collation: * 6 B–2E 8<br />
Size: 224x138 mm<br />
The son <strong>of</strong> a Lincolnshire cobbler who was also an<br />
amateur mathematician and lens grinder, George Boole<br />
was a promising student, but his family circumstances<br />
prevented him from obtaining more than an ordinary<br />
school education. After leaving school at age 15, he<br />
found work as an assistant teacher in the area and, with<br />
his father’s encouragement, set up his own school. In<br />
his spare time he mastered Latin, Greek and several<br />
European languages, as well as mathematics.<br />
He found ample opportunity to satisfy his wide-ranging<br />
intellectual curiosity when, in 1834, the Mechanics<br />
Institution was founded in Lincoln, and Boole was<br />
hired to be in charge <strong>of</strong> the reading room. His first<br />
mathematical paper appeared in 1840, when he was 25<br />
years old, and in 1844 his seminal paper, “On a general<br />
method <strong>of</strong> analysis,” appeared in the Philosophical<br />
Transactions <strong>of</strong> the Royal Society, which resulted in<br />
his receiving the first Royal Society Gold Medal for<br />
Mathematics. His most famous work, which established<br />
the principles <strong>of</strong> symbolic logic, is The mathematical<br />
analysis <strong>of</strong> logic, being an essay towards a calculus <strong>of</strong><br />
deductive reasoning, published in 1847.<br />
B 198<br />
In 1849, he was appointed to the pr<strong>of</strong>essorship <strong>of</strong><br />
mathematics at Queen’s College, Cork, despite his lack<br />
<strong>of</strong> formal qualifications. He made many contributions<br />
to mathematics, but his most significant work was the<br />
creation <strong>of</strong> mathematical logic. Several people, most<br />
notably Leibniz and DeMorgan, had attempted some<br />
type <strong>of</strong> algebraic treatment <strong>of</strong> logic prior to Boole, but<br />
none had managed to overcome the difficulties that<br />
arose when considering anything beyond the most trivial<br />
situations.<br />
Boole’s entry into this field was due to a simple argument<br />
between DeMorgan and the Scottish philosopher W.<br />
Hamilton. Hamilton had derided some <strong>of</strong> DeMorgan’s<br />
attempts to introduce the systems <strong>of</strong> algebra into logic,<br />
asserting that logic was the realm <strong>of</strong> the philosopher and<br />
that mathematics was dangerous and useless. Boole,<br />
using Hamilton’s own arguments, showed that logic was<br />
not part <strong>of</strong> philosophy. He then proceeded to examine<br />
whether logic, like geometry, might be founded on a<br />
group <strong>of</strong> axioms (see entry for Boole, The mathematical<br />
analysis <strong>of</strong> logic, 1847).<br />
In recent times, Boolean logic has found widespread use<br />
in the design <strong>of</strong> digital computers and communications<br />
systems.<br />
In the present book, Boole applied algebraic methods to<br />
logic and initiated a revolution in mathematics, to say<br />
nothing <strong>of</strong> philosophy and linguistics. While his earlier<br />
171
publications presented preliminary results, this volume<br />
provided a complete exposition <strong>of</strong> Boole’s system,<br />
which was, indeed, the description <strong>of</strong> an entirely new<br />
form <strong>of</strong> algebra.<br />
The work is dedicated to John Ryall, Pr<strong>of</strong>essor <strong>of</strong> Greek<br />
in Queen’s College, a personal friend and uncle to<br />
Boole’s wife.<br />
172<br />
Illustrations available:<br />
Title page<br />
Erwin Tomash Library<br />
Boole, George Boole, George<br />
B 199<br />
Boole, George (1815–1864)<br />
B 199<br />
The mathematical analysis <strong>of</strong> logic, being an essay<br />
towards a calculus <strong>of</strong> deductive reasoning.<br />
Year: 1847<br />
Place: Cambridge<br />
Publisher: Macmillan, Barclay & Macmillan<br />
Edition: 1st<br />
Language: English<br />
Binding: modern paper boards<br />
Pagination: pp. [2], 82<br />
Collation: π 2 B–F 8<br />
Size: 205x128 mm<br />
the first entry for Boole and entries for DeMorgan). It<br />
was this volume that began the revolution that led to the<br />
development <strong>of</strong> mathematical logic.<br />
Illustrations available:<br />
Title page<br />
B 200<br />
Boole, George (1815–1864)<br />
Studies in logic and probability<br />
Year: 1952<br />
Place: La Salle, IL<br />
Publisher: Open Court Publishing<br />
Edition: 1st<br />
Language: English<br />
Figures: portrait frontispiece<br />
Binding: original cloth boards; with dust jacket<br />
Pagination: pp. 500<br />
Collation: A–2G 8 2H 10<br />
Size: 210x137 mm<br />
This is volume 1 <strong>of</strong> Boole’s papers, edited by R.<br />
Rhees. In addition to the original works (from the 1847<br />
Mathematical analysis <strong>of</strong> logic to an 1862 work, On the<br />
theory <strong>of</strong> Probabilities) and editorial notes, it contains<br />
Boole’s own annotations and revisions that he may have<br />
made in subsequent years.<br />
Illustrations available:<br />
Title page with frontispiece <strong>of</strong> Boole’s portrait.<br />
This is Boole’s first work on logic, in the introduction to<br />
which he first refuted W. Hamilton’s claim that logic was<br />
a part <strong>of</strong> philosophy and that no mathematician could<br />
possibly contribute anything to this field (see remarks in B 200
Erwin Tomash Library<br />
Boole, George Booth, Andrew Donald<br />
B 201<br />
Boole, George (1815–1864)<br />
A treatise on the calculus <strong>of</strong> finite differences.<br />
Year: 1860<br />
Place: Cambridge<br />
Publisher: Macmillan<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards<br />
Pagination: pp. [viii], 248<br />
Collation: π 4 1–15 8 16 4<br />
Size: 190x126 mm<br />
This work contains material for which George Boole was<br />
well known in his lifetime but which is now so completely<br />
overshadowed by his contributions to mathematical logic<br />
as to be almost forgotten.<br />
Illustrations available:<br />
Title page<br />
B 202<br />
Booth, Andrew Donald (1918–)<br />
Numerical methods<br />
George Boole, B 200<br />
Year: 1955<br />
Place: London<br />
Publisher: Butterworths Scientific Publications<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards<br />
Pagination: pp. viii, 196<br />
Size: 218x136 mm<br />
B 201<br />
Booth was a member <strong>of</strong> staff at Birkbeck College in<br />
London. He became interested in computation early in<br />
his career. Immediately after World War II, he had an<br />
opportunity to visit the United States and see computer<br />
developments there. In particular, he spent some time<br />
at the <strong>Institute</strong> for Advanced Study. Upon his return to<br />
England, he commenced the construction <strong>of</strong> a small<br />
relay-based computer (he was unable to afford electronic<br />
components, and, more importantly, the infrastructure that<br />
would be required to both experiment with and construct<br />
the final circuits). He was aided in this project by his<br />
father, a fine mechanical engineer, and Miss Kathleen<br />
Britten, who later became his wife. These projects are<br />
described in the works noted in other entries.<br />
Booth was known for the creation <strong>of</strong> a number <strong>of</strong><br />
computing machines all based upon the same basic<br />
design. He and his father eventually went into business<br />
as Wharf Engineering and produced magnetic drums that<br />
were widely used on early computers. In the early 1960s,<br />
Booth again visited the U.S., then moved to Canada as<br />
dean <strong>of</strong> engineering at the <strong>University</strong> <strong>of</strong> Saskatchewan,<br />
where he continued to make small transistor computers<br />
for experimental use. He later became president <strong>of</strong><br />
Lakehead <strong>University</strong> in Canada.<br />
This work on numerical methods was published just<br />
as the computer revolution was beginning and was<br />
one <strong>of</strong> the first books to be oriented towards this new<br />
technology. The students who used this text at Birkbeck<br />
173
174<br />
Erwin Tomash Library<br />
Booth, Andrew Donald Booth, Andrew Donald<br />
College were introduced to the world <strong>of</strong> computers<br />
much earlier than others studying numerical methods<br />
and, as a consequence, were <strong>of</strong>ten subjected to much<br />
less <strong>of</strong> the drudgery <strong>of</strong> hand computation than their<br />
contemporaries.<br />
Illustrations available:<br />
Title page<br />
B 203<br />
Booth, Andrew Donald (1918–)<br />
B 202<br />
Two calculating machines for X-ray crystal structure<br />
analysis In Journal <strong>of</strong> Applied Physics, Volume 18, No.<br />
7, July 1947.<br />
Year: 1947<br />
Place: Lancaster, PA<br />
Publisher: American <strong>Institute</strong> <strong>of</strong> Physics<br />
Edition: 1st<br />
Language: English<br />
Binding: original paper wrappers<br />
Pagination: pp. 664–666<br />
Size: 269x201 mm<br />
This short paper describes two analog machines <strong>of</strong> use<br />
in the analysis <strong>of</strong> crystal structures. The first is rather<br />
specialized, but the second is a simple device for<br />
summing cosines.<br />
Illustrations available:<br />
None<br />
B 204<br />
Booth, Andrew Donald (1918–) and Kathleen H. V.<br />
Booth<br />
Automatic digital calculators<br />
Year: 1953<br />
Place: London<br />
Publisher: Butterworths Scientific Publications<br />
Edition: 1st<br />
Language: English<br />
Figures: 4 photographic plates<br />
Binding: original boards<br />
Pagination: pp. viii, 232<br />
Size: 216x137 mm<br />
Reference: Ran ODC, p. 408<br />
B 204<br />
This is a very early work on electronic computers.<br />
After an simple introduction to mechanical calculating<br />
machines and a description <strong>of</strong> their electronic equivalents,<br />
it discusses the design <strong>of</strong> a computer and how it might be<br />
implemented using electronics. By this time the Booths<br />
had acquired considerable experience with the creation<br />
<strong>of</strong> different types <strong>of</strong> memory devices. This experience is<br />
shown in the very well-developed section on computer<br />
memories, ranging from mechanical devices invented by<br />
the Booths (see illustration), through magnetic drums, to<br />
delay line and electrostatic memory devices. They even<br />
have a small section on magnetic core memory and an<br />
aside that implies that they had been thinking about thin–<br />
film plated memory. The book finishes with a discussion
Erwin Tomash Library<br />
Booth, Andrew Donald Booth, Andrew Donald<br />
<strong>of</strong> programming, the use <strong>of</strong> subroutines and some<br />
examples such as X-ray crystal structure analysis—a<br />
subject in which the Booths had previous experience.<br />
This book, which has the feel <strong>of</strong> being written by someone<br />
who actually knows the material very well and can<br />
explain it in a way that is easily understood, was a success<br />
in Britain but, while known and appreciated by some in<br />
America, did not receive the same acknowledgement<br />
here.<br />
Illustrations available:<br />
Title page<br />
A.P.E.(R)C. machine<br />
Disk/pin mechanical memory<br />
A.P.E.(R)C. machine, B 204<br />
Disk/pin mechanical memory, B 204<br />
B 205<br />
Booth, Andrew Donald (1918–) and Kathleen H. V.<br />
Booth<br />
Automatic digital calculators<br />
Year: 1956<br />
Place: London<br />
Publisher: Butterworths Scientific Publications<br />
Edition: 2nd<br />
Language: English<br />
Figures: 4 photographic plates<br />
Binding: original cloth boards; with dust jacket<br />
Pagination: pp. xii, 262<br />
Size: 216x138 mm<br />
This second edition has been extended by the new<br />
discoveries <strong>of</strong> the Booths and others. Although the same<br />
material is covered as in the first edition, there is, for<br />
example, a more detailed treatment <strong>of</strong> magnetic core<br />
memory.<br />
A third edition (also in the collection) was published<br />
in 1965 after the Booths had moved from Britain to<br />
Canada. While they provided a major revision for this<br />
later edition, it soon became clear that this book was not<br />
appropriate for the middle <strong>of</strong> the 1960s. Some <strong>of</strong> the<br />
material, for example, the mechanical memory and relay–<br />
based circuits, was simply out-<strong>of</strong>-date, and readers were<br />
in search <strong>of</strong> programming descriptions more applicable<br />
to individual machines. The frontispiece was changed to<br />
show a new M3 computer that the Booths had developed<br />
at the <strong>University</strong> <strong>of</strong> Saskatchewan.<br />
Illustrations available:<br />
Title page<br />
B206.<br />
Booth, Andrew Donald (1918–) and Kathleen H.V.<br />
Britten<br />
Principles and progress in the construction <strong>of</strong> highspeed<br />
digital computers. In Quarterly Journal <strong>of</strong><br />
Mechanics and Applied Mathematics, Vol. II, Pt 2, June<br />
1949.<br />
Year: 1949<br />
Place: Oxford<br />
Publisher: Clarendon Press<br />
Edition: 1st<br />
Language: English<br />
Binding: original paper wrappers<br />
Pagination: pp. 182–197<br />
Collation: K–R 8<br />
Size: 233x155 mm<br />
At this time Kathleen Britten was an assistant to A. D.<br />
Booth at Birkbeck College and was shortly to become<br />
Mrs. Booth.<br />
This is a very early discussion <strong>of</strong> the principles <strong>of</strong> the<br />
stored program computer as they were understood in<br />
1947, when the paper was first written. After a brief<br />
discussion <strong>of</strong> digital versus analog computers, the basic<br />
structure <strong>of</strong> the stored program computer is explained.<br />
The paper finishes with a discussion <strong>of</strong> the state <strong>of</strong><br />
computer projects in the United States (A. D. Booth<br />
having just returned from a trip there), including those<br />
<strong>of</strong> Aiken’s Mark II, the Bell Model V, the EDVAC and<br />
von Neumann’s IAS machine. Several noteworthy items<br />
appear in this paper, including the distinction between<br />
175
176<br />
Erwin Tomash Library<br />
Borda, Jean <strong>Charles</strong> de Borghi, Pietro<br />
serial and parallel machine architecture and a description<br />
<strong>of</strong> the operation code for the Booth ARC (Automatic<br />
Relay Computer).<br />
It should be noted that this paper was written (but not<br />
published) before an operating stored program computer<br />
existed.<br />
Illustrations available:<br />
ARC instruction set.<br />
B 207<br />
Borda, Jean <strong>Charles</strong> de (1733–1799)<br />
Tables trigonométriques décimales, ou table des<br />
logarithmes des sinus, sécantes et tangentes, suivant<br />
la division du quart de cercle en 100 degrés, du degré<br />
en 100 minutes, et de la minute en 100 secondes.<br />
Précédées de la table des logarithmes des nombres<br />
depuis dix mille jusqu’à cent mille, et de plusiers tables<br />
subsidiares.<br />
Year: 1801<br />
Place: Paris<br />
Publisher: Imprimerie de la République<br />
Edition: 1st<br />
Language: French<br />
Binding: quarter bound leather, marbled boards<br />
Pagination: pp. [4],120, [510]<br />
Collation: π 2 a–p 4 a–2d 4 2e 2 A–2N 4 2O 1<br />
Size: 237x187 mm<br />
Reference: Glais RCMT, pp. 88–89; Kno NTMV, p. 71<br />
Borda was a major figure in the French Navy who<br />
participated in several scientific voyages and in the<br />
American Revolution. He was a member <strong>of</strong> the group<br />
B 207<br />
responsible for measuring the length <strong>of</strong> the meridional<br />
arc from the North Pole to the equator and thus was<br />
active in establishing the metric system. He attained<br />
the rank <strong>of</strong> Capitaine de Vaisseau and was appointed as<br />
inspector <strong>of</strong> the French naval academy in 1784. Borda<br />
was taken prisoner by the British during a naval action<br />
in the Antilles in 1782; thereafter his health suffered<br />
to the point where he was unable to take up his former<br />
sea duties. His main contributions were to the design <strong>of</strong><br />
ships and in studies showing Newton was incorrect in his<br />
theory <strong>of</strong> fluid flow. He invented a surveying instrument<br />
(circle de réflexion), and these tables may well have<br />
begun as an adjunct to its use.<br />
This is the first publication <strong>of</strong> a table <strong>of</strong> logarithms <strong>of</strong><br />
trigonometric functions calculated according to the one<br />
hundred-degree division <strong>of</strong> the quadrant that was initially<br />
proposed for the metric system. The tables have entries<br />
for each degree, minute and second <strong>of</strong> this division<br />
scheme. It contains two prefaces, the first <strong>of</strong> 38 pages<br />
by Borda and the second <strong>of</strong> 76 pages by Delambre, who<br />
saw the work through the press after Borda died.<br />
Illustrations available:<br />
Title page<br />
Tape <strong>of</strong> the tables<br />
B 208<br />
Borghi, Pietro (–1494)<br />
Qui comenza la nobel opera de arithmethica ne la<br />
qual se tracta tute cosse amercantia pertinente facta e<br />
compilata p[er] Piero Borgi da veniesia.<br />
First page: SDSU Chi d’arte mathematice ha paicere<br />
… [17 line sonnet]<br />
Year: 1484<br />
Place: Venice<br />
Publisher: Erhard Ratdolt<br />
Edition: 1st<br />
Language: Italian<br />
Binding: later limp vellum<br />
Pagination: ff. [1], 116, [1] (misnumbered 22 as 32, 23 as 32,<br />
102 as 103)<br />
Collation: π 8 b–o 8 p 6<br />
Size: 202x152 mm<br />
Reference: Smi Rara, pp. 16-18<br />
Pietro Borghi (Piero Borgi) was a Venetian who died<br />
sometime after 1494, but nothing more is known <strong>of</strong> his<br />
life.<br />
This is an important book in the history <strong>of</strong> arithmetic.<br />
It is the second arithmetic book printed in Italy (after<br />
the Treviso arithmetic). The description done by Smith<br />
(Rara) cannot be bettered, and what follows is drawn<br />
freely from that source.
Erwin Tomash Library<br />
Borghi, Pietro Borghi, Pietro<br />
B 208<br />
The first and last folios contain poems headed by the<br />
initials SDSU (some read it as SHSU), about which there<br />
has been much speculation. Smith seems to think that the<br />
letters S H S U which appear twice are thought to stand<br />
for J H S U, Jesus, possibly changed on account <strong>of</strong> some<br />
conjectured pronunciation.<br />
This work is more elaborate than the Treviso arithmetic<br />
and had far greater influence on education. More than<br />
any other book, it set a standard for the arithmetics <strong>of</strong> the<br />
succeeding century. Borghi first treats notation, carrying<br />
his numbers as high as 1 numero de million de million de<br />
million and making no mention whatever <strong>of</strong> the Roman<br />
numerals. In the same spirit, he eliminates all <strong>of</strong> the<br />
medieval theory <strong>of</strong> numbers, asserting that he does this<br />
because he is preparing a practical book for the use <strong>of</strong><br />
merchants.<br />
The sequence <strong>of</strong> material is unusual because<br />
multiplication is the first operation Borda considers.<br />
This is followed by division, despite the fact that both<br />
<strong>of</strong> these use addition and subtraction. The multiplication<br />
table (see illustration) gives the products <strong>of</strong> all pairs <strong>of</strong><br />
numbers from 1 – 10 but also includes the products <strong>of</strong><br />
12, 16, 20, 24, 32, 36 because they were useful factors<br />
for the currency then in use. The author gives the method<br />
<strong>of</strong> checking by casting out 7s and 9s. Multiplication per<br />
colonna (i.e., by reference to the columns <strong>of</strong> the table)<br />
follows, with its checks by 7 and 9, and per crocetta<br />
(cross multiplication), showing that these methods<br />
were in common use in Venice <strong>of</strong> the day. Division is<br />
then explained by the galley form; our present method,<br />
then known as the method <strong>of</strong> giving, a danda, was<br />
not mentioned. Then follow addition, subtraction,<br />
denominate numbers, common fractions (also beginning<br />
with multiplication), rule <strong>of</strong> three, partnership, barter,<br />
alligation and false position. The examples are generally<br />
practical, and they reveal much information concerning<br />
business customs at the close <strong>of</strong> the fifteenth century.<br />
Illustrations available:<br />
First folio with “SDSU” poem<br />
First page<br />
Multiplication table<br />
Galley division<br />
Last folio with “SDSU” poem and colophon<br />
Division examples, B 208<br />
Multiplication table, B 208<br />
177
178<br />
Erwin Tomash Library<br />
Borgnis, Giuseppe Antonio Borough, William<br />
B 209<br />
Borgnis, Giuseppe Antonio (ca.1781– )<br />
Traité complet de mécanique appliquée aux arts,<br />
contenant l’exposition méthodique des théories et<br />
des expériences les plus utiles pour diriger le choix,<br />
l’invention, la construction et l’emploi de toutes les<br />
espèces de machines … Des machines imitatives et des<br />
machines théâtrales<br />
Year: 1820<br />
Place: Paris<br />
Publisher: Bachelier<br />
Edition: 1st<br />
Language: French<br />
Figures: 27 engraved folding plates<br />
Binding: half-bound over marbled paper boards<br />
Pagination: pp. [4], viii, [4], 298<br />
Collation: π 2 a 2 b 4 1–37 4 38 1<br />
Size: 249x198 mm<br />
B 209<br />
This is volume 8 <strong>of</strong> an eight-volume set <strong>of</strong> books in which<br />
Borgnis attempted to refine the empirical tradition <strong>of</strong><br />
mechanical engineering into a more scientifically based<br />
approach. His first volume analyzed the elementary<br />
mechanisms such as the lever, and subsequent volumes<br />
dealt in depth with machinery from different application<br />
areas. This eighth volume was devoted to automata,<br />
calculating and measuring machines, telegraph systems<br />
and the machinery used in the theatre. The section on<br />
calculating machines includes linear and circular slide<br />
rules, Pascal’s machine and various devices for drawing<br />
curves or producing correct perspective. The illustration<br />
<strong>of</strong> the internal workings <strong>of</strong> Pascal’s machine is taken<br />
from the Diderot encyclopedia.<br />
Illustrations available:<br />
Title page<br />
Slide rules and top <strong>of</strong> Pascal’s machine<br />
Internal workings <strong>of</strong> Pascal’s machine<br />
B 210<br />
Borough, William (1537–1599)<br />
Pascal’s calculator, B 209<br />
A discourse <strong>of</strong> the variation <strong>of</strong> the compasse, or<br />
magneticall needle. Wherin is mathematically shewed,<br />
the manner <strong>of</strong> the observation effects, and application<br />
ther<strong>of</strong>, made by W. B. And is to be annexed to the new<br />
attractive <strong>of</strong> R. N.<br />
b/w: Norman, Robert; The new attractive, 1592<br />
Year: 1592<br />
Place: London<br />
Publisher: Edward Allde for Hugh Astley<br />
Edition: 3rd<br />
Language: English<br />
Binding: contemporary half-bound leather over marbled<br />
boards; spine gilt<br />
Pagination: ff. [30]<br />
Collation: A–G 4 H 2<br />
Size: 191x137 mm<br />
Reference: STC, 18649; Tay MP I, #26 #58<br />
While most <strong>of</strong> the items in this collection are directly<br />
related to the history <strong>of</strong> computation, there are a few, like<br />
this one, relating to magnetism.
Erwin Tomash Library<br />
Borrel, Jean Böschenstein, Johann<br />
B 210<br />
Borough, who was a comptroller <strong>of</strong> the British Navy,<br />
began his naval career, aged 16, by sailing to Russia in<br />
1553. He continued in maritime trade for the next ten<br />
years and spent most <strong>of</strong> his life connected either with<br />
trade or the Navy.<br />
This work on the variation <strong>of</strong> the compass was not in the<br />
1581 first edition <strong>of</strong> Norman. It was added in the 1585<br />
second edition. Borough edited later editions <strong>of</strong> this<br />
work, including this one, and added additional material<br />
<strong>of</strong> interest to navigators, such as a table <strong>of</strong> star positions.<br />
Some book dealers have claimed that this editing did not<br />
begin until the fourth edition in 1596, but that is likely<br />
in error - see entry for Norman, 1592, where it is clearly<br />
stated on the title page that it has been Newly corrected<br />
and amended by M.W.B.<br />
The original work by Norman (1592) was dedicated to<br />
Borough.<br />
The date has been incorrectly printed as 1562 on the title<br />
page.<br />
Illustrations available:<br />
Borough’s title page<br />
Illustration <strong>of</strong> an instrument for noting variation in the compass<br />
Borrel, Jean (ca.1492–ca.1564/1572)<br />
See Buteo, Johannes; De quadratura circoli libri duo,<br />
ubi multorum quadraturæ confutantur, 1559<br />
B 211<br />
Böschenstein, Johann (1472–1540)<br />
Ain New geordnet Rechen biechlin mit den zyffern den<br />
angenden schülern zu nutz. Inhaltêt die Siben species<br />
Algorithmi mit sampt der Regel de Try. Und sechs<br />
regeln d[er] prüch. Un[d] der regel susti mit vil andern<br />
güten fragen den kündern zum anfang nützbarlich …<br />
Year: 1514<br />
Place: Augsburg<br />
Publisher: Erhart Oeglin<br />
Edition: 1st<br />
Language: German<br />
Figures: woodcut on title page<br />
Binding: later dark blue morocco; raised bands<br />
Pagination: ff. [24]<br />
Collation: A 6 B 4 C 6 D–E 4<br />
Size: 199x142 mm<br />
Reference: Smi Rara, p. 100<br />
Böschenstein was a pr<strong>of</strong>essor <strong>of</strong> Hebrew at Ingolstadt<br />
and Heidelberg and also taught for a time at Antwerp<br />
and Nürnberg. He is chiefly remembered for the fact that<br />
both Luther and Melanchthon were his students.<br />
It is interesting that in the same year that Köbel published<br />
his arithmetic (Ain new geordnet rechen biechlin)<br />
devoted to teaching the subject only by use <strong>of</strong> the table<br />
abacus, Böschenstein should publish this similar work,<br />
which is completely oriented toward the use <strong>of</strong> algorism.<br />
Even the two title pages have a strong similarity—both<br />
with woodcuts, one showing the abacus and the other<br />
algorism on a slate. Smith (Rara) describes this work<br />
as … mercantile in character and presents in condensed<br />
form the essentials <strong>of</strong> business arithmetic. Böschenstein<br />
first starts with consideration <strong>of</strong> the seven basic operations<br />
(numeration, addition, subtraction, mediation, duplation,<br />
multiplication and division) and includes illustrations<br />
involving fractions as well as integers. He then continues<br />
with examples <strong>of</strong> the rule <strong>of</strong> three, etc.<br />
Illustrations available:<br />
Title page<br />
Division with fractions<br />
Colophon<br />
Compas variation instrument, B 210<br />
179
180<br />
Erwin Tomash Library<br />
Bosmans, H. Bossut, <strong>Charles</strong><br />
B 211<br />
Division examples, B 211<br />
Colophon, B 211<br />
Bosmans, H., editor<br />
See Stevin, Simon; La “Thiende de Simon Stevin,”<br />
1924<br />
B 212<br />
Bossut, <strong>Charles</strong> (1730–1814)<br />
Essai sur l’histoire génerale des mathematiques.<br />
Year: 1802<br />
Place: Paris<br />
Publisher: Louis<br />
Edition: 1st<br />
Language: French<br />
Figures: engraved portrait frontispiece<br />
Binding: original red cloth boards; spine gilt<br />
Pagination: v.1: pp. xii, 394, 2; v.2: pp. [4], 426<br />
Collation: v.1: π 6 1–24 8 25 6 ; v.2: π 2 1–26 8 27 5 (-276)<br />
Size: 220x132 mm<br />
Reference: Cre CL, p. 103<br />
Bossut was raised by a paternal uncle after his father<br />
died. He began his study <strong>of</strong> mathematics at the Jesuit<br />
Collège de Lyon, at the age <strong>of</strong> 14, as a student <strong>of</strong> Père<br />
Béraud, who also taught Jean Etienne Montucla and<br />
Joseph Lalande. He was a pr<strong>of</strong>essor at several notable<br />
universities in France, is known to have authored several<br />
textbooks, and is remembered for his contributions<br />
to mathematical education rather than for his own<br />
mathematical studies. He edited an edition <strong>of</strong> the work<br />
<strong>of</strong> Blaise Pascal and contributed to the editing <strong>of</strong> Denis<br />
Diderot’s encyclopedia.<br />
In this two-volume history <strong>of</strong> mathematics, Bossut<br />
laments the lack <strong>of</strong> a decent history <strong>of</strong> the subject.<br />
B 212
Erwin Tomash Library<br />
Bossut, <strong>Charles</strong> Bowden, Bertram Vivian<br />
Montucla had written one previously, but Bossut<br />
considered it<br />
… inelegant, and too much embarrassed with<br />
repetitions; and in his account <strong>of</strong> some modern<br />
discoveries, he displays a spirit <strong>of</strong> nationality,<br />
which ought never to be found in a strict and<br />
impartial historian (see 1803 edition).<br />
The history is <strong>of</strong> interest mainly because Bossut was a<br />
contemporary <strong>of</strong> most <strong>of</strong> the people mentioned in the<br />
second volume and was well acquainted with them and<br />
their work. According to the Biographie Générale, these<br />
people were not pleased with his biographies, and their<br />
recriminations may have contributed to his death in<br />
1814. His translator (see entry for 1803 edition) notes<br />
in a preface:<br />
… it remains only to observe that he (Bossut)<br />
alone must be considered as responsible for the<br />
opinions he maintains, with respect to certain<br />
discoveries, and other points, which, involving<br />
some <strong>of</strong> the highest claims <strong>of</strong> genius and<br />
invention, have given occasion to many violent<br />
disputes, both <strong>of</strong> a personal and even <strong>of</strong> a national<br />
cast.<br />
The first volume treats the history <strong>of</strong> mathematics from<br />
ancient times to the beginnings <strong>of</strong> the calculus, while the<br />
second consists <strong>of</strong> a history to Bossut’s day.<br />
The printing is unusual in that the text only occupies the<br />
top ¾ <strong>of</strong> each page. The frontispiece is a fine engraved<br />
portrait <strong>of</strong> Bossut.<br />
Illustrations available:<br />
Title page<br />
Frontispiece<br />
Frontispiece, B 212<br />
B 213<br />
Bossut, <strong>Charles</strong> (1730–1814) – [John Bonnycastle<br />
(1750?–1821), editor and T. O. Churchill, translator]<br />
A general history <strong>of</strong> mathematics from the earliest<br />
times, to the middle <strong>of</strong> the eighteenth century.<br />
Year: 1803<br />
Place: London<br />
Publisher: J. Johnson<br />
Edition: 1st<br />
Language: English<br />
Binding: later half-bound leather over marbled boards, black<br />
leather label<br />
Pagination: pp. xxvi, 540, [4]<br />
Collation: A 8 a 4 b 1 B–2M 8<br />
Size: 210x128 mm<br />
Bonnycastle, in his earlier publications, described himself<br />
as a teacher <strong>of</strong> mathematics. From 1782 to 1785, he was<br />
a pr<strong>of</strong>essor at the Royal Military Academy in Woolwich,<br />
England. Leigh Hunt describes him as having thought<br />
a little more highly <strong>of</strong> his talents than the amount <strong>of</strong><br />
them strictly warranted (Leigh Hunt, Lord Byron and his<br />
contemporaries).<br />
This is an English translation <strong>of</strong> Bossut’s history <strong>of</strong><br />
mathematics. Bonnycastle appends a list <strong>of</strong> the most<br />
eminent mathematicians <strong>of</strong> ancient and modern times<br />
but does not list any alive at the time, perhaps because<br />
he did not want to be subject to the same problems<br />
Bossut encountered with his contemporaries (see entry<br />
for Bossut, 1802).<br />
Although the translation is rather good, Bonnycastle did<br />
manage to get the author’s name wrong. On the title page<br />
it is given as John Bossut when it was actually <strong>Charles</strong>.<br />
Illustrations available:<br />
Title page<br />
Bossut, <strong>Charles</strong>, editor (1730–1814)<br />
See Pascal, Blaise; Oeuvres de Blaise Pascal<br />
B 214<br />
Bowden, Bertram Vivian (1910–1989)<br />
Faster than thought. A symposium on digital computing<br />
machines<br />
Year: 1953<br />
Place: London<br />
Publisher: Pitman<br />
Edition: 1st<br />
Language: English<br />
Figures: 19 photo plates incl. frontispiece; 2 folding plates<br />
Binding: original boards<br />
Pagination: pp. xx, 416<br />
Size: 228x150 mm<br />
Reference: Ran ODC, p. 408; Dub MWCB, p. 4<br />
181
182<br />
Erwin Tomash Library<br />
Bowden, Bertram Vivian Bowditch, <strong>Charles</strong> Pickering<br />
B 214<br />
Lord Vivian Bowden was an employee <strong>of</strong> Ferranti<br />
Ltd., the manufacturer <strong>of</strong> the Ferranti Mark I originally<br />
designed at Manchester <strong>University</strong>. The Ferranti Mark I<br />
was the first electronic digital computer to be delivered to<br />
a commercial customer (despite the claims <strong>of</strong> UNIVAC).<br />
Ferranti’s first machine was delivered to Manchester<br />
<strong>University</strong>. Essentially a highly placed representative<br />
<strong>of</strong> Ferranti, Bowden was assigned to publicize their<br />
machines and, it was hoped, sell several. This book was<br />
an effort to raise the awareness <strong>of</strong> this new technology in<br />
the hopes <strong>of</strong> kindling interest that would result in sales.<br />
Lord Bowden told the amusing story <strong>of</strong>, when he was<br />
on a trans-Atlantic voyage, meeting a man who was a<br />
lighthouse salesman and recounting that they spent some<br />
time debating which <strong>of</strong> them had the more secure job.<br />
This is, by far, the best anthology on computing<br />
from the 1950s. The contributors are a Who’s Who <strong>of</strong><br />
British computing in that era. Chief among them were<br />
the computer designers T. Kilburn, F. Williams, M.<br />
Wilkes and A. Turing, but the other names listed all<br />
made significant contributions to the development <strong>of</strong><br />
computers, s<strong>of</strong>tware, or education. All the names are<br />
well known today (perhaps with the exception <strong>of</strong> Audrey<br />
Bates, who changed her name to Sharp when she married<br />
Ian Sharp).<br />
After a brief history <strong>of</strong> computing machines, the<br />
contents are divided into theory (today we would term<br />
this computer architecture), reports <strong>of</strong> British computer<br />
projects, a very short summary <strong>of</strong> those in America, and<br />
applications. The last section contains Digital Computer<br />
Applied to Games by Alan Turing—a very early<br />
description <strong>of</strong> programming a computer to play games.<br />
An appendix contains a reprint <strong>of</strong> Lovelace’s paper on<br />
<strong>Babbage</strong>’s Analytical Engine (see Menabrea, Luigi).<br />
A number <strong>of</strong> photographic plates illustrate computers<br />
or their components <strong>of</strong> the era, and the frontispiece is a<br />
portrait <strong>of</strong> Ada Augusta, Countess <strong>of</strong> Lovelace.<br />
The book remained in print until the late 1960s but was<br />
by then out <strong>of</strong> date. A second copy <strong>of</strong> this volume (with<br />
dust jacket) is available in the collection.<br />
Illustrations available:<br />
Title page<br />
Frontispiece (Countess <strong>of</strong> Lovelace)<br />
Frontispiece, B 214<br />
B 215<br />
Bowditch, <strong>Charles</strong> Pickering (1842–1921)<br />
The numeration, calendar systems and astronomical<br />
knowledge <strong>of</strong> the Mayas<br />
Year: 1910<br />
Place: Cambridge<br />
Publisher: Cambridge <strong>University</strong> Press<br />
Edition: 1st<br />
Language: English<br />
Figures: 23 engraved plates (19 double-page)<br />
Binding: original cloth boards<br />
Pagination: pp. xviii, 346, [38]
Erwin Tomash Library<br />
Bowditch, <strong>Charles</strong> Pickering Bowditch, Nathaniel<br />
Collation: π 9 (-π10)1–20 8 21 6 22 7 (-22 8 )[23] 19 (-23 20 )<br />
Size: 253x165 mm<br />
<strong>Charles</strong> P. Bowditch was the man who founded the<br />
Maya collections <strong>of</strong> the Peabody Museum at Harvard<br />
<strong>University</strong> and the person after whom their Bowditch<br />
pr<strong>of</strong>essorship is named.<br />
The system <strong>of</strong> numeration used by a civilization is not<br />
a machine, but it certainly is machinery. Without it very<br />
little could be accomplished in the way <strong>of</strong> numeration<br />
or, especially, arithmetic; because <strong>of</strong> this, works on<br />
numeration are <strong>of</strong> particular interest to this collection.<br />
This work was one <strong>of</strong> the first attempts to systematically<br />
set forth the numeration and calendar systems <strong>of</strong> the<br />
Maya. It not only explains them but also examines all<br />
extant Maya material for examples <strong>of</strong> the glyphs used<br />
and their interpretation.<br />
Illustrations available:<br />
Title page<br />
Examples <strong>of</strong> Maya numeration<br />
Maya numeration, B 215<br />
B 215<br />
B 216<br />
Bowditch, Nathaniel (1773–1838)<br />
The new American practical navigator<br />
Year: 1802<br />
Place: Newburyport, MA<br />
Publisher: Edmund M. Blount for Brown & Stansbury, New<br />
York<br />
Edition: 1st<br />
Language: English<br />
Figures: 1 engraved folding frontispiece chart, 7 engraved<br />
plates (1 tinted)<br />
Binding: contemporary leather; rebacked; red leather label<br />
Pagination: pp. 246, [274], 533–589, [15]<br />
Collation: A–2H 4 A–B 4 (A)–(2S) 4<br />
Size: 224x133 mm<br />
Reference: Glais RCMT, p. 89; not in Karp MWPA<br />
Nathaniel Bowditch was a self-educated seaman and<br />
mathematician who had only three years <strong>of</strong> schooling<br />
when he began working in his father’s cooper’s shop at<br />
the age <strong>of</strong> ten. Later he was apprenticed to a firm <strong>of</strong> ship’s<br />
chandlers who encouraged his mathematical interests. At<br />
the age <strong>of</strong> twenty-two he became a seaman and spent the<br />
next nine years aboard ship, sailing on long voyages to<br />
the Caribbean, Portugal and the East Indies.<br />
In the course <strong>of</strong> these voyages, Bowditch became<br />
celebrated as a skilled navigator and found himself<br />
spending long hours correcting the navigational tables<br />
then in use. He then turned his attention to the standard<br />
navigational text <strong>of</strong> his time, John Hamilton Moore’s The<br />
practical navigator and seaman’s new daily assistant,<br />
London, 1772. He completely reworked and extended<br />
Moore’s book and decided to publish his revised version<br />
as The new American practical navigator, a title clearly<br />
reflecting its heritage. This work is much more than an<br />
improved set <strong>of</strong> navigational tables, for it also contains<br />
useful sections ranging from a short dictionary <strong>of</strong> sea<br />
terms to explanations <strong>of</strong> the parts <strong>of</strong> a ship (see the<br />
illustration <strong>of</strong> the colored plate and its text). Also included<br />
are standard forms for various contracts for freight and<br />
charters and other financial and legal documents.<br />
Bowditch found and corrected some eight thousand<br />
errors in the Moore version <strong>of</strong> the tables. Most were <strong>of</strong><br />
little consequence, but some were quite significant. For<br />
example, Moore’s incorrect identification <strong>of</strong> 1800 as a<br />
leap year introduced a twenty-three mile error in some<br />
results and caused the loss <strong>of</strong> both ships and men.<br />
Bowditch’s reputation as a legendary navigator was<br />
reinforced when Harvard <strong>University</strong> awarded him an<br />
honorary M.A. degree. He knew nothing <strong>of</strong> this honor,<br />
but being stranded in the port <strong>of</strong> Boston by adverse winds,<br />
he serendipitously decided to visit Harvard. Finding its<br />
graduation ceremonies in progress, he sat in the audience<br />
183
184<br />
Erwin Tomash Library<br />
Bowman, Elias W. Bowring, John<br />
and, to his astonishment, heard his name being called out<br />
as a recipient <strong>of</strong> an honorary degree.<br />
In mid-career, Bowditch left the sea to become an<br />
insurance company executive. He maintained a<br />
scholarly interest in mathematics for the rest <strong>of</strong> his<br />
life and eventually translated Pierre Simon Laplace’s<br />
Mécanique céleste into English.<br />
Navigational tables are still <strong>of</strong>ten referred to as<br />
Bowditch’s Tables, whether or not they stem from this<br />
original publication.<br />
Illustrations available:<br />
Title page<br />
Colored plate <strong>of</strong> ships<br />
Colored plate text<br />
B 216<br />
B 217<br />
Bowman, Elias W. and William Shakespeare, Jr.<br />
“Quick” interest calculator. Time and maturity tables.<br />
Year: 1939<br />
Place: Indianapolis, IN<br />
Publisher: Levey Printing Company<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards<br />
Pagination: ff. [100]<br />
Size: 163x250 mm<br />
This is a ready reckoner for interest on any amount from<br />
$1.00 to $10,000.00 for periods from one day to four<br />
years.<br />
Illustrations available:<br />
Title page<br />
Sample table page.<br />
B 218<br />
Bowring, John (1792–1872)<br />
B 217<br />
The decimal system in numbers, coins and accounts:<br />
especially with reference to the decimalisation <strong>of</strong> the<br />
currency and accountancy <strong>of</strong> the United Kingdom.<br />
Year: 1854<br />
Place: London<br />
Publisher: Nathaniel Cooke<br />
Edition: 1st<br />
Language: English<br />
Figures: engraved portrait frontispiece; 21 engraved plates (p.<br />
22, 60, 68, 72, 76, 92, 100, 102, 178, 180, 208, 210,<br />
212)<br />
Binding: original cloth boards<br />
Pagination: pp. [4], 246<br />
Collation: A 2 B–I 8 J 8 K–P 8 Q 3<br />
Size: 189x124 mm<br />
John Bowring was a linguist fluent in at least fifteen<br />
languages, including most <strong>of</strong> the European ones as<br />
well as Chinese and Arabic. He traveled the world on<br />
both commercial ventures and as a representative <strong>of</strong><br />
the British government. At the time <strong>of</strong> writing, he had<br />
just been appointed General Consul in Canton (he was<br />
later Governor <strong>of</strong> Hong Kong), and he indicates in his<br />
foreword that he is much rushed by the impossibility <strong>of</strong><br />
delaying his departure for the scene <strong>of</strong> his duties in a<br />
distant land.<br />
Bowring, with support from Prince Albert, Queen<br />
Victoria’s husband, was responsible for the introduction<br />
<strong>of</strong> the 2 Shilling coin, usually called a florin. This was<br />
the first step in the decimalization <strong>of</strong> British currency<br />
(2 shillings were one tenth <strong>of</strong> a Pound). After this step,
Erwin Tomash Library<br />
Bowring, John Boyer, Jacques<br />
B 218<br />
the process was abandoned until 1968–1971, when a<br />
complete decimalization occurred, and 2 Shillings was<br />
equated to 10 new pence (1 Pound = 100 new pence)<br />
After his success in establishing the florin, Bowring<br />
published this work. It is an investigation <strong>of</strong> decimal<br />
systems in numbers, coins and accounts from various<br />
parts <strong>of</strong> the world. It contains examples <strong>of</strong> decimal<br />
coins; the uses <strong>of</strong> decimal numbers in societies from<br />
China, Egypt and Greece; and reports from Members <strong>of</strong><br />
Parliament. The difficulty <strong>of</strong> working in a non-decimal<br />
system is illustrated with problems involving calculating<br />
the worth <strong>of</strong> an impure bar <strong>of</strong> gold. The arithmetic is<br />
pedantically set down, and after two pages <strong>of</strong> work, the<br />
much simpler decimal solution <strong>of</strong> the problem is shown.<br />
In the discussion <strong>of</strong> decimal numbers, he refers to the<br />
work Arithmetic by George Peacock, then Dean <strong>of</strong> Ely<br />
Cathedral and life-long friend <strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong>. The<br />
discussion is illustrated with examples from Peacock’s<br />
book and a portrait <strong>of</strong> Peacock, the only one known to<br />
have been published (another hangs in Ely Cathedral).<br />
The work also contains similar portraits <strong>of</strong> other <strong>Babbage</strong><br />
friends and associates, namely Herschel, DeMorgan,<br />
Airy (with whom <strong>Babbage</strong> disagreed) and others. The<br />
frontispiece illustrates Bowring himself.<br />
Illustrations available:<br />
Title page<br />
Portrait <strong>of</strong> Peacock<br />
Portrait <strong>of</strong> DeMorgan<br />
Portrait <strong>of</strong> Herschel<br />
First step in solving a non-decimal problem<br />
Frontispiece <strong>of</strong> Bowring<br />
Peacock, B 218<br />
B 219<br />
Boyer, Jacques (1869–)<br />
Histoire des mathematiques<br />
Herschel, B 218<br />
DeMorgan, B 218<br />
Year: 1900<br />
Place: Paris<br />
Publisher: Gauthier-Villars<br />
Edition: 1st<br />
Language: French<br />
Figures: 26 engraved plates<br />
Binding: contemporary three-quarter bound cloth boards;<br />
original paper wrappers mounted<br />
Pagination: pp. xii, 260<br />
Collation: π 6 1–16 8 17 2<br />
Size: 219x134 mm<br />
Jacques Boyer should not be confused with <strong>Charles</strong> B.<br />
Boyer, who also wrote a history <strong>of</strong> mathematics in 1968.<br />
Jacques’ history <strong>of</strong> mathematics is noteworthy for its<br />
description <strong>of</strong> French mathematics and mathematicians<br />
in the nineteenth century. It contains a number <strong>of</strong> portraits<br />
185
186<br />
Erwin Tomash Library<br />
Boys, <strong>Charles</strong> Vernon Boys, <strong>Charles</strong> Vernon<br />
<strong>of</strong> mathematicians, mainly French, and a frontispiece<br />
reproducing a seventeenth-century engraving showing<br />
the construction and use <strong>of</strong> mathematical instruments.<br />
Boyer does not indicate the source <strong>of</strong> the frontispiece,<br />
but it is the same as that published in later editions<br />
<strong>of</strong> Bion, and the work does contain reproductions <strong>of</strong><br />
mathematical instruments from Bion.<br />
Illustrations available:<br />
Title page<br />
Frontispiece<br />
B 220<br />
Boys, <strong>Charles</strong> Vernon (1855–1944)<br />
B 219<br />
Calculating machines. In Journal <strong>of</strong> the Society <strong>of</strong> Arts<br />
Vol. XXXVI, No. 1737, March 3, 1886<br />
Year: 1886<br />
Place: London<br />
Publisher: George Bell and Sons<br />
Edition: 1st<br />
Language: English<br />
Binding: half-bound marbled boards<br />
Pagination: pp. 376–389<br />
Size: 250x165 mm<br />
Sir <strong>Charles</strong> Boys was born in Leicestershire and<br />
became a well-known physicist and designer <strong>of</strong><br />
scientific instruments. He is best remembered for his<br />
radiomicrometer, improvements to the torsion balance, a<br />
calorimeter and a special camera with movable lens.<br />
Boys presented this paper in conjunction with an exhibit<br />
<strong>of</strong> calculating machines at the London International<br />
Inventions Exhibition. While Boys clearly knew a lot<br />
about calculating machines, judging from his answers to<br />
questions after the presentation, his time was obviously<br />
limited. The paper itself only mentions the well-known<br />
machines such as those <strong>of</strong> Thomas, Edmondson and<br />
Tate, with a few short references to items such as log<br />
tables, ready reckoners and Napier’s bones.<br />
At the end <strong>of</strong> the paper are indicated the machines<br />
exhibited and their owners. Prominent among the names<br />
is General <strong>Babbage</strong>, Henry P. <strong>Babbage</strong>, the son <strong>of</strong><br />
<strong>Charles</strong> <strong>Babbage</strong>. After <strong>Charles</strong>’ death in 1871, Henry<br />
<strong>Babbage</strong> became his father’s champion. Evidently,<br />
the machines collected by <strong>Charles</strong> during his lifetime,<br />
(Morland, Stanhope, etc.) were now owned by Henry.<br />
Illustrations available:<br />
none<br />
Integrating instrument, B 221<br />
B 221<br />
Boys, <strong>Charles</strong> Vernon (1855–1944)<br />
An integrating machine. In The London, Edinburgh<br />
and Dublin Philosophical Magazine, and Journal <strong>of</strong><br />
Science. Fifth Series. No. 69, May 1881<br />
Year: 1881<br />
Place: London<br />
Publisher: Taylor and Francis<br />
Edition: 1st<br />
Language: English
Erwin Tomash Library<br />
Bradbury, Fred Brahe, Tycho<br />
Binding: original paper wrappers<br />
Pagination: pp. 342–348<br />
Size: 225x142 mm<br />
In this paper, Boys proposes and describes a new type<br />
<strong>of</strong> integrating mechanism in contrast with existing<br />
integrating machines such as Amsler’s planimeter,<br />
where rolling mechanisms were employed to form the<br />
integral <strong>of</strong> the area being traced by a pointer. At the time<br />
this paper was written, Boys had built only a feasibility<br />
model. A few years later, Bruno Abdank-Abakanowicz<br />
described in great detail a complete design using the<br />
same principle. The Abakanowicz book acknowledges<br />
the fact that Boys had presented this same approach at<br />
the meetings <strong>of</strong> the British Association in 1882.<br />
Illustrations available:<br />
Plate showing instrument.<br />
B 222<br />
Bradbury, Fred<br />
Jacquard mechanism and harness mounting<br />
Year: 1912<br />
Place: (Halifax)<br />
Publisher: Author<br />
Edition: 1st<br />
Language: English<br />
Figures: 1 photolith plate<br />
Binding: original cloth boards<br />
Pagination: pp. 355, xii, [1]<br />
Collation: A–Y 8 (+W 8 )<br />
Size: 210x135 mm<br />
Bradbury was known for his books on various industrial<br />
subjects. He had already produced similar works<br />
on Carpet manufacture and Calculations in Yarns<br />
and Fabrics, and this book has advertisements and<br />
testimonials for both.<br />
After an introduction to the history <strong>of</strong> pattern weaving,<br />
this work deals with the Jacquard loom in all its forms,<br />
including a discussion <strong>of</strong> the creation <strong>of</strong> Jacquard cards.<br />
The book is well illustrated with technical drawings <strong>of</strong><br />
the various devices.<br />
Illustrations available:<br />
Title page<br />
B 223<br />
Brahe, Tycho (1546–1601)<br />
Astronomiæ instauratæ mechanica<br />
Year: 1602<br />
Place: Nürnberg<br />
Publisher: Levinus Hulsius<br />
Edition: 2nd<br />
Language: Latin<br />
B 222<br />
Figures: engraved portrait <strong>of</strong> Brahe on title, 25 illustrations (7<br />
engraved, 18 woodcut), 4 smaller illustrations in text<br />
Binding: contemporary vellum<br />
Pagination: ff. [54]<br />
Collation: )::( 4 A–E 6 F 4 G–H 6 I 4<br />
Size: 314x207 mm<br />
Reference: Gin HLB, Vol. XIX, #2, p. 129; Cro CL, #104<br />
Tycho Brahe, one the greatest and most celebrated<br />
astronomers in history, was born in Knudstrup, Denmark<br />
(present-day Sweden), into a noble family. His Danish<br />
given name was Tyge, and he adopted the Latinized<br />
version (Tycho) when he was fifteen years old. From the<br />
age <strong>of</strong> two, Tycho lived with and was reared by his paternal<br />
uncle, Jörgen Brahe. Jörgen saw to it that he was tutored<br />
in Latin and Greek and otherwise prepared for university<br />
studies. As befitted a person <strong>of</strong> his rank and position, he<br />
studied law at the <strong>University</strong> <strong>of</strong> Copenhagen and later<br />
at the <strong>University</strong> <strong>of</strong> Leipzig. His interest in astronomy<br />
was aroused by attending lectures on the subject, but his<br />
uncle strongly discouraged further studies, and he was<br />
reduced to learning the subject in secret.<br />
The conjunction <strong>of</strong> Saturn and Jupiter in August 1563<br />
seems to have been a seminal event for Tycho. He followed<br />
it meticulously and recorded his observation <strong>of</strong> the time<br />
<strong>of</strong> closest approach. When he computed this same time<br />
using both the Alphonsine tables and the Prutenic tables,<br />
the discrepancy between the observed and calculated<br />
results was striking. In fact, the Alphonsine tables were<br />
<strong>of</strong>f by nearly a month and the Prutenic tables by a few<br />
187
188<br />
Erwin Tomash Library<br />
Brahe, Tycho Brahe, Tycho<br />
B 223<br />
days, and this discrepancy forced him to conclude that<br />
the tables were seriously flawed.<br />
Brahe understood that it would require an extended<br />
program <strong>of</strong> observations, made with the best instruments<br />
available, to correct the tables. It took more than a decade<br />
for him to obtain the necessary facilities and financial<br />
support, but in early 1576, King Frederick II <strong>of</strong>fered<br />
Brahe the life-long use <strong>of</strong> the island <strong>of</strong> Hven in the Danish<br />
Sound for the erection <strong>of</strong> an observatory there to be fitted<br />
with the most accurate instruments to be had. The <strong>of</strong>fer<br />
brought with it sources <strong>of</strong> income, which, when added<br />
to Brahe’s not inconsiderable means, meant that Brahe<br />
could build the finest observatory in the world.<br />
Uraniborg, B 223<br />
Armillary sphere, B 223<br />
This book describes Brahe’s observatory, Uraniborg, on<br />
the island <strong>of</strong> Hven and gives a catalog <strong>of</strong> the instruments<br />
he used to obtain the precise measurements that allowed<br />
Kepler to determine planetary orbits. The work also<br />
contains Brahe’s autobiography and a description <strong>of</strong> how<br />
he divided his scales with transverse lines in order to make<br />
more accurate observations. Brahe was the last <strong>of</strong> the<br />
great observational astronomers before the invention <strong>of</strong><br />
the telescope, although others after him also used nakedeye<br />
sights on their instruments. Although dated after<br />
Brahe’s death, this work was first published privately in<br />
1598 in a very limited edition <strong>of</strong> about forty copies. This<br />
1602 edition was the first sold commercially and is today<br />
the only one generally available. The engraving <strong>of</strong> the<br />
equatorial armillary sphere on C6 appears for the first<br />
time in this edition, replacing a woodcut, and the title<br />
page has an engraved portrait <strong>of</strong> Brahe, also replacing<br />
a woodcut.<br />
The instruments described here are unlike those shown<br />
in most other instrument volumes <strong>of</strong> this period. These<br />
are precision instruments <strong>of</strong> the highest caliber, whereas<br />
many <strong>of</strong> the other works <strong>of</strong> the time describe instruments<br />
that could be obtained by amateur gentlemen interested<br />
in astronomy.<br />
Illustrations available:<br />
Title page (portrait <strong>of</strong> Brahe)<br />
Diagonally divided scale<br />
Armillary sphere<br />
Uraniborg – Brahe’s “heavenly castle” observatory<br />
Large quadrant
Erwin Tomash Library<br />
Brahe, Tycho Brainerd, John Grist<br />
B 224<br />
B 224<br />
Brahe, Tycho (1546–1601) [Hans Henning Ræder; Elis<br />
Strömgren and Bengt Strömgren, translators]<br />
Tycho Brahe’s description <strong>of</strong> his instruments and<br />
scientific work as given in Astronomiæ Instauratæ<br />
Mechanica, Wandesburgi, 1598.<br />
Year: 1946<br />
Place: Cambridge<br />
Publisher: I Kommission Hos Ejnar Munksgaard<br />
Edition: 1st (?)<br />
Language: English<br />
Binding: original paper wrappers; uncut<br />
Pagination: pp. 144<br />
Collation: 1–16 4 17 2 18 6<br />
Size: 270x210 mm<br />
Brahe had published a description <strong>of</strong> his instruments in<br />
Astronomiae Instauratae Mechanica in 1598. At the time<br />
he had left his observatory in Denmark but had not yet<br />
gone to Prague. The Royal Danish Academy <strong>of</strong> Science<br />
and Letters decided that there should be Danish and<br />
English versions <strong>of</strong> this important work and, to celebrate<br />
the quadricentennial <strong>of</strong> Brahe’s birth, commissioned this<br />
translation. The original Latin was first translated into<br />
Danish by H. Raeder, and then, after consultation with<br />
astronomers, the English text was produced. The volume<br />
includes reproductions <strong>of</strong> the original 1598 illustrations.<br />
Illustrations available:<br />
Title page<br />
B 225<br />
Brainerd, John Grist (1904–1988) and T. Kite Sharpless<br />
(1913–1967)<br />
The ENIAC. In Electrical Engineering, Vol. 67, No. 2,<br />
February 1948<br />
Year: 1948<br />
Place: New York<br />
Publisher: American <strong>Institute</strong> <strong>of</strong> Electrical Engineers<br />
Edition: 1st<br />
Language: English<br />
Binding: original paper wrappers<br />
Pagination: pp. 163–172<br />
Size: 296x219 mm<br />
Reference: Ran ODC, p. 409<br />
The ENIAC (Electronic Numerical Integrator and<br />
Computer) was the first large-scale, electronic, general<br />
purpose, digital calculating machine. This paper, while<br />
not the first to mention it in print, is an early description<br />
<strong>of</strong> the device.<br />
Brainerd, while technically in charge <strong>of</strong> the Moore<br />
School <strong>of</strong> Electrical Engineering, had little to do with the<br />
actual creation <strong>of</strong> the ENIAC. His role was very much as<br />
an administrator; however, he and Sharpless would have<br />
been the only ones from the original ENIAC team left in<br />
the Moore School when this paper was written. Sharpless<br />
was a graduate <strong>of</strong> the Moore School and a skilled<br />
Accumulator panel, B 225<br />
189
190<br />
Erwin Tomash Library<br />
Brainerd, John Grist Bramer, Benjamin<br />
engineer on the project. After the ENIAC team broke up<br />
in 1945, he remained on staff as chief engineer for the<br />
EDVAC project. He left in 1947 to become one <strong>of</strong> the<br />
founding partners <strong>of</strong> Technitrol Engineering Company<br />
which, among other things, manufactured components<br />
for many <strong>of</strong> the first-generation computer projects.<br />
While considerable portions <strong>of</strong> the paper are taken up<br />
with a discussion <strong>of</strong> basic concepts such as electronic<br />
versus mechanical, this paper does provide some items<br />
that are otherwise difficult to find. Diagrams are given<br />
for the exact layout <strong>of</strong> the ENIAC and for the front<br />
control panels <strong>of</strong> the accumulators.<br />
Illustrations available:<br />
Layout <strong>of</strong> ENIAC<br />
Accumulator control panel<br />
Accumulator front panel<br />
Accumulator, B 225<br />
B 226<br />
Bramer, Benjamin (ca.1588–1650)<br />
B 226<br />
Apolonius Cattus, oder, Kern der gantzen Geometriæ in<br />
drei Theil. In dessen ersten Theil Euclidis Geometrische<br />
demonstrationes erhoben, und zu ihrem Objecto<br />
perfectionis angefüret werden… Apolonius Catti,<br />
oder, Kerns der gantzen Geometriæ in ander Theil.<br />
De sectione cylindri … Dritter Theil oder Anhang<br />
eines Berichts von M. Johsten Burgi. Geometrischen<br />
triangular Instrument, zu gar leicht kurtzen, und doch<br />
gewissen Land und Feldmessen. Wie auch andere<br />
höhen, tieffen, längen und breiten zuermessen dienlich<br />
b/w: Kohlhans, Johann Christoph; Neu-erfundene<br />
Mathematische und Optische Cüriositaten,<br />
bestehend So wohl in einem sattsamen Unterricht,<br />
zum Feldmessen und itzt üblichen Fortification.<br />
Year: 1684<br />
Place: Kassel<br />
Publisher: Ingebrands<br />
Edition: 2nd<br />
Language: German<br />
Figures: engraved portrait (Burgi) frontispiece; title in red and<br />
black; 51 copper plates (23 double page, 26 single page,<br />
2 folding)<br />
Binding: contemporary vellum<br />
Pagination: pp. [14], 102, [2], 61, [1], [8], 22, [2]<br />
Collation: ):( 3 ):():( 4 A–N 4 A–G 4 H 3 A–D 4<br />
Size: 196x133 mm<br />
Reference: Pogg Vol. I, p. 274<br />
After the death <strong>of</strong> his father in 1591, Benjamin Bramer<br />
was taken care <strong>of</strong> by his sister, who was married to the
Erwin Tomash Library<br />
Bramer, Benjamin Bramer, Benjamin<br />
Joost Bürgi, B 226<br />
clock and instrument maker Joost (Jobst) Bürgi. He<br />
spent five years with Bürgi at the imperial court in Prague,<br />
returning to Kassel in 1604. In 1612, he was appointed<br />
master builder in the court at Marburg. He is known<br />
for earlier publications on mathematics and surveying<br />
instruments that are almost unique in that he credits his<br />
predecessors (including Bürgi) with the ideas he expands<br />
upon—this in an era in which most instruments makers<br />
were very secretive about their sources and techniques.<br />
In this work Bramer continues his unusual<br />
acknowledgement <strong>of</strong> the work <strong>of</strong> his predecessors,<br />
particularly Bürgi, whose portrait appears in the<br />
frontispiece. Leone Battista Alberti (1435), Albrecht<br />
Dürer (1525) and Joost Bürgi (1604) had each<br />
investigated the problem <strong>of</strong> how to create an instrument<br />
that would allow one to produce accurate geometric<br />
perspective drawings. Bramer continued this tradition<br />
by developing his own set <strong>of</strong> instruments, particularly<br />
one to draw conic sections. The device was evidently an<br />
improvement on one devised by Christoph Scheiner.<br />
After describing conic curves and instruments for<br />
drawing ellipses, Bramer introduces his universal conic<br />
instrument and then illustrates its use. The latter part <strong>of</strong><br />
the book is mainly concerned with the production <strong>of</strong><br />
sundials on all orientations <strong>of</strong> surfaces—a process that<br />
makes use <strong>of</strong> many conic section curves.<br />
Illustrations available:<br />
Title page – color<br />
Frontispiece – Joost Bürgi portrait<br />
Conic instrument<br />
B 227<br />
Bramer, Benjamin (ca.1588–1650)<br />
Bericht und gebrauch Eines Proportional Linials:<br />
Neben kurtzem Underricht Eines Parallel Instruments<br />
Year: 1617<br />
Place: Marburg<br />
Publisher: Paul Egenolff<br />
Edition: 1st<br />
Language: German<br />
Figures: 3 engraved plates, (2 folding)<br />
Binding: modern full morocco<br />
Pagination: pp. 58<br />
Collation: A–G 4 H 1<br />
Size: 189x149 mm<br />
Reference: Cro CL, #133<br />
Bramer’s sector, one <strong>of</strong> the three main instruments<br />
described in this work, is interesting for its use <strong>of</strong> a<br />
removable arm, hinged with a pin through a hole at the<br />
end <strong>of</strong> each scale, which avoids the problem <strong>of</strong> making<br />
a complex hinge. This innovation also allowed him to<br />
construct each scale on an individual line, thus avoiding<br />
the problem <strong>of</strong> interfering scale graduations near the<br />
hinge (where all scales come together at a point in the<br />
Hingeless sector, B 227<br />
191
192<br />
Erwin Tomash Library<br />
Bramer, Benjamin Bramer, Benjamin<br />
usual form <strong>of</strong> the instrument). The sector was equipped<br />
with scales for arithmetic (usually termed a line <strong>of</strong><br />
lines), a line <strong>of</strong> circles, a geometric line (for working<br />
with triangles), a line <strong>of</strong> planes (for manipulating areas)<br />
and a line <strong>of</strong> solids (for volumes) as well as others for<br />
gnomic calculations. This instrument is notable for the<br />
early date, just eleven years after Galileo published his<br />
Le operazioni del compasso geometrico in 1606.<br />
The second device was simply a parallel frame with<br />
pointers, <strong>of</strong> use in drawing figures or etching lines. The<br />
third instrument, a combination <strong>of</strong> plumb bob and angle<br />
measuring device, was <strong>of</strong> use in architectural situations.<br />
Illustrations available:<br />
Title page<br />
Portrait <strong>of</strong> Bramer<br />
Bramer sector<br />
Triangulation instrument<br />
B 228<br />
Bramer, Benjamin (ca.1588–1650)<br />
B 227<br />
Beschreibunge und Underricht Eines Neuwen leicht<br />
und sehr bequemen Instruments zum Grundtlegen und<br />
Theylung der Circkel Linien.<br />
Year: 1616<br />
Place: Marburg<br />
Publisher: Paul Egenolff<br />
Edition: 1st<br />
Language: German<br />
Figures: Figures <strong>of</strong> protractor and sighting instruments in text<br />
Binding: later vellum<br />
Pagination: pp. 32<br />
Collation: A–D 4<br />
Size: 190x150 mm<br />
Reference: Pogg Vol. I, p. 274<br />
This small volume is a description <strong>of</strong> a simple sighting<br />
instrument and a protractor-like device, both for use by<br />
surveyors.<br />
Illustrations available:<br />
Title page<br />
Protractor<br />
Sighting instrument<br />
Benjamin Bramer, B 227<br />
Sighting instrument, B 228
Erwin Tomash Library<br />
Bramer, Benjamin Bramer, Benjamin<br />
B 229<br />
Bramer, Benjamin (ca.1588–1650)<br />
B 228<br />
Dritter Theil oder anhang eines berichts von M.<br />
Johsten Burgi. Geometrischen Triangular Instrument,<br />
Zu gar leicht kurtzen, und doch gewissen Land und<br />
Feldmessen, wie auch andere Höhen, Tieffen, Längen<br />
und Breiten zuermessen dienlich<br />
b/w: Kohlhans, Johann Christoph; Neu-erfundene<br />
Mathematische und Optische Cüriositaten,<br />
bestehend So wohl in einem sattsamen Unterricht,<br />
zum Feldmessen und isstüblichen Fortification.<br />
b/w: Bramer, Benjamin; Appolonius Cattus, Oder, Kern<br />
der gantzen Geometriæ In Drei Theil.<br />
Year: 1684<br />
Place: Kassel<br />
Publisher: Ingebrands<br />
Edition: 2nd<br />
Language: German<br />
Figures: engraved portrait (Burgi) frontispiece; 21 engraved<br />
copperplates<br />
Binding: contemporary vellum<br />
Pagination: pp. [8], 22, [2]<br />
Collation: A–D 4<br />
Size: 196x133 mm<br />
Bramer credits the instrument described here to his<br />
brother-in-law, Joost (Jobst) Bürgi. Bürgi is most<br />
famous for his independent invention <strong>of</strong> logarithms.<br />
However, he did not publish until 1620, about six<br />
years after John Napier had produced his work. A<br />
fine instrument maker and mathematician, Bürgi was<br />
responsible for the design <strong>of</strong> several different sectors and<br />
other instruments. Little is known <strong>of</strong> his early life, but<br />
from 1579 on, he was a watch and instrument maker at<br />
the court <strong>of</strong> Duke Wilhelm IV. The instruments he made<br />
there brought him to the notice <strong>of</strong> Emperor Rudolf II, and<br />
Bürgi moved to his court at Prague about 1603. While<br />
Survey instrument in use, B 229<br />
193
194<br />
Erwin Tomash Library<br />
Bramer, Benjamin Bramer, Benjamin<br />
there he worked as an assistant to Kepler, mainly doing<br />
calculations. See Bramer, 1684 (Apolonius Cattus), for<br />
a portrait <strong>of</strong> Joost Bürgi.<br />
This volume is a description <strong>of</strong> a simple triangular<br />
instrument used for surveying tasks. Its use is illustrated<br />
with many examples taken from civilian and military<br />
life. One <strong>of</strong> the most interesting is the description <strong>of</strong> the<br />
instrument being used underground in a mine.<br />
Illustrations available:<br />
Title page<br />
Triangular instrument in use.<br />
B 230<br />
Bramer, Benjamin (ca.1588–1650)<br />
B 229<br />
Trigonometria planorum mechanica. Oder Unterricht<br />
unnd Beschreibung eines neuwen und sehr bequemen<br />
Geometrischen Instruments zu allerhand Abmessung<br />
und Solvirung der Planischen Triangel derogleichen<br />
bisshero nicht gesehen geworden<br />
Year: 1617<br />
Place: Marburg<br />
Publisher: Paul Egenolff<br />
Edition: 1st<br />
Language: German<br />
Figures: 3 engraved folding plates,<br />
Binding: modern vellum<br />
Pagination: pp. 101, [1]<br />
Collation: A–M 4 N 3<br />
Size: 119x152 mm<br />
Reference: Pogg Vol. I, p. 274<br />
This small work describes a plane table (see Ceneri,<br />
Angelo Maria; L’uso dello strumento geometrico detto<br />
la tavoletta pretoriana, 1728, and the Appendix essay<br />
on surveying instruments) that is slightly different from<br />
others in that the table is marked with angles and divided<br />
to resemble squared graph paper to make it easier to read<br />
distances from scaled drawings.<br />
Bramer wrote at least three <strong>of</strong> these small volumes in<br />
the 1616–1617 period, and the publisher used the same<br />
title page format on this volume as on the 1616 work<br />
(Beschreibunge und Utterricht).<br />
Illustrations available:<br />
Title page<br />
Plane table<br />
B 230<br />
Plane table, B 230
Erwin Tomash Library<br />
Brander, George Friedrich Brander, George Friedrich<br />
B 231<br />
Brander, George Friedrich (1713–1783)<br />
Arithmetica binaria sive dyadica, das ist Die Kunst nur<br />
mit zwey Zahlen in allen vorkommenden Fällen sicher<br />
und leicht zu rechnen<br />
Year: 1769<br />
Place: Augsburg<br />
Publisher: Widow <strong>of</strong> Eberhard Kletts<br />
Edition: 2nd<br />
Language: German<br />
Figures: 1 engraved folding table<br />
Binding: contemporary marbled boards<br />
Pagination: pp. 40<br />
Collation: A–B 8 C 4<br />
Size: 185x110 mm<br />
Reference: Pogg Vol. I, p. 277<br />
An instrument maker in Augsburg, Brander was known<br />
as one <strong>of</strong> the finest workmen <strong>of</strong> his day, and many <strong>of</strong> his<br />
instruments are in museums today. He is known to have<br />
had almost a hundred different instruments <strong>of</strong> his own<br />
design for sale and is also known to have written several<br />
books on these instruments and their use (see Brander,<br />
Beschreibung und Gebrauch …, 1780).<br />
This work on binary numbers was a very early explanation<br />
<strong>of</strong> the system. In the introduction he credits Leibniz with<br />
earlier work. The slim volume starts with an explanation<br />
<strong>of</strong> the system; proceeds to describe addition, subtraction,<br />
multiplication, division and the extraction <strong>of</strong> roots;<br />
then concludes with a table <strong>of</strong> the binary equivalents <strong>of</strong><br />
numbers from 0 to 500,000.<br />
Illustrations available:<br />
Title page<br />
Binary multiplication examples<br />
Binary table<br />
B 231<br />
B 232<br />
Brander, George Friedrich (1713–1783)<br />
Beschreibung und Gebrauch eines geometrischen<br />
Instruments in Gestalt eines Proportionalzirkels,<br />
welches in allen praktischen Fällen der Feldmesskunst<br />
leicht und gut zu gebrauchen; auch zu astronomischen<br />
Vergnügen dienet, und auf Reisen sehr bequem mit sich<br />
geführet werden kann: nebst angehängter Beschreibung<br />
eines Systems von Maassstäben zu Zeichnungen<br />
Year: 1780<br />
Place: Augsburg<br />
Publisher: Eberhard Kletts<br />
Edition: 1st<br />
Language: German<br />
Figures: 2 engraved folding plates<br />
Binding: paper boards<br />
Pagination: pp. 64<br />
Collation: A–D 8<br />
Size: 170x101 mm<br />
Reference: Pogg Vol. I, p. 277<br />
Binary table, B 231<br />
Binary multiplication, B 231<br />
195
196<br />
Erwin Tomash Library<br />
Brander, George Friedrich Brasser, Franciscus<br />
This work describes a sighting instrument that could be<br />
used for general survey work. It is constructed much<br />
like a sector with sights, but some care has been taken<br />
in the mechanical arrangements with various locking<br />
devices and finely graduated scales. There is also a<br />
description <strong>of</strong> other simple instruments, such a plane<br />
scale. An interesting item is a list, produced by Johann<br />
Gabriel Doppelmayer, <strong>of</strong> temperature variation around<br />
Nurnberg throughout the year.<br />
Illustrations available:<br />
Title page<br />
Sighting instrument<br />
Temperature variations<br />
Sighting instrument, B 232<br />
B 232<br />
B 233<br />
Brasser, Franciscus<br />
B 233<br />
Ein Newe Rechens-Buch Auff alle Kauffmans-<br />
Handlunge für die anfangende Schülers … Nun aber<br />
durch einem Liebhaber der Kunst auffs new mit fleisse<br />
corrigiret und auf begehren mit vielen nützlichen<br />
Exempeln vermehret<br />
Year: 1658<br />
Place: Lübeck<br />
Publisher: Schmalhertz?<br />
Edition: late<br />
Language: German<br />
Binding: later blue paper boards<br />
Pagination: ff. [76]<br />
Collation: A–I 8 K 4<br />
Size: 162x91 mm<br />
Reference: Smith Rara, p. 393; H&J AM, Vol. I, B23.17, p. 53<br />
Little is known about the author, but DeMorgan<br />
(Arithmetical books) indicates that Brasser seems to<br />
have been a celebrated teacher.<br />
The work begins with a short description <strong>of</strong> the<br />
traditional table abacus and the balance based on the use<br />
<strong>of</strong> algorism. It deals with the elementary arithmetical<br />
operations, including very short mentions <strong>of</strong> duplation<br />
and mediation, then repeats the same material when<br />
dealing with fractions. The rest <strong>of</strong> the work is concerned<br />
with examples <strong>of</strong> various types <strong>of</strong> commercial arithmetic,<br />
including a table <strong>of</strong> various conversion factors at the<br />
end <strong>of</strong> the book. At one point he uses a strange set <strong>of</strong><br />
symbols, the origin and uses <strong>of</strong> which are obscure (see<br />
illustration).
Erwin Tomash Library<br />
Brasser, Franciscus Breckenridge, William Edwin<br />
Although printed a hundred years after Adam Riese’s,<br />
the book is reminiscent <strong>of</strong> his publications, with a title<br />
page portrait <strong>of</strong> Brasser that is similar to the one used by<br />
Riese in 1550.<br />
Illustrations available:<br />
Title page<br />
Table abacus<br />
Conversion table<br />
Numerical symbols<br />
Numeral symbols, B 233<br />
Table abacus, B 233<br />
B 234<br />
Brearley, Harry C.<br />
Time telling through the ages<br />
Year: 1919<br />
Place: New York<br />
Publisher: Doubleday, Page & Co. for Robert H. Ingersoll &<br />
Bro.<br />
Edition: 1st<br />
Language: English<br />
Figures: 24 photolith plates<br />
Binding: original cloth boards<br />
Pagination: pp. 294<br />
Size: 235x160 mm<br />
This is a history <strong>of</strong> clock and watch making from the<br />
earliest times to the beginning <strong>of</strong> the twentieth century.<br />
A series <strong>of</strong> appendices describe how a modern watch<br />
movement operates and provide a list <strong>of</strong> manufacturers<br />
and an Encyclopedic Dictionary <strong>of</strong> names and terms<br />
associated with the subject. Examples <strong>of</strong> timekeeping<br />
and mechanisms are provided on the photolith plates.<br />
Illustrations available:<br />
Title page<br />
B 235<br />
Breckenridge, William Edwin (1869–)<br />
B 234<br />
The log log duplex slide rule. A self teaching manual<br />
with tables <strong>of</strong> settings, equivalents and gauge points.<br />
Year: 1926<br />
Place: Hoboken<br />
Publisher: Keuffel & Esser<br />
Edition: 1st<br />
Language: English<br />
Binding: original printed stiff paper wrappers<br />
Pagination: pp. [2], 138, [2]<br />
Size: 201x133 mm<br />
197
198<br />
Erwin Tomash Library<br />
Breckenridge, William Edwin Breckenridge, William Edwin<br />
Breckenridge was with the Mathematics Department at<br />
Columbia <strong>University</strong> in New York City.<br />
This instruction manual illustrates the use <strong>of</strong> the Keuffel<br />
& Esser model N4092-3 rule.<br />
Illustrations available:<br />
Title page<br />
B 236<br />
Breckenridge, William Edwin (1869–)<br />
B 235<br />
The Mannheim slide rule. A self teaching manual with<br />
tables <strong>of</strong> settings, equivalents and gauge points.<br />
Year: 1924<br />
Place: Hoboken<br />
Publisher: Keuffel & Esser<br />
Edition: 1st<br />
Language: English<br />
Binding: original printed stiff paper wrappers<br />
Pagination: pp. [2], 72, [2]<br />
Size: 202x134 mm<br />
This instruction manual contains advertisements that<br />
illustrate some <strong>of</strong> the types <strong>of</strong> slide rule that were being<br />
produced by the Keuffel & Esser Co. They include<br />
Mannheim, Polyphase, Duplex, Stadia, Roylance<br />
Electrical, Surveyor’s, Merchant’s and Chemist’s Slide<br />
Rule.<br />
Illustrations available:<br />
Title page<br />
Slide rules<br />
B 237<br />
Breckenridge, William Edwin (1869–)<br />
The Mannheim slide rule. A self teaching manual with<br />
tables <strong>of</strong> settings, equivalents and gauge points.<br />
Place: Hoboken<br />
Publisher: Keuffel & Esser<br />
Edition: unknown<br />
Language: English<br />
Binding: original printed stiff paper wrappers<br />
Pagination: pp. [2], 74, [3]<br />
Size: 202x134 mm<br />
This edition <strong>of</strong> the Breckenridge instructional manual<br />
for the Mannheim rule is essentially identical to that<br />
produced in 1924 (see that entry).<br />
Illustrations available:<br />
None<br />
B 238<br />
Breckenridge, William Edwin (1869–)<br />
The Mannheim slide rule Nos. 4031S, N4035S, N4041<br />
and 4051. A self teaching manual with tables <strong>of</strong><br />
settings, equivalents and gauge points.<br />
Year: 1938<br />
Place: Hoboken<br />
Publisher: Keuffel & Esser<br />
Edition: unknown<br />
Language: English<br />
Binding: original printed stiff paper wrappers<br />
Pagination: pp. [2], 75, [2]<br />
Size: 200x132 mm<br />
The contents <strong>of</strong> this are almost identical to 1927 edition,<br />
but the title page has been changed slightly.<br />
Illustrations available:<br />
Title page<br />
Year: 1927 B 238
Erwin Tomash Library<br />
Breckenridge, William Edwin Brentel, Georg<br />
B 239<br />
Breckenridge, William Edwin (1869–)<br />
The polyphase duplex slide rule. A self teaching manual<br />
with tables <strong>of</strong> settings, equivalents and gauge points.<br />
Year: 1924<br />
Place: Hoboken<br />
Publisher: Keuffel & Esser<br />
Edition: 1st<br />
Language: English<br />
Binding: original printed stiff paper wrappers; split<br />
Pagination: pp. [2], 88, [2]<br />
Size: 200x137 mm<br />
This is another <strong>of</strong> Breckenridge’s variations on his<br />
instruction manual. A second copy <strong>of</strong> this is in the<br />
collection.<br />
Illustrations available:<br />
Title page<br />
B 240<br />
Breckenridge, William Edwin (1869–)<br />
B 239<br />
The polyphase duplex slide rule No. 4088. A self<br />
teaching manual with tables <strong>of</strong> settings, equivalents and<br />
gauge points.<br />
Year: 1938<br />
Place: Hoboken<br />
Publisher: Keuffel & Esser<br />
Edition: late<br />
Language: English<br />
Binding: original printed stiff paper wrappers; split<br />
Pagination: pp. [2], 88, [2]<br />
Size: 200x137 mm<br />
A later edition <strong>of</strong> the instruction manual that is essentially<br />
identical to the 1924 version.<br />
Illustrations available:<br />
Title page<br />
B 241<br />
Breckenridge, William Edwin (1869–)<br />
The polyphase slide rule. A self teaching manual with<br />
tables <strong>of</strong> settings, equivalents and gauge points.<br />
Year: 1925<br />
Place: Hoboken<br />
Publisher: Keuffel & Esser<br />
Edition: 1st<br />
Language: English<br />
Binding: original printed stiff paper wrappers; split<br />
Pagination: pp. [2], 83, [3]<br />
Size: 200x133 mm<br />
Another variation on Breckenridge’s manuals. A second<br />
copy <strong>of</strong> this is in the collection.<br />
Illustrations available:<br />
Title page<br />
B 242<br />
Breckenridge, William Edwin (1869–)<br />
The polyphase slide rule. No. N4053. A self teaching<br />
manual with tables <strong>of</strong> settings, equivalents and gauge<br />
points.<br />
Year: 1938<br />
Place: Hoboken<br />
Publisher: Keuffel & Esser<br />
Edition: 1st<br />
Language: English<br />
Binding: original printed stiff paper wrappers<br />
Pagination: pp. [2], 85<br />
Size: 196x130 mm<br />
A later version, essentially identical to the 1925 edition.<br />
Illustrations available:<br />
Title page<br />
B 243<br />
Brentel, Georg (fl.1610) – [Galgemair, Georg (1495–<br />
1552)]<br />
Herrn Georgij Galgemairs Kurtzer gründlicher<br />
gebesserter unnd vermehrter underricht, zubereitung<br />
und gebrauch, Der hochnutzlichen mathematischen<br />
Instrumenten, Proportional Schregmäss und Circkels,<br />
benebens dem fundament dess visierens. Allen<br />
Künstliebenden zu sonderen Ehren unnd wolgefallen.<br />
Year: 1615<br />
Place: Ulm<br />
199
200<br />
Erwin Tomash Library<br />
Brentel, Georg Brentel, Georg<br />
B 243<br />
Publisher: Johann Meder<br />
Edition: 2nd<br />
Language: German<br />
Figures: 1 large folding plates<br />
Binding: contemporary vellum<br />
Pagination: pp. [8], 48, 47–130 (misnumbered 47 as 45, 110 as<br />
100), [2]<br />
Collation: A–R 4 S 3<br />
Size: 191x153 mm<br />
Reference: Zin GBAL, p. 61, 271, 318, 324, 330, 339, 347,<br />
353, 362, 364, 367, 371, 384, 395; Not in Pogg Vol. I<br />
Georg Brentel was a painter and engraver who published<br />
plans for sundials (the paper could be glued to boards to<br />
make a dial). Little is known about him other than that<br />
he was a pupil <strong>of</strong> Philipp Apian (the son <strong>of</strong> the famous<br />
mathematician and instrument maker Peter Apian). See<br />
Galgemair, Georg, in the Addenda.<br />
Proportional compass, B 243<br />
This expanded version <strong>of</strong> Brentel’s 1610 publication<br />
treats the same basic instruments (sector and proportional<br />
compass) but includes many examples <strong>of</strong> finding<br />
volumes, gauging, weights and measures, etc.<br />
The illustration <strong>of</strong> the sector has been redone and much<br />
improved from the earlier work, but the one for the<br />
proportional compass was little changed. Gaspar Schott<br />
(Mathesis Caesarea, 1662) used this same illustration in<br />
his description <strong>of</strong> the sector in 1662. An unusual printer’s<br />
device occupies the final page.<br />
Illustrations available:<br />
Title page<br />
Sector illustration<br />
Proportional compass illustration<br />
Gauging example<br />
Printer’s mark and colophon<br />
Printer’s device and colophon, B 243<br />
Gauging, B 243
Erwin Tomash Library<br />
Brentel, Georg Brentel, Georg<br />
B 244<br />
Brentel, Georg (fl.1610)<br />
Quadrantis astronomici et geometrici utilitates. Ein<br />
Tractat vom Astronomischen und Geometrischen<br />
Quadranten, auss welchem dess Tags oder dess Nachts,<br />
durch die Sonn, Mond und andere Planeten oder<br />
Firstern die Stunden mögen gefünden: dess gleichen<br />
allerley höhe, länge, tieffe ohn oder durch Rechnung<br />
künstlich und gewiss abgemessen werden…<br />
b/w: Hulsius, Ocularis …, 1596<br />
Year: 1611<br />
Place: Nürnberg<br />
Publisher: Jacob Winter<br />
Edition: 1st<br />
Language: German<br />
Figures: title enclosed by 4-piece woodcut border, each page <strong>of</strong><br />
text enclosed by borders <strong>of</strong> type ornaments, 3 woodcuts<br />
in text<br />
Binding: contemporary red stained vellum.<br />
Pagination: pp. [8], 62<br />
Collation: A–H 4 I 3<br />
Size: 183x141 mm<br />
Reference: Zin GBAL, #4302<br />
Brentel’s other work in this collection (Georgii<br />
Galgemaris Kurtzer unnd gründtlicher underricht,<br />
wie der Künstliche Proportional-Circul ausszutheilen<br />
und ausszuzeichnensen auff etlicher begern, 1610)<br />
is remarkable for including fine full-sized diagrams<br />
<strong>of</strong> his instruments. In contrast, this work is lacking in<br />
illustrations, showing only two crude diagrams <strong>of</strong> a<br />
quadrant in use for surveying related to aqueducts. In the<br />
text he notes surveying applications <strong>of</strong> a quadrant and<br />
provides tables listing the positions <strong>of</strong> major stars and<br />
other markings on a quadrant for both astronomical and<br />
survey uses.<br />
Illustrations available:<br />
Title page<br />
Aqueduct survey problem<br />
B 245<br />
Brentel Georg (fl.1610) [Galgemair, Georg (1495–1552)]<br />
Georgij Galgemaris Kurtzer unnd gründtlicher<br />
Underricht, wie der Künstliche Proportional-Circul<br />
ausszutheilen und auffzuzeichnen sey. Auff etlicher<br />
begern. Allen denen so sich dess Circuls gebrauchen,<br />
zu sonderlichem Nutz und vilfeitigem Vortheil in Truck<br />
gegeben durch Georgen Brentel…<br />
separate title page (ff. E1r):<br />
Fundament der Proportional-Circul … was ober dem<br />
mond, ewig bsteht. Was unter dem mond, bald vergeht<br />
Year: 1610<br />
Place: Lauingen<br />
Publisher: Jacob Winter<br />
B 244<br />
Aqueduct survey, B 244<br />
201
202<br />
Erwin Tomash Library<br />
Brentel, Georg Brerewood, Edward<br />
Edition: 1st<br />
Language: German<br />
Figures: 2 folding plates<br />
Binding: modern marbled boards<br />
Pagination: pp. 40<br />
Collation: A–C 4 D 8<br />
Size: 194x146 mm<br />
B 245<br />
In these two works Brentel has used information given<br />
to him by Georg Galgemair (see Addenda entry for<br />
Galgemair) to write about both the proportional compass<br />
and the sector, which he called Schregmess. The dates for<br />
Galgemair are uncertain. Following Brental’s practice <strong>of</strong><br />
producing full-size broadsheets for sundials, he includes<br />
full-sized plans for both instruments in this work. He also<br />
includes tables giving the positions at which each scale<br />
should be marked. Any instrument maker possessing this<br />
work could easily have reproduced each device.<br />
Illustrations available:<br />
Title page<br />
Proportional compass<br />
Sector<br />
B 246<br />
Brerewood, Edward (1565–1613)<br />
De ponderibus, et pretiis veterum nummorum,<br />
eorumque; cum recentioribus collatione, liber unus.<br />
Year: 1614<br />
Place: London<br />
Publisher: Joannem Billium (John Bill)<br />
Edition: 1st<br />
Language: Latin<br />
Binding: contemporary vellum<br />
Pagination: pp. [8], 56<br />
Collation: A–H 4<br />
Size: 191x142 mm<br />
Reference: STC, 3612<br />
Brerewood was born and educated in Chester. At the<br />
age <strong>of</strong> fifteen, he enrolled in Oxford. In 1590, after<br />
graduating with an M.A., he applied for a fellowship<br />
there, but lacking the right connections, he was not given<br />
the position. However, Oxford did recommend him for<br />
the job as the first pr<strong>of</strong>essor <strong>of</strong> astronomy at Gresham<br />
College. Ward describes him (Lives <strong>of</strong> the Pr<strong>of</strong>essors<br />
<strong>of</strong> Gresham College, 1740) as very communicative,<br />
and ready to impart what he knew to others, either in<br />
conversation, or by writing, but he never published<br />
anything during his lifetime. A nephew, Robert<br />
Sector, B 245
Erwin Tomash Library<br />
Bressieu, Maurice Brewster, David<br />
Brerewood, saw this (and nine other works) through the<br />
press after his uncle died <strong>of</strong> a sudden fever.<br />
This is a treatise on the weights and values <strong>of</strong> Greek,<br />
Roman and other ancient coins. The book is set up in<br />
three columns. References are given in the left column,<br />
with monetary values or weights in the right-hand<br />
column.<br />
Illustrations available:<br />
Title page<br />
B 247<br />
Bressieu, Maurice (a.1608)<br />
B 246<br />
Astronomical libri quatuor hæc maximam partem<br />
nova est rerum astronomicarum & geographicarum<br />
per plana sphericáque triangula dimensionis ratio,<br />
veteríque impendiò expeditior & compendiosior.<br />
Year: 1581<br />
Place: Paris<br />
Publisher: Ægidius Gorbinus<br />
Edition: 1st<br />
Language: English<br />
Figures: 1 large folding plate<br />
Binding: contemporary vellum<br />
Pagination: pp. [8], 40, 84<br />
Collation: a 4 b 6 c 4 c 8 e 2 A–B 6 C 4 D 6 E 4 F 4 G–H 6 (e1 signed C1)<br />
Size: 334x225 mm<br />
Bressieu, a native <strong>of</strong> Grenoble, held the chair <strong>of</strong><br />
mathematics at the <strong>University</strong> <strong>of</strong> Paris from 1576 until<br />
his death in 1608. Pierre de la Ramée, who is mentioned<br />
in the colophon, endowed this chair before his death<br />
in 1572. The colophon also mentions the hospitality <strong>of</strong><br />
Ronsard, a poet.<br />
This is a treatise on spherical geometry as used in<br />
astronomical calculations. It contains a number <strong>of</strong><br />
tables, one being printed in red and black to differentiate<br />
different columns <strong>of</strong> entries.<br />
Illustrations available:<br />
Title page<br />
Sample table page (color)<br />
B 248<br />
Brewster, David (1781–1868)<br />
B 247<br />
Letters on natural magic, addressed to Sir Walter Scott,<br />
Bart.<br />
Year: 1832<br />
Place: London<br />
Publisher: John Murray<br />
Edition: 1st<br />
Language: English<br />
Binding: contemporary leather<br />
Pagination: pp. xii, 352<br />
Collation: π 6 A–Y 8<br />
Size: 144x91 mm<br />
Reference: Ran ODC, p. 409<br />
Best remembered for his work on optics and polarization<br />
<strong>of</strong> light, the Scottish physicist David Brewster displayed<br />
his scientific abilities early. He had made a telescope<br />
by the age <strong>of</strong> ten and started at Edinburgh <strong>University</strong> at<br />
the age <strong>of</strong> twelve. After abandoning a wish to become<br />
203
204<br />
Erwin Tomash Library<br />
Brewster, David Brewster, David<br />
a clergyman because <strong>of</strong> extreme nervousness in public<br />
speaking, he became a private tutor. He then edited the<br />
Edinburgh Encyclopedia for twenty-two years before<br />
becoming principal <strong>of</strong> Edinburgh <strong>University</strong> (1859–<br />
1868)—an institution that had earlier refused him the<br />
chair <strong>of</strong> mathematics.<br />
The term natural magic in the title arises from natural<br />
philosophy, a term used in Scotland up until the 1970s—<br />
it was, for example, only then that the <strong>University</strong> <strong>of</strong><br />
Glasgow changed the name <strong>of</strong> their department from<br />
Natural Philosophy to Physics. He was an admirer <strong>of</strong><br />
<strong>Charles</strong> <strong>Babbage</strong> and strongly supported his attempts<br />
to construct a Difference Engine. This work describes<br />
optical and aural illusions, mechanical automata,<br />
chemistry, secret writing, etc. He mentions <strong>Babbage</strong>’s<br />
engine on pp. 291–296.<br />
Illustrations available:<br />
Title page<br />
B 249<br />
Brewster, David (1781–1868)<br />
B 248<br />
On machinery for calculating and printing<br />
mathematical tables. In Edinburgh Philosophical<br />
Journal Vol. VII<br />
Year: 1822<br />
Place: Edinburgh<br />
Publisher: Archibald Constable and Co.<br />
Edition: 1st<br />
Language: English<br />
Binding: modern paper wrappers<br />
Pagination: pp. 274–281<br />
Size: 211x132 mm<br />
Reference: Van S CBCP, #70; Babb CBLP #71, #73; Ran<br />
ODC, p. 405<br />
Brewster presented this paper in Edinburgh as part <strong>of</strong><br />
a concerted effort to obtain funding for development<br />
<strong>of</strong> the Difference Engine. Brewster indicates that his<br />
material was drawn mainly from Mr. <strong>Babbage</strong>’s printed<br />
letter on the subject (see <strong>Babbage</strong>, <strong>Charles</strong>; A letter to<br />
Sir Humphrey Davy, 1822). After explaining the concept<br />
<strong>of</strong> the difference engine, he describes the proposed<br />
implementation and concludes with a plea for financial<br />
support for <strong>Babbage</strong>.<br />
Illustrations available:<br />
Title page<br />
Journal cover, B 249<br />
Brewster, David, editor<br />
See <strong>Babbage</strong>, <strong>Charles</strong>; On the theoretical principles <strong>of</strong><br />
the machinery for calculating tables, 1823.<br />
See <strong>Babbage</strong>, <strong>Charles</strong>; Works <strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong><br />
M.A. F.R.S. &c. [A Collection <strong>of</strong> seventeen items by<br />
and about <strong>Babbage</strong>].
B 250<br />
Briggs, Henry (1561–1631)<br />
Arithmetica logarithmica sive logarithmorum chiliades<br />
triginta, pro numeris naturali serie crescentibus ab<br />
unitate ad 20,000: et a 90,000 ad 100,000.<br />
Year: 1624<br />
Place: London<br />
Publisher: W. Jones<br />
Edition: 1st<br />
Language: Latin<br />
Binding: contemporary reverse leather; rebacked; brown<br />
leather label<br />
Pagination: pp. [8], 88, [300]<br />
Collation: a–m 4 A–Q 6 R 4 4H 8 4I–4O 6 * 6<br />
Size: 324x199 mm<br />
Reference: Pogg Vol. I, p. 298; DSB II, p. 462; Hend BTM,<br />
#18, p. 40; Horb CC, #38, pp. 33; Car PMM, #116, pp.<br />
69–70<br />
Henry Briggs graduated from Oxford with an M.A. in<br />
1585 and remained there as a junior academic. He was<br />
elected as a Fellow <strong>of</strong> St. John’s College in 1589. In 1596,<br />
he was invited to be the founding pr<strong>of</strong>essor <strong>of</strong> geometry<br />
at the newly created Gresham College in London, where<br />
he worked lecturing and creating navigational tables.<br />
Shortly after Napier published his Mirifici logarithmorum<br />
canonis descriptio in 1614, Briggs obtained a copy<br />
and immediately recognized their value for navigation<br />
and other computations. He began to teach them to his<br />
students and soon saw that they would be easier to use if<br />
the base was changed to 10. Briggs visited with Napier<br />
Erwin Tomash Library<br />
Briggs, Henry Briggs, Henry<br />
B 250<br />
Briggs’ logarithms, B 250<br />
in the summer <strong>of</strong> 1615 and again in 1616, and after the<br />
two men had agreed on the proposed changes, Briggs<br />
began calculating the new base 10 logarithms. Napier<br />
took no part in this work as he was not well and died the<br />
following year. In 1617, Briggs supervised the printing<br />
<strong>of</strong> a translation <strong>of</strong> Napier’s work produced by Edward<br />
Wright, who had also died shortly after finishing it. In a<br />
preface to this translation, he justifies the change to base<br />
10 and includes a small table <strong>of</strong> logarithms <strong>of</strong> numbers<br />
from 1 to 1000 (the first chiliad).<br />
This volume contains logarithms for numbers from 1 to<br />
20,000 and from 90,000 to 100,000. It took until 1624<br />
to produce the table in this volume. Briggs did not start<br />
calculating logarithms in succession, but he used a number<br />
<strong>of</strong> critical logarithms (see illustrations) for 0, 10 1/2 , 10 3/4 ,<br />
etc. to calculate the others. Briggs wrote a preface in<br />
which he explained how to use logarithms and gave a<br />
plan for calculating the missing 70,000 numbers—even<br />
<strong>of</strong>fering to supply special paper divided into columns<br />
for anyone willing to help. He provided the difference<br />
between each adjacent value (see illustrations) and a<br />
method <strong>of</strong> calculating logarithms by interpolation from<br />
differences. The missing seventy chiliads were included<br />
in the second edition <strong>of</strong> this work published by Adrian<br />
Vlacq in 1628, although Briggs had, by this time, nearly<br />
completed the calculations himself. It was in the preface<br />
to this work that Briggs coined the terms characteristic<br />
and mantissa for the two portions (on either side <strong>of</strong> the<br />
decimal point) <strong>of</strong> a logarithmic number.<br />
Some copies <strong>of</strong> this work have an additional six pages<br />
containing the logarithms for 100,001 to 101,000 and a<br />
table <strong>of</strong> square roots from 1 to 200. This volume does<br />
not contain these extra pages, but they are to be found<br />
in another issue in this collection (see entry for Briggs,<br />
Henry; Arithmetica Logarithmica, 1624–another issue).<br />
These logarithms, together with those <strong>of</strong> Adriaan Vlacq<br />
mentioned above, form the basis from which almost all<br />
other logarithm tables were produced. At the end <strong>of</strong> the<br />
eighteenth century, the French produced the Tables du<br />
Cadastre, which are only available in manuscript form<br />
(see entry for Prony). Towards the end <strong>of</strong> the nineteenth<br />
century, Edward Sang (1805–1890) published a seven-<br />
205
206<br />
Erwin Tomash Library<br />
Briggs, Henry Briggs, Henry<br />
figure table <strong>of</strong> logarithms for numbers up to 200,000,<br />
the last half <strong>of</strong> which had been newly calculated. With<br />
these two exceptions, all other pre-twentieth century<br />
tables were simply edited copies <strong>of</strong> the original Briggs<br />
and Vlacq computations (see the entry for <strong>Babbage</strong>,<br />
<strong>Charles</strong>; Notice respecting some errors common to<br />
many tables <strong>of</strong> logarithms, 1829).<br />
Illustrations available:<br />
Title page<br />
Critical logarithms<br />
First page <strong>of</strong> log table<br />
B 251<br />
Briggs, Henry (1561–1631)<br />
Arithmetica logarithmica sive logarithmorum chiliades<br />
triginta, pro numeris naturali serie crescentibus ab<br />
unitate ad 20,000: et a 90,000 ad 100,000. Quorum<br />
ope multa perficiuntur arithmetica problemata et<br />
geometrica.<br />
Year: 1624<br />
Place: London<br />
Publisher: W. Jones<br />
Edition: 1st (another issue)<br />
Language: Latin<br />
Binding: contemporary leather; gilt embossed covers<br />
Pagination: pp. [8], 88, [300], [12]<br />
Collation: a–m 4 A–Q 6 R 4 4H 8 4I–4O 6 * 6 6<br />
Size: 324x215 mm<br />
Reference: Pogg Vol. I, p. 298; DSB II, p. 462; Hend BTM,<br />
#18, p. 40; Horb CC, #38, pp. 33; Car PMM, #116, pp.<br />
69–70<br />
This is another issue <strong>of</strong> the first edition <strong>of</strong> Briggs’<br />
logarithms. It is identical to the first issue with the<br />
exception that it contains six additional pages with the<br />
logarithms for number from 100,001 to 101,000 and<br />
a table <strong>of</strong> square roots for the numbers from 1 to 100.<br />
These six additional sheets are pasted in.<br />
Illustrations available:<br />
Title page<br />
Square root table<br />
B 252<br />
Briggs, Henry (1561–1631)<br />
The first chiliad <strong>of</strong> logarithmes, called in the discourse<br />
aforegoing the table <strong>of</strong> numbers.<br />
b/w: Gunter, Edmund; Canon triangulorum, or a<br />
logarithmeticall table: wherein are set downe<br />
logarithmes <strong>of</strong> the sines, & tangents <strong>of</strong> all<br />
the degrees, & minutes <strong>of</strong> the quadrant. The<br />
logarithme <strong>of</strong> the radius, or semy-diameter beeing<br />
100000000, 1626<br />
Year: 1626<br />
Place: Oxford<br />
Publisher: n/p<br />
Edition: 1st (English)<br />
Language: English<br />
Binding: contemporary leather; red leather label<br />
Pagination: ff. [109]<br />
Collation: A8B4 –R8S4T1 B 252<br />
Size: 106x50 mm<br />
Reference: STC, 3742; Kno NTMV, p. 222<br />
This is a very small set <strong>of</strong> logarithmic tables for values<br />
between 1 and 1,000. The logarithms are to eight decimal<br />
digits, and the differences between each logarithm are<br />
noted (differences are useful for interpolating between<br />
values). There is no explanation <strong>of</strong> any kind, the only text<br />
being the title page. This was not the first time Briggsian<br />
logarithms had been printed, but it is the first in such a<br />
portable format and the first in English (if you count an<br />
English title page). The Briggs tables occupy the first 22<br />
leaves and Gunter’s the rest <strong>of</strong> the volume.<br />
Illustrations available:<br />
Title page<br />
Sample table page<br />
B 253<br />
Briggs, Henry (1561–1631)<br />
Logarithmicall arithmeticke. Or tables <strong>of</strong> logarithmes<br />
for absolute numbers from an unite to 100000, as also<br />
for sines, tangentes and secantes for every minute<br />
<strong>of</strong> a quadrant, with a plaine description <strong>of</strong> their use<br />
in arithmetike, geometrie, geographie, astronomie,<br />
navigation, &c<br />
b/w: de Decker, Ezechiel; Tweede deel van de nievwe<br />
tel-konst <strong>of</strong>te wonderliicke konstighe tafel,<br />
inhoudende de logarithmi, voor de getallen van 1<br />
af tot 100000 toe. Eerst ghevonden van Iohanne<br />
Nepero, …
Erwin Tomash Library<br />
Briggs, Henry Briggs, Henry<br />
Year: 1631<br />
Place: London<br />
Publisher: George Miller<br />
Edition: 1st<br />
Language: English<br />
Binding: 18th-century half-bound leather; red leather label, red<br />
edges<br />
Pagination: pp. [2], 54, 8<br />
Collation: A–H 4<br />
Size: 300x185 mm<br />
Reference: Pogg Vol. I, p. 298; Hend BTM, #26.0, p. 58<br />
This work is bound with the very rare work by Ezechiel<br />
de Decker. The tables themselves are not present in this<br />
copy. When Vlacq issued his Arithmetica Logarithmica,<br />
Gouda, 1628, he printed more copies than were needed.<br />
After the death <strong>of</strong> Briggs, Miller bought up copies <strong>of</strong><br />
the tables and issued them with a new title page and<br />
introduction in English.<br />
Illustrations available:<br />
Title page<br />
B 254<br />
Briggs, Henry (1561–1631)<br />
B 253<br />
Table des logarithmes, pour les nombres d’un, à 10000<br />
b/w: Wells, John; Sciographia, or the art <strong>of</strong> shadowes.<br />
Plainly demonstrating, out <strong>of</strong> the sphere, how to<br />
project both great and small circles, upon any<br />
plane whatsoever: with a new conceit <strong>of</strong> reflecting<br />
the sunne beames upon a diall, contrived on a<br />
plane, which the direct beames can never shine<br />
upon …<br />
Year: 1626<br />
Place: Gouda<br />
Publisher: Pierre Rammasein<br />
Edition: 1st<br />
Language: French<br />
Binding: contemporary leather rebacked<br />
Pagination: pp. [264]<br />
Collation: A–K 8 L 4 M 2 A–E 8 F 6<br />
Size: 190x115 mm<br />
Reference: Hend BTM, #24.0, p. 56<br />
These tables were published by Rammasein prior to his<br />
publishing the famous tables by Vlacq in 1628. See entry<br />
for Wells, John; Sciographia, …, 1635.<br />
Illustrations available:<br />
Title page in entry for Wells, John: Sciographia …, 1635<br />
B 255<br />
[Briggs, Henry (1561–1631)] – Thomas Smith (1638–<br />
1710)<br />
Vitæ quorundam eruditissimorum et illustrium virorum.<br />
Quorum nomina exstant in pagina sequenti.<br />
Year: 1707<br />
Place: London<br />
Publisher: David Mortier<br />
Edition: 1st<br />
Language: Latin<br />
Figures: engraved frontispiece<br />
Binding: contemporary leather; gilt spine<br />
Pagination: pp. [2], xvi, [2], 148, [2], 62, [2], 16, 16, 38, 34,<br />
48, 102, [2]<br />
Collation: * 3 ** 4 *** 3 A–2G 4 2H 3 3A–3P 4 4A–4N 4<br />
Size: 200x150 mm<br />
See entry for Smith, Thomas, 1707, where illustrations<br />
may also be found.<br />
Illustrations available:<br />
None<br />
B 256<br />
Briggs, Henry (1561–1631) and Henry Gellibrand<br />
(1597–1636/7)<br />
Trigonometria Britannica: sive de doctrina<br />
triangulorum libri duo. Quorum prior continet<br />
constructionem canonis sinuum tangentium &<br />
secantium, unà cum logarithmis sinuum & tangentium<br />
ad gradus & graduum centesimas & ad minuta &<br />
secunda centesimis respondentia: A clarrissimo<br />
doctissimo integerrimoque Viro Henrico Briggio…<br />
Posterior verò usum sive applicationem canonis<br />
in resolutione triangulorum tam planorum quam<br />
sphæricorum e geometricis fundamentis petitâ, calculo<br />
facillimo, eximiisque compendiis exhibet: Ab Henrico<br />
Gellibrand…<br />
Year: 1633<br />
207
208<br />
Erwin Tomash Library<br />
Briggs, Henry British Association<br />
Place: Gouda<br />
Publisher: Peter Rammesein<br />
Edition: 1st<br />
Language: Latin<br />
Binding: modern leather<br />
Pagination: pp. [8], 112, [272]<br />
Collation: π 4 A–O 4 a–y 6 z 4<br />
Size: 350x215 mm<br />
After completing his calculation (see Briggs, 1624) <strong>of</strong><br />
logarithms <strong>of</strong> the natural numbers, Henry Briggs began<br />
the immense task <strong>of</strong> creating a table <strong>of</strong> sines, tangents,<br />
secants, logarithms <strong>of</strong> sines and logarithms <strong>of</strong> tangents.<br />
He completed the calculations but was not able to finish<br />
an introduction before his death. His friend Henry<br />
Gellibrand, a pr<strong>of</strong>essor <strong>of</strong> astronomy at Gresham College<br />
in London, took on the task <strong>of</strong> finishing the preface<br />
(explaining the tables and their application to plane and<br />
spherical trigonometry) and seeing the work through the<br />
press. Adrian Vlacq arranged for the work to be printed<br />
in Gouda by Peter Rammesein.<br />
Like Briggs’ logarithms <strong>of</strong> numbers, this table contains<br />
the differences between each entry, allowing the user to<br />
interpolate if necessary. It was seldom necessary because<br />
these tables contained an entry for each one hundredth<br />
<strong>of</strong> a degree (with the equivalent minutes and seconds<br />
being shown in the rightmost column <strong>of</strong> each page – see<br />
illustrations). This move to having an entry for every<br />
hundredth <strong>of</strong> a degree was copied by Nathaniel Roe<br />
(1633), William Oughtred (1657) and John Newton<br />
(1658), but the tables <strong>of</strong> Vlacq, based on the old<br />
sexagesimal division <strong>of</strong> a degree, were so popular that<br />
this change was ignored by others.<br />
Illustrations available:<br />
Title page<br />
Page from the tables<br />
Briggs, Henry (1600–1666)<br />
See Vlacq, Adriaan; Arithmetica logarithmica, 1628.<br />
See Faulhaber, Johann; Zehntausent logarithmi,<br />
der absolut oder ledigen zahlen von 1. biss auff<br />
10000,1631<br />
B 257<br />
Brink, Raymond Woodward (1890–)<br />
Logarithmic and trigonometric tables.<br />
Year: 1928<br />
Place: New York<br />
Publisher: D. Appleton-Century Company<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards<br />
Pagination: pp. [6], 110<br />
Size: 197x135 mm<br />
B 256<br />
A small book <strong>of</strong> logarithms and other useful tables,<br />
suitable for student use.<br />
Illustrations available:<br />
Title page<br />
B 258<br />
British Association for the Advancement <strong>of</strong> Science<br />
Report <strong>of</strong> the Fifty-Eighth Meeting <strong>of</strong> the British<br />
Association for the Advancement <strong>of</strong> Science. Held at<br />
Bath in September 1888<br />
Year: 1889<br />
Place: London<br />
Publisher: John Murray<br />
Edition: 1st<br />
Language: English<br />
Binding: contemporary buckram<br />
Pagination: pp. xcvi, 988, 116, 32<br />
Collation: A 8 a–e 8 B–3Q 8 3R 4 3S 2 A–G 8 H 2 B–C 8<br />
Size: 215x138 mm<br />
This contains a very short item reporting on a presentation<br />
by Henry <strong>Babbage</strong>, the son <strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong>, about<br />
his father’s Analytical Engine. It mentions that a section,<br />
working to twenty-nine digits, including the anticipatory<br />
carry device, was shown to those at the meeting.<br />
Illustrations available:<br />
Entire item.
Erwin Tomash Library<br />
British Calculators, Ltd. Brodetsky, Selig<br />
B 259<br />
British Calculators, Ltd.<br />
The Bri-Cal adding : : machines<br />
Year: ca.1912<br />
Place: Stoke Newington<br />
Publisher: British Calculators, Ltd.<br />
Edition: 1st<br />
Language: English<br />
Binding: original printed paper wrappers<br />
Pagination: pp. 20<br />
Size: 217x140 mm<br />
The Bri-Cal was a circular, stylus-driven adding machine.<br />
This is a price list and description for its various models<br />
A, B, F, U, D, W and R.<br />
Illustrations available:<br />
Title page<br />
Bri-Cal model A<br />
B 259<br />
B 260<br />
Brodetsky, Selig (1888–1954)<br />
A first course in nomography<br />
Year: 1925<br />
Place: London<br />
Publisher: G. Bell and Sons<br />
Edition: 2nd<br />
Language: English<br />
Binding: original cloth boards; gilt spine<br />
Pagination: pp. xii; 160<br />
Collation: π 6 A–K 8<br />
Size: 204x138 mm<br />
Brodetsky was a mathematician and Zionist leader. Born<br />
in the Ukraine, he moved with his family to London in<br />
1893. He placed first (for all England) in the Cambridge<br />
local examinations in 1905 and won a scholarship to<br />
Trinity College. He obtained a Ph.D. in astronomy<br />
from Leipzig and, in 1914, became a lecturer at Bristol<br />
<strong>University</strong>, becoming chair <strong>of</strong> mathematics in Leeds in<br />
1924. In 1949, he moved to Israel, where he became<br />
president <strong>of</strong> the Hebrew <strong>University</strong> in Jerusalem.<br />
See the Appendix essay on nomography for details<br />
about the subject. Brodetsky provides a short history <strong>of</strong><br />
nomography, and the rest <strong>of</strong> the work teaches various<br />
aspects <strong>of</strong> the topic.<br />
Illustrations available:<br />
Title page<br />
BRI-CAL adding machine, B 259 B 260<br />
209
210<br />
Erwin Tomash Library<br />
Brooker, Ralph Anthony Brooks, Edward<br />
B 261<br />
Brooker, Ralph Anthony (1925 – )<br />
The solution <strong>of</strong> algebraic equations on the EDSAC. In<br />
Proceedings <strong>of</strong> the Cambridge Philosophical Society,<br />
Vol. 48, Part 2, April 1952, pp. 255–270<br />
Year: 1952<br />
Place: Cambridge<br />
Publisher: Cambridge <strong>University</strong> Press<br />
Edition: 1st<br />
Language: English<br />
Binding: original paper wrappers<br />
Pagination: pp. 255–270<br />
Size: 257x182 mm<br />
Ralph Anthony (Tony) Brooker began his career<br />
in Cambridge but later moved to the <strong>University</strong> <strong>of</strong><br />
Manchester, where he became very influential in the<br />
development <strong>of</strong> s<strong>of</strong>tware in Britain. He was responsible<br />
for the Autocode compilers for Manchester’s Ferranti<br />
Mark I and Mercury. Along with Derrick Morris, he<br />
devised the concept <strong>of</strong> the Compiler Compiler–a program<br />
that, given the syntactic and semantic description <strong>of</strong> a<br />
programming language, would create a compiler for it.<br />
This is an early paper describing a mathematical<br />
application for EDSAC. It discusses three different<br />
methods <strong>of</strong> solving for the roots <strong>of</strong> polynomial equations<br />
and then gives results from EDSAC.<br />
Illustrations available:<br />
None<br />
B 262<br />
Brooks, Edward (1831–1912)<br />
Key to the new normal mental arithmetic: And methods<br />
<strong>of</strong> teaching mental arithmetic, containing, also,<br />
methods for arithmetical contractions, and a collection<br />
<strong>of</strong> problems <strong>of</strong> an interesting and amusing character,<br />
for class exercises.<br />
Year: 1873<br />
Place: Philadelphia<br />
Publisher: Christopher Sower<br />
Edition: 1st<br />
Language: English<br />
Binding: original printed cloth boards<br />
Pagination: pp. 160<br />
Collation: 1–13 6 14 2<br />
Size: 167x106 mm<br />
Brooks was the superintendent <strong>of</strong> public schools in<br />
Philadelphia and had previously been the principal <strong>of</strong><br />
the Pennsylvania State Normal School. He was known<br />
for his books on arithmetic, geometry, trigonometry,<br />
algebra, etc., all <strong>of</strong> which were used as teaching aids.<br />
This work, designed for the teacher <strong>of</strong> arithmetic,<br />
provides a number <strong>of</strong> instructional hints and games that<br />
may be played with students. The majority <strong>of</strong> the work<br />
consists <strong>of</strong> the answers to hundreds <strong>of</strong> drill problems<br />
that appeared in the student’s text (see another entry for<br />
Brooks, The new normal mental arithmetic, 1873).<br />
Illustrations available:<br />
Title page<br />
B 263<br />
Brooks, Edward (1831–1912)<br />
The new normal mental arithmetic: A thorough and<br />
complete course by analysis and induction.<br />
Year: 1873<br />
Place: Philadelphia<br />
Publisher: Christopher Sower Company<br />
Edition: unknown<br />
Language: English<br />
Binding: original embossed cloth boards<br />
Pagination: pp. 176, [4]<br />
Collation: 1–11 8<br />
Size: 167x107 mm<br />
A student textbook on elementary arithmetic, the vast<br />
majority <strong>of</strong> the work is a collection <strong>of</strong> drill problems.<br />
The preface makes reference to Recorde’s Whetsone <strong>of</strong><br />
Wit.<br />
Illustrations available:<br />
Title page<br />
B 263
Erwin Tomash Library<br />
Brooks, Edward Brooks, Edward<br />
B 264<br />
Brooks, Edward (1831–1912)<br />
The new normal primary arithmetic designed as an<br />
introduction to a thorough and complete course in<br />
mental and written arithmetic.<br />
Year: 1893<br />
Place: Philadelphia<br />
Publisher: Christopher Sower<br />
Edition: revised<br />
Language: English<br />
Binding: original printed cloth boards<br />
Pagination: pp. vi, 7–112<br />
Collation: 1–7 8<br />
Size: 168x107 mm<br />
A revised version <strong>of</strong> Brooks’ earlier work. Brooks had,<br />
in the meantime, apparently earned a Ph.D. that was not<br />
noted in his earlier publications.<br />
Illustrations available:<br />
Title page<br />
B 265<br />
Brooks, Edward (1831–1912)<br />
The normal mental arithmetic. A thorough and complete<br />
course by analysis and induction. Revised edition with<br />
a treatise on mental algebra<br />
Year: 1863<br />
Place: Philadelphia<br />
Publisher: Sower, Potts & Co.<br />
Edition: revised<br />
Language: English<br />
Binding: original paper wrappers<br />
Pagination: pp. [2], viii, 7–168<br />
Collation: 1–14 6 15 2<br />
Size: 150x98 mm<br />
See earlier entries for Edward Brooks.<br />
Illustrations available:<br />
Title page<br />
B 266<br />
Brooks, Edward (1831–1912)<br />
The normal union arithmetic, graded course. Part II<br />
Year: 1877<br />
Place: Philadelphia<br />
Publisher: Sower, Potts & Co.<br />
Edition: unknown<br />
Language: English<br />
Binding: original printed cloth boards<br />
Pagination: pp. 230<br />
Collation: 1–9 12 10 7<br />
Size: 185x116 mm<br />
This volume is more advanced than Brooks’ other mental<br />
arithmetic publications. After a much shorter introduction<br />
to the standard arithmetical operations, there are sections<br />
on fractions, factoring, mixed radix numbers (lengths,<br />
weights, etc.), and calendar and business problems. An<br />
interesting paragraph in the section on numeration lists,<br />
after Roman numerals, the lumbermen’s notation.<br />
The union in the title refers to his union <strong>of</strong> mental and<br />
written arithmetic in one volume and has nothing to do<br />
with trade unions.<br />
Illustrations available:<br />
Title page<br />
Lumberman’s notation<br />
B 267<br />
Brooks, Edward (1831–1912)<br />
B 266<br />
Notation system, B 266<br />
The normal union arithmetic, graded course. Part III<br />
Year: 1877<br />
Place: Philadelphia<br />
Publisher: Sower, Potts & Co.<br />
Edition: unknown<br />
Language: English<br />
211
212<br />
Erwin Tomash Library<br />
Brooks, Edward Brooks, Edward<br />
Binding: original printed cloth boards<br />
Pagination: pp. viii, 231–429, [1]<br />
Collation: A–H 12 I 8<br />
Size: 184x114 mm<br />
This is Part III <strong>of</strong> Brooks’ advanced treatment <strong>of</strong><br />
arithmetic. This volume contains sections on business<br />
problems such as percentages on bonds and investments,<br />
ratios, arithmetic and geometric series, and menstruation<br />
<strong>of</strong> surfaces and volumes. An appendix contains problems<br />
on the metric system and insurance <strong>of</strong> various kinds.<br />
Illustrations available:<br />
Title page<br />
B 268<br />
Brooks, Edward (1831–1912)<br />
The normal written arithmetic, by analysis and<br />
synthesis. Designed for common schools, normal<br />
schools, high schools, academies, etc.<br />
Year: 1869<br />
Place: Philadelphia<br />
Publisher: Sower, Potts & Co.<br />
Edition: 2nd (?)<br />
Language: English<br />
Binding: original printed cloth boards<br />
Pagination: pp. vi, 9–337, [1]<br />
Collation: 1–28 6<br />
Size: 184x108 mm<br />
This is a more advanced work than Brooks’ mental<br />
arithmetic series. It treats the same elementary<br />
numeration and arithmetic operations, but then deals<br />
with decimal fractions and many <strong>of</strong> the same types <strong>of</strong><br />
advanced problems that were repeated in the union<br />
publications.<br />
Illustrations available:<br />
Title page<br />
B 269<br />
Brooks, Edward (1831–1912)<br />
The philosophy <strong>of</strong> arithmetic as developed from the<br />
three fundamental processes <strong>of</strong> synthesis, analysis, and<br />
comparison containing also a history <strong>of</strong> arithmetic.<br />
Year: 1880<br />
Place: Lancaster, PA<br />
Publisher: Normal Publishing<br />
Edition: 2nd<br />
Language: English<br />
Binding: original cloth boards<br />
Pagination: pp. x, 11–570, 2<br />
Collation: 1–35 8 36 6<br />
Size: 222x144 mm<br />
This is by far the most significant <strong>of</strong> Brooks’ publications,<br />
although perhaps the least popular. It begins with a<br />
history and comments on the origins and old names for<br />
arithmetical processes, particularly the old Latin and<br />
Italian names for the various methods used for division.<br />
The <strong>chapter</strong> on Arithmetical Language includes the<br />
erroneous speculations on the shapes <strong>of</strong> the digits arising<br />
from the number <strong>of</strong> straight lines or angles contained<br />
in the character but also includes, without illustration,<br />
the more plausible theory <strong>of</strong> their origin from Sanskrit<br />
characters. A section <strong>of</strong> different number bases discusses<br />
the origin <strong>of</strong> the binary system, which, he indicates, was<br />
communicated to Leibniz by Bouvet, a Jesuit missionary<br />
in China. An extensive description <strong>of</strong> the base 12 scale<br />
is complete with a proposed set <strong>of</strong> names and characters<br />
for the digits as well as an addition and multiplication<br />
table. The last half <strong>of</strong> the book tends to treat the same<br />
topics as were in his union series <strong>of</strong> arithmetic books, but<br />
from a much more academic standpoint. In his discussion<br />
<strong>of</strong> decimal fractions, he points out that they were first<br />
used by Simon Stevin and that the first English work to<br />
use them with regularity was by Richard Witt in 1613,<br />
although Stevin’s Disme was translated into English by<br />
Richard Norton in 1608.<br />
Despite the inclusion <strong>of</strong> several speculations, this<br />
work has much to recommend it as a study <strong>of</strong> early<br />
arithmetic.<br />
Illustrations available:<br />
Title page<br />
Origin <strong>of</strong> numeral shapes<br />
Description <strong>of</strong> the creation <strong>of</strong> decimal fractions<br />
B 269
Erwin Tomash Library<br />
Brown, George Brown, George<br />
B 270<br />
Brown, George (1650–1730)<br />
Arithmetica infinita or the accurate accomptant’s best<br />
companion contriv’d and calculated …<br />
Year: 1717/1718 Julian/Gregorian<br />
Place: [Edinburgh]<br />
Publisher: Brown<br />
Edition: 1st<br />
Language: English<br />
Figures: engraved portrait frontispiece<br />
Binding: contemporary panelled leather<br />
Pagination: pp. [4], 14, 126, 10<br />
Collation: π 2 a 7 A–H 8 I 4<br />
Size: 95x120 mm<br />
B 270<br />
George Brown was a Scottish minister who apparently<br />
graduated from the <strong>University</strong> <strong>of</strong> Aberdeen in 1675<br />
(another account has him graduating from Edinburgh<br />
<strong>University</strong> in 1664, but he would only have been 14 at<br />
that time – not impossible for the time, but unusual).<br />
He apparently served in various parishes in Scotland,<br />
but after the revolution <strong>of</strong> 1688, he lost his license to<br />
practice. He created a device known as a Rotula, a<br />
circular instrument for performing elementary arithmetic<br />
operations, and published works on arithmetic and tables<br />
for the conversion <strong>of</strong> English to Scots currency. For<br />
information on the Rotula, see Duncan Wilson, “The<br />
Rotula, a seventeenth century calculating device,” The<br />
Scottish Educational Journal, April 14, 1933, pp. 432–<br />
433.<br />
Brown’s last publication, this small book <strong>of</strong> tables was<br />
engraved, excepting one typeset page bearing a letter<br />
from the astronomer John Keill recommending the use<br />
<strong>of</strong> the tables. The two tables are each concerned with<br />
interest and do not use a decimal point but rather a small<br />
∟ symbol. A manuscript page, pasted into the front,<br />
explains that the tables are artificial numbers, adopted to<br />
our English money: 1₤ or twenty shillings sterling being<br />
the Integer (see illustration).<br />
Illustrations available:<br />
Title page<br />
Frontispiece <strong>of</strong> Brown<br />
Sample table page<br />
Manuscript page <strong>of</strong> explanation<br />
B 271<br />
Brown, George (1650–1730)<br />
George Brown, B 270<br />
Table, B 270<br />
A compendious, but a compleat system <strong>of</strong> decimal<br />
arithmetick, containing more exact rules for ordering<br />
infinites, than any hitherto extant.<br />
Year: 1701<br />
Place: Edinburgh<br />
Publisher: Brown<br />
Edition: 1st<br />
Language: English<br />
Binding: contemporary leather<br />
Pagination: pp. 68<br />
Collation: A–E 4 F–G 2 H–I 4 K 2<br />
Size: 175x142 mm<br />
This is an elementary arithmetic beginning with a<br />
description <strong>of</strong> the four basic operations. The last half<br />
presents the rule <strong>of</strong> three and a few simple business<br />
problems. The final section on compound interest<br />
illustrates the process with logarithms but does not<br />
include a table.<br />
Illustrations available:<br />
Title page<br />
213
214<br />
Erwin Tomash Library<br />
Brown, Gordon Stanley Brown, John<br />
B 272<br />
Brown, Gordon Stanley (1907–) and Donald Pierce<br />
Campbell<br />
Principles <strong>of</strong> servomechanisms. Dynamics and<br />
synthesis <strong>of</strong> closed-loop control systems<br />
Year: 1948<br />
Place: New York<br />
Publisher: John Wiley<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards<br />
Pagination: pp. xiv, 400<br />
Size: 230x147 mm<br />
Brown was the director <strong>of</strong> the MIT Servomechanisms<br />
Laboratory, the organization that was responsible for<br />
the development <strong>of</strong> the Whirlwind computer. Campbell<br />
was a pr<strong>of</strong>essor <strong>of</strong> electrical engineering at MIT. This<br />
book is not about the Whirlwind but about the closed<br />
loop control equipment that was a mainstay <strong>of</strong> industrial<br />
machinery. It was the failure <strong>of</strong> this type <strong>of</strong> control<br />
system as applied to aircraft trainers that led them to<br />
investigate the electronic digital systems that eventually<br />
resulted in Whirlwind.<br />
This highly technical description <strong>of</strong> control systems was<br />
produced at the end <strong>of</strong> the era <strong>of</strong> mechanical/hydraulic<br />
systems, when they were about to be replaced by their<br />
electronic equivalents.<br />
Illustrations available:<br />
Title page<br />
B 271<br />
B 273<br />
Brown, John (fl.1648–1695)<br />
The description and use <strong>of</strong> the carpenter’s-rule:<br />
Together with the use <strong>of</strong> the line <strong>of</strong> numbers commonly<br />
call’d Gunter’s-line. Applyed to the measuring <strong>of</strong> all<br />
superficies and solids, as board, glass, plaistering,<br />
wainscot, tyling, paving, flooring &c. Timber, stone,<br />
square or round, gauging <strong>of</strong> vessels, &c. Also military<br />
orders, simple and compound interest, and tables <strong>of</strong><br />
reduction, with the way <strong>of</strong> working by arithmetick, in<br />
the most <strong>of</strong> them. Together with the use <strong>of</strong> the glasiers<br />
and Mr. White’s sliding rules. Rendered plain and easie<br />
for ordinary capacities.<br />
Year: 1704<br />
Place: London<br />
Publisher: Printed for R. Mount<br />
Edition: 4th<br />
Language: English<br />
Figures: 1 engraved plate (follows p. 6)<br />
Binding: contemporary leather rebacked<br />
Pagination: pp. 190<br />
Collation: A–G 12 H 11<br />
Size: 133x72 mm<br />
Reference: Tay MP I, p. 418<br />
This work examines the use <strong>of</strong> Gunter’s line <strong>of</strong> numbers—<br />
a logarithmic scale first proposed by Edmund Gunter;<br />
later, by incorporating two such scales, Oughtred created<br />
the slide rule. Initially, Gunter’s line was to be used by<br />
measuring distances with a pair <strong>of</strong> dividers.<br />
After explaining the use <strong>of</strong> the rule for simple arithmetic,<br />
this work illustrates its use by various problems from the<br />
domestic purchase <strong>of</strong> coal to interpretation <strong>of</strong> surveys<br />
White’s title, B 273
Erwin Tomash Library<br />
Brown, John Brown, John<br />
and currency exchange. A small table <strong>of</strong> squares and<br />
cubes appears, at first glance, to be for arbitrary values<br />
but in fact demonstrates that to use the logarithmic scale<br />
to find roots requires the user to appreciate the number <strong>of</strong><br />
digits being used (e.g., the cube root <strong>of</strong> 1728, 17576 and<br />
175616 are easily confused).<br />
Brown’s revision <strong>of</strong> White’s Use <strong>of</strong> the line <strong>of</strong> numbers<br />
on a sliding (or Glasier’s) rule has its own separate title<br />
page, but with continuous pagination.<br />
Illustrations available:<br />
Brown’s title page<br />
White’s title page<br />
Table <strong>of</strong> roots<br />
Brown’s title, B 273<br />
Table <strong>of</strong> roots, B 273<br />
B 274<br />
Brown, John (fl.1648–95)<br />
Horologiographia: or the art <strong>of</strong> dyalling, being the<br />
second book <strong>of</strong> the use <strong>of</strong> the trianguler-quadrant.<br />
Shewing the natural, artificial, and instrumental way,<br />
<strong>of</strong> making <strong>of</strong> sun dials, on any flat superficies: with<br />
plain and easie directions, to discover their nature and<br />
affections, by the horizontal projection. With the way<br />
<strong>of</strong> drawing the usual ornaments on any plain: also, a<br />
familiar easie way to draw those lines on the ceiling <strong>of</strong><br />
a room, by the trianguler quadrant. Also the use <strong>of</strong> the<br />
same instrument in navigation; both for observation,<br />
and operation. Performing the use <strong>of</strong> several seainstruments<br />
still in use.<br />
Year: 1671<br />
Place: London<br />
Publisher: Printed by John Darby for John Wingfield, also by<br />
John Brown and John Seller<br />
Edition: 1st<br />
Language: English<br />
Figures: 25 engraved plates pasted to text leaves<br />
Binding: contemporary leather; spine gilt in compartments<br />
Pagination: pp. 305, [7]<br />
Collation: A–T 8 V 4<br />
Size: 1413x90 mm<br />
This is a very nice book on dialing. It manages to cover<br />
almost every possible aspect <strong>of</strong> the subject and discusses<br />
dials on all surfaces. Brown has added an appendix On<br />
the use <strong>of</strong> the Triangular Quadrant in Navigation.<br />
Illustrations available:<br />
Title page<br />
B 274<br />
215
216<br />
Erwin Tomash Library<br />
Brown, John Brown, Richard<br />
B 275<br />
Brown, John and John Wallace<br />
Mathematical tables, containing the logarithms <strong>of</strong><br />
numbers, logarithmic sines, tangents, and secants, and<br />
a traverse table; to which are prefixed, logarithmical<br />
arithmetic, and plane trigonometry; also examples on<br />
the mensuration <strong>of</strong> heights and distances. For the use <strong>of</strong><br />
schools.<br />
Year: 1808<br />
Place: Edinburgh<br />
Publisher: Peter Hill and Longman [et al.]<br />
Edition: 2nd<br />
Language: English<br />
Binding: contemporary leather; red leather label<br />
Pagination: pp. [4], 72, [86], 8<br />
Collation: π 2 A–I 4 2a–2r 2 2s 4 2t–2u 2 2x 5<br />
Size: 204x117 mm<br />
Reference: Hend BTM, #120.0, pp. 104–105<br />
Nothing is known about Brown other than the fact he<br />
calls himself a mathematician on the title page. The<br />
name <strong>of</strong> the Rev. John Wallace, although not on the title<br />
page, comes from the initials J.W., which appear on an<br />
advertisement prior to the table <strong>of</strong> contents.<br />
This table <strong>of</strong> logarithms begins with an introduction<br />
including the use <strong>of</strong> the tables for both scientific and<br />
business calculations. The table itself would have been<br />
particularly difficult to use as it is set in small type<br />
with few breaks in the layout to guide the eye (see<br />
illustration).<br />
On the front fly leaf is penciled in a contemporary<br />
hand:<br />
May angles help my lovely favir impowered by<br />
heaven above come & g[?] yee power vouchsafe<br />
you to gauird the maid I love. The author Jane<br />
Thoms, Chesninton by Dundee NB<br />
Illustrations available:<br />
Title page<br />
Log table typography, B 275<br />
Table page<br />
Fly leaf notation<br />
B 276<br />
Brown, Richard (1856–1918)<br />
A history <strong>of</strong> accounting and accountants<br />
Year: 1905<br />
Place: Edinburgh<br />
Publisher: T. C. & E. C. Jack<br />
Edition: 1st<br />
Language: English<br />
Figures: 25 photolith plates<br />
Binding: half bound; uncut<br />
Pagination: pp. xvi, 459, [1]<br />
Collation: π 8 A–2E 8 2F 6<br />
Size: 259x193 mm<br />
B 275<br />
On the fiftieth anniversary <strong>of</strong> the incorporation <strong>of</strong><br />
accountants in Scotland (the first country in which<br />
Chartered Accountants were created), it was decided to<br />
produce a volume about the history <strong>of</strong> the organization.<br />
This plan soon grew to include a history <strong>of</strong> accounting<br />
itself. While not ready in time for the actual anniversary,<br />
this is a comprehensive work beginning with the<br />
development <strong>of</strong> numerical notation in ancient Greece,<br />
showing early forms <strong>of</strong> accounts from Egypt and<br />
elsewhere and culminating with the creation <strong>of</strong> the<br />
accounting pr<strong>of</strong>ession in Britain, Europe, America,<br />
Japan, South America and a few other places.
Erwin Tomash Library<br />
Brozek, Jan Brozek, Jan<br />
This is number 57 <strong>of</strong> a deluxe limited edition <strong>of</strong> 250<br />
signed copies.<br />
Illustrations available:<br />
Title page<br />
B 277<br />
Brozek, Jan (1585–1652)<br />
Arithmetica integrorum edita.<br />
B 276<br />
Year: 1620<br />
Place: Cracow<br />
Publisher: Matthiæ Andreoviensis (Maciej Andrzejowczyk)<br />
Edition: 1st<br />
Language: Latin<br />
Figures: 1 large folding plate<br />
Binding: later paper boards<br />
Pagination: pp. [16], 252, [4]<br />
Collation: A 8 A–Q 8<br />
Size: 143x95 mm<br />
Reference: DSB, v2, p. 526<br />
Jan Brozek is acknowledged as the best Polish<br />
mathematician <strong>of</strong> his day. He held a number <strong>of</strong> different<br />
positions at Polish universities and eventually became<br />
Rector <strong>of</strong> the <strong>University</strong> <strong>of</strong> Krakow. He published in<br />
excess <strong>of</strong> thirty works, some on mathematical topics but<br />
also many to do with religious controversies.<br />
The DSB indicates that this book introduced logarithms<br />
into Polish schools. Although Brozek was clearly familiar<br />
with Napier, there is no obvious mention <strong>of</strong> logarithms<br />
in this work and certainly no tables or instruction on how<br />
they were to be used. It would appear that the author <strong>of</strong><br />
the DSB biography has mistaken references to Napier’s<br />
bones for logarithms.<br />
This arithmetic begins with numeration and then treats<br />
the fundamental operations, including mediation and<br />
duplation. This section is illustrated with an example <strong>of</strong><br />
finger numerals that differ from the usual ones <strong>of</strong> Bede<br />
and Pacioli. A very large gelosia diagram illustrates<br />
multiplication along with another in which Brozek first<br />
calculates all nine multiples <strong>of</strong> the multiplicand—a<br />
technique also used in his illustration <strong>of</strong> division. After<br />
discussion <strong>of</strong> arithmetic and geometric progressions, he<br />
deals with squares and cubes.<br />
The most interesting section deals with John Napier and<br />
his Rabdologiae (1617) and appears a mere three years<br />
after Napier’s own publication. He not only includes the<br />
usual Napier’s Bones but also prefaces it with a lengthy<br />
description <strong>of</strong> Napier’s binary (chessboard) abacus,<br />
which Brozek refers to as abaco Scacchiae. This is one<br />
<strong>of</strong> the few published references in the contemporary<br />
literature to this device.<br />
B 277<br />
Finger numerals, B 277<br />
217
218<br />
Erwin Tomash Library<br />
Bruno, Giordano Bruno, Giordano<br />
Gelosia multiplication, B 277<br />
Illustrations available:<br />
Title page<br />
Finger numerals for a problem <strong>of</strong> 8 times 6<br />
Gelosia multiplication<br />
Multiples <strong>of</strong> the multiplicand<br />
Napier’s chessboard abacus<br />
B 278<br />
Bruno, Giordano (1548–1600)<br />
De lampade combinatria Lulliana<br />
b/w: Bruno, Giordano; De specierum scrutinio<br />
b/w: Bruno, Giordano; De progressu & lampade<br />
venatoria logicorum<br />
b/w: Agrippa, Heinrich Cornelius von Nettesheim;<br />
Commentaria Agrippae in artem brevem Lullian<br />
b/w: Lull, Ramon; Opera ea quæ ad adinventam ab<br />
ipso artem universalem, scientiarum artiumque<br />
omnium brevi compendio, firmaque memoria<br />
apprehendendarum, locupletissmaque vel<br />
oratione ex tempore pertractandarum, pertinent.<br />
Ut et in eandem quorundam interpretum scripti<br />
commentarij: quae omnia sequens indicatbit<br />
pagina: & hoc demùn tempore coniunction<br />
emendatiora locupletioraq[ue] non nihil edita<br />
sunt. Accessit index cum capitum, tum rerum ac<br />
verborum ac verborum locupletissimus.<br />
Year: 1598<br />
Place: Strasbourg<br />
Publisher: Lazar Zetzner<br />
Edition: 1st<br />
Language: Latin<br />
Figures: 3 folding plates<br />
Binding: contemporary vellum; red edges<br />
Pagination: pp. [24], 992, [32] (mis# 80 as 34)<br />
Collation: (?) 4 ):( 8 a–z 8 A–2S 8<br />
Size: 179x106 mm<br />
See entry for Lull, Ramon; Opera, 1598<br />
Illustrations available:<br />
None<br />
B 279<br />
Bruno, Giordano (1548–1600)<br />
De progressu & lampade venatoria logicorum<br />
b/w: Bruno, Giordano; De specierum scrutinio<br />
b/w: Bruno, Giordano; De lampade combinatria<br />
Lulliana<br />
b/w: Agrippa, Heinrich Cornelius von Nettesheim;<br />
Commentaria Agrippae in artem brevem Lullian<br />
b/w: Lull, Ramon; Opera ea quæ ad adinventam ab<br />
ipso artem universalem, scientiarum artiumque<br />
omnium brevi compendio, firmaque memoria<br />
apprehendendarum, locupletissimaque vel<br />
oratione extempore pertractandarum, pertinent.<br />
Ut et in eandem quorundam interpretum scripti<br />
commentarij: quae omnia sequens indicabit<br />
pagina: & hoc demùn tempore coniunctim<br />
emendatiora locupletioraq[ue] non nihil edita<br />
sunt. Accessit index cum capitum, tùm rerum ac<br />
verborum ac verborum locupletissimus.<br />
Year: 1598<br />
Place: Strasbourg<br />
Publisher: Lazar Zetzner<br />
Edition: 1st<br />
Language: Latin<br />
Figures: 3 folding plates<br />
Binding: contemporary vellum; red edges<br />
Pagination: pp. [24], 992, [32] (mis# 80 as 34)<br />
Collation: (?) 4 ):( 8 a–z 8 A–2S 8<br />
Size: 179x106 mm<br />
See entry for Lull, Ramon; Opera, 1598<br />
Illustrations available:<br />
None<br />
B 280<br />
Bruno, Giordano (1548–1600)<br />
De specierum scrutinio<br />
b/w: Bruno, Giordano; De lampade combinatria<br />
Lulliana<br />
b/w: Bruno, Giordano; De progressu & lampade<br />
venatoria logicorum<br />
b/w: Agrippa, Heinrich Cornelius von Nettesheim;<br />
Commentaria Agrippae in artem brevem Lullian<br />
b/w: Lull, Ramon; Opera ea quæ ad adinventam ab<br />
ipso artem universalem, scientiarum artiumque<br />
omnium brevi compendio, firmaque memoria<br />
apprehendendarum, locupletissimaque vel<br />
oratione extempore pertractandarum, pertinent.<br />
Ut et in eandem quorundam interpretum scripti<br />
commentarij: quae omnia sequens indicabit<br />
pagina: & hoc demùn tempore coniunctim<br />
emendatiora locupletioraq[ue] non nihil edita
sunt. Accessit index cum capitum, tùm rerum ac<br />
verborum ac verborum locupletissimus.<br />
Year: 1598<br />
Place: Strasbourg<br />
Publisher: Lazar Zetzner<br />
Edition: 1st<br />
Language: Latin<br />
Figures: 3 folding plates<br />
Binding: contemporary vellum; red edges<br />
Pagination: pp. [24], 992, [32] (misnumbered 80 as 34)<br />
Collation: (?) 4 ):( 8 a–z 8 A–2S 8<br />
Size: 179x106 mm<br />
See entry for Lull, Ramon; Opera, 1598<br />
Illustrations available:<br />
None<br />
B 281<br />
Bruns, Robert A. and Robert M. Saunders<br />
Analysis <strong>of</strong> feedback control systems. Servomechanisms<br />
and automatic regulators<br />
Year: 1955<br />
Place: New York<br />
Publisher: McGraw-Hill<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards<br />
Pagination: pp. xvi, 383, [1]<br />
Size: 229x148 mm<br />
Bruns and Saunders were pr<strong>of</strong>essors at the <strong>University</strong><br />
<strong>of</strong> California at Berkeley, but at the time this book was<br />
written, Bruns had moved to take a position at the Jet<br />
Propulsion Laboratory.<br />
This is a highly technical account <strong>of</strong> both the theory and<br />
practice <strong>of</strong> servomechanisms. The theoretical part is<br />
Erwin Tomash Library<br />
Bruns, Robert A. Buchholz, Werner<br />
B 281<br />
B 282<br />
balanced by some very practical considerations, e.g., the<br />
explanation <strong>of</strong> how to eliminate backlash in spur gears.<br />
Illustrations available:<br />
Title page<br />
B 282<br />
Bubnov, Nikolai Mikhailovitch (1858–); [Joseph<br />
Lezius (1860 – ), translator]<br />
Arithmetische Selbständigkeit der europäischen Kultur.<br />
Ein Betrag zur Kulturgeschichte.<br />
Year: 1914<br />
Place: Berlin<br />
Publisher: R. Friedländer & Sohn<br />
Edition: 1st (German)<br />
Language: German<br />
Binding: three-quarter leather over marbled boards<br />
Pagination: pp. viii, 285, [1]<br />
Collation: π 4 1–17 8 18 7<br />
Size: 225x149 mm<br />
This is a history <strong>of</strong> arithmetic in Europe, originally<br />
written in Russian by a pr<strong>of</strong>essor at Kiev and translated<br />
by a pr<strong>of</strong>essor at the same institution. It contains a<br />
lengthy section on the use <strong>of</strong> the European table abacus.<br />
Unfortunately, it is not illustrated.<br />
This copy ex-libris Otto Neugebauer.<br />
Illustrations available:<br />
Title page<br />
219
220<br />
Erwin Tomash Library<br />
Buchholz, Werner Buchholz, Werner<br />
B 283<br />
Buchholz, Werner, editor<br />
The computer issue. In Proceedings <strong>of</strong> the I. R. E., Vol.<br />
41, No. 10, October 1953.<br />
Year: 1953<br />
Place: New York<br />
Publisher: <strong>Institute</strong> <strong>of</strong> Radio Engineers<br />
Edition: 1st<br />
Language: English<br />
Binding: original paper wrappers<br />
Pagination: pp. 1219–1554<br />
Size: 280x215 mm<br />
This special issue <strong>of</strong> the Proceedings <strong>of</strong> the IRE was<br />
created by the IRE Pr<strong>of</strong>essional Group on Electronic<br />
Computers (PGEC). PGEC was founded two years<br />
previously and had grown to over two thousand members.<br />
Like the AFIPS volume (see AFIPS, Proceedings <strong>of</strong><br />
the Joint AIEE-IRE Computer Conference. Review <strong>of</strong><br />
electronic digital computers, 1952) <strong>of</strong> the preceding year,<br />
this issue dramatically illustrates the growth <strong>of</strong> interest,<br />
and advances made, in the early days <strong>of</strong> computers.<br />
The volume contains forty-one papers, <strong>of</strong> which a number<br />
are <strong>of</strong> secondary interest. The following are the major<br />
papers (the paper’s title is usually a very clear indicator<br />
<strong>of</strong> its contents):<br />
Buchholz, Werner<br />
The system design <strong>of</strong> the IBM Type 701<br />
computer, pp. 1262–1275<br />
Buchholz was a major designer <strong>of</strong> IBM<br />
computers. He worked on the IBM 701 and the<br />
IBM 7030 (Stretch).<br />
Burks, Arthur Walter (1915–) and Jesse B.<br />
Wright<br />
Theory <strong>of</strong> logical nets, pp. 1357–1365<br />
Arthur Burks was a member <strong>of</strong> the ENIAC<br />
team and later a pr<strong>of</strong>essor at the <strong>University</strong> <strong>of</strong><br />
Michigan. See the entry for Burks, Theory <strong>of</strong><br />
logical nets, 1953.<br />
Crosman, Loring P.<br />
The Remington Rand Type 409-2 Electronic,<br />
pp. 1332–1340<br />
Crossman was an engineer with Remington<br />
Rand, Laboratory <strong>of</strong> Advanced Research, South<br />
Norwalk, Connecticut.<br />
Eckert, John Adam Presper, Jr. (1919–1995)<br />
A survey <strong>of</strong> digital computer memory systems,<br />
pp. 1393–1406<br />
Eckert, one <strong>of</strong> the principle designers <strong>of</strong> ENIAC<br />
and the UNIVAC I, was one <strong>of</strong> the foremost<br />
engineers in this field. He was always concerned<br />
with memory systems and recognized them as<br />
the key to computer design. This is one <strong>of</strong> the<br />
best survey papers on early computer memory<br />
systems.<br />
Elbourn, Robert D. and Richard P. Witt.<br />
Dynamic circuit techniques used in SEAC and<br />
DYSEAC, pp. 1380–1387<br />
Both authors were with the National Bureau<br />
<strong>of</strong> Standards and were part <strong>of</strong> the group that<br />
designed the SEAC and DYSEAC circuits.<br />
Erickson, Robert S.<br />
The Logistics Computer, pp. 1325–1332<br />
Erickson was an engineer with Engineering<br />
Research Associates (ERA), which by this time<br />
had become a division <strong>of</strong> Remington Rand. He<br />
later joined Control Data Corporation (CDC).<br />
Frizzell, Clarence E.<br />
Engineering description <strong>of</strong> the IBM Type 701<br />
computer, pp. 1275–1287<br />
Frizzell was an engineer with IBM’s Engineering<br />
Laboratory in Poughkeepsie, NY.<br />
Gluck, S. E.; H. J. Gray Jr.; C.T. Leondes;<br />
and Morris Rubin<strong>of</strong>f<br />
The design <strong>of</strong> logical OR-AND-OR pyramids<br />
for digital computers, pp. 1388–1392<br />
All the authors were with the Moore School<br />
<strong>of</strong> Electrical Engineering <strong>of</strong> the <strong>University</strong> <strong>of</strong><br />
Pennsylvania.
Erwin Tomash Library<br />
Buchholz, Werner Buchholz, Werner<br />
Greenwald, Sidney; R. C. Haueter and<br />
Samuel Nathan Alexander (1910–1967)<br />
SEAC, pp. 1300–1313<br />
The authors were with the National Bureau <strong>of</strong><br />
Standards, where they were instrumental in the<br />
design and construction <strong>of</strong> SEAC.<br />
Hopper, Grace Brewster Murray (1906–1992)<br />
and John William Mauchly (1907–1980)<br />
Influence <strong>of</strong> programming techniques on the<br />
design <strong>of</strong> computers, pp. 1250–1254<br />
Grace Hopper began her computer career with<br />
Howard Aiken at Harvard, but by this time<br />
she was a member <strong>of</strong> the staff <strong>of</strong> the UNIVAC<br />
Division <strong>of</strong> Remington Rand. Mauchly was<br />
one <strong>of</strong> the principle designers <strong>of</strong> ENIAC and<br />
UNIVAC I.<br />
Huskey, Harry Douglas (1916–); R.<br />
Thorenson; B. F. Ambrosio; and E. C. Yowell<br />
The SWAC - Design features and operating<br />
experience, pp. 1294–1299<br />
The authors were the principal figures in<br />
the creation <strong>of</strong> SWAC, the National Bureau<br />
<strong>of</strong> Standards computer at UCLA, their Los<br />
Angeles site. By this time, Huskey, who had<br />
started his career as a member <strong>of</strong> the ENIAC<br />
team and had worked at the National Physical<br />
Laboratory with Alan Turing for a year, was on<br />
the staff <strong>of</strong> Wayne <strong>University</strong>, Detroit.<br />
King, Gilbert W.; George W. Brown and<br />
Louis Nicot Ridenour, Jr. (1911–1959)<br />
Photographic techniques for information<br />
storage, pp. 1421–1428<br />
The authors were on staff <strong>of</strong> the International<br />
Telemeter Corporation in Los Angeles, the<br />
parent firm <strong>of</strong> Telemeter Magnetics, an early<br />
supplier <strong>of</strong> magnetic core memories. All the<br />
authors had distinguished careers: King became<br />
Director <strong>of</strong> Research at IBM, Brown was a<br />
pr<strong>of</strong>essor at UCLA and UC Irvine, and Ridenour,<br />
who had edited the MIT Radiation Laboratory<br />
series <strong>of</strong> books after the war, became the chief<br />
scientist for the Air Force.<br />
Lewis, W. D.<br />
Electronic computers and telephone switching,<br />
pp. 1242–1244<br />
Lewis was an engineer with Bell Telephone<br />
Laboratories.<br />
Palevsky, Max<br />
The design <strong>of</strong> the Bendix Digital Differential<br />
Analyzer, pp. 1352–1356<br />
Palevsky joined Bendix Aviation’s Computer<br />
Division in 1952. He later founded Scientific<br />
Data Systems (SDS), which produced the Sigma<br />
line <strong>of</strong> computers (later purchased by Xerox to<br />
form XDS).<br />
Rajchman, Jan A. (1911–1989)<br />
A myriabit magnetic-core matrix memory, pp.<br />
1407–1421<br />
Rajchman was a pioneer research engineer with<br />
RCA Laboratories. He was very interested in<br />
memory systems and designed the Selectron<br />
memory tubes used on the Johnniac computer.<br />
Ross, Harold D., Jr.<br />
The arithmetic element <strong>of</strong> the IBM Type 701<br />
computer, pp. 1287–1294<br />
Ross was a member <strong>of</strong> the staff at the IBM<br />
Engineering Laboratory in Poughkeepsie, NY.<br />
Rubin<strong>of</strong>f, Morris<br />
Analogue vs. digital computers - A<br />
comparison, pp. 1254–1262<br />
Rubin<strong>of</strong>f was an engineer with the Moore School<br />
<strong>of</strong> Electrical Engineering at the <strong>University</strong> <strong>of</strong><br />
Pennsylvania and later a faculty member.<br />
Samuel, Arthur Lee (1901–1990)<br />
Computing bit by bit or digital computers<br />
made easy, pp. 1223–1230<br />
After an early career at MIT and the <strong>University</strong><br />
<strong>of</strong> Illinois, Samuel moved to IBM in 1949,<br />
221
222<br />
Erwin Tomash Library<br />
Buchholz, Werner Buchholz, Werner<br />
where he remained until retiring in 1966 to take<br />
a post at Stanford <strong>University</strong>. He is best known<br />
for his early work in artificial intelligence,<br />
particularly the creation <strong>of</strong> an early checkersplaying<br />
computer program.<br />
Serrell, Robert<br />
Elements <strong>of</strong> Boolean algebra for the study <strong>of</strong><br />
information-handling systems, pp. 1366–1380<br />
Serrell was an engineer with the RCA David<br />
Sarn<strong>of</strong>f Research Center in Princeton.<br />
Shannon, Claude Elwood (1916–2001)<br />
Computers and Automata, pp. 1234–1241<br />
Shannon was a member <strong>of</strong> the technical staff<br />
at Bell Telephone Laboratories. He is best<br />
remembered for his groundbreaking theoretical<br />
work on coding and information transmission.<br />
Shannon, Claude Elwood (1916–2001) and<br />
Edward F. Moore<br />
Machine aid for switching circuit design, pp.<br />
1348–1351<br />
Both authors were with Bell Telephone<br />
Laboratories in Murray Hill, NJ.<br />
Sherertz, Paul C.<br />
Electronic circuits <strong>of</strong> the NAREC computer,<br />
pp. 1313–1320<br />
NAREC, the Naval Research (Laboratory)<br />
Computer, was just being put into operation at<br />
the Naval Research Laboratory when this paper<br />
was written. Sherertz was an engineer on the<br />
project.<br />
Thomas, Walker H.<br />
Fundamentals <strong>of</strong> digital computer<br />
programming, pp. 1245–1249<br />
Walker, from IBM’s Engineering Laboratory<br />
in Poughkeepsie, NY, presented a short tutorial<br />
on how to program a simple, hypothetical<br />
computer.<br />
Ware, Willis Howard (1920–)<br />
The logical principles <strong>of</strong> a new kind <strong>of</strong> binary<br />
counter, pp. 1429–1437<br />
Ware, an engineer with the Rand Corporation,<br />
was one <strong>of</strong> the principal designers <strong>of</strong> the<br />
Johnniac computer. Here he is reporting on<br />
work that had been done for the von Neumann<br />
computer project at the <strong>Institute</strong> for Advanced<br />
Study, Princeton.<br />
Wheeler, David J. (1927– 2004) and James E.<br />
Robertson<br />
Diagnostic programs for the Illiac, pp. 1320–<br />
1325<br />
Wheeler, working as a graduate student under<br />
Maurice Wilkes, was a designer <strong>of</strong> the EDSAC<br />
computer in Cambridge. He is responsible<br />
for, among other things, the concept <strong>of</strong> the<br />
subroutine jump instruction (initially known as<br />
the Wheeler Jump). He spent his entire career<br />
at the <strong>University</strong> <strong>of</strong> Cambridge, but at the time<br />
<strong>of</strong> this paper, he was on leave working at the<br />
<strong>University</strong> <strong>of</strong> Illinois ILLIAC project.<br />
Wilkes, Maurice Vincent (1913–)<br />
Can machines think?, pp. 1230–1234<br />
B 283
Erwin Tomash Library<br />
Buchner, Johann Paul Buckley, Arabella Burton<br />
This is a repeat <strong>of</strong> a paper by Wilkes that was<br />
originally published in the May 1953 issue <strong>of</strong><br />
Discovery in London.<br />
Illustrations available:<br />
Cover page<br />
B 284<br />
Buchner, Johann Paul<br />
B 284<br />
Frontispiece, B 284<br />
Tabula radicum, quadratorum & cuborum, In Welcher<br />
von allen gegebenen Cubis und Quadratis der Radix bis<br />
auf 12000 als<strong>of</strong>ort ohne eintziges Rechnensammt der<br />
darinnen steckenden surdischen oder irrational-Zahl<br />
extrahiret zu finden: …<br />
Year: 1701<br />
Place: Nürnberg<br />
Publisher: Johann Helmers<br />
Edition: 1st<br />
Language: German<br />
Figures: engraved frontispiece; title in red and black<br />
Binding: contemporary leather<br />
Pagination: pp. [14], 252<br />
Collation: A 7 B–Q 8 R 6<br />
Size: 185x78 mm<br />
Reference: Not in NUC<br />
This is a set <strong>of</strong> tables <strong>of</strong> squares and cubes <strong>of</strong> all integers<br />
from 2 to 12,000. A short introduction provides a few<br />
examples <strong>of</strong> the use <strong>of</strong> the tables. The frontispiece is a<br />
nicely engraved scene with a cupid figure, indicating<br />
that the volume <strong>of</strong> a cubic stone can be determined by<br />
reference to this book. Although there is a short errata at<br />
the end <strong>of</strong> the volume, the tables are replete with other<br />
errors. Many corrections have been manually entered in<br />
the tables, sometimes as many as seventeen per page.<br />
Illustrations available:<br />
Title page (color)<br />
Frontispiece<br />
Table page with corrections<br />
B 285<br />
Buckley, Arabella Burton (1840–1929)<br />
A short history <strong>of</strong> natural science<br />
Year: 1879<br />
Place: London<br />
Publisher: Edward Stanford<br />
Edition: 2nd<br />
Language: English<br />
Binding: contemporary buckram leather<br />
Pagination: pp. xxix, [1], 505, [3]<br />
Collation: π 15 B–2I 8 2K 6<br />
Size: 183x119 mm<br />
B 285<br />
223
224<br />
Erwin Tomash Library<br />
Buckner, Hans Bull, Ludlow<br />
This is a history <strong>of</strong> science for use in schools. It is written<br />
in a simple style matching its intended audience but also<br />
simplifies some matters more than is, perhaps, justified.<br />
Illustrations available:<br />
Title page<br />
B 286<br />
Buckner, Hans<br />
Uber die Entwicklung des Integromat. In Probleme der<br />
Entwicklung programmgesteuerter rechengeräte und<br />
Integrieranlagen<br />
Year: 1953<br />
Place: Aachen<br />
Publisher: Rhein-Westf. Technische Hochschule<br />
Edition: 1st<br />
Language: German<br />
Binding: cloth boards; original paper wrappers bound in<br />
Pagination: pp. [2], XIV, 75, [1], 10<br />
Size: 207x145 mm<br />
See entry for Cremer; Probleme der Entwicklung<br />
programmgesteuerte Rechengeräte …, 1953.<br />
Illustrations available:<br />
None<br />
B 287<br />
Budelius, Renerus (16th Century)<br />
De monetis, et re numaria, libri duo<br />
Year: 1591<br />
Place: Cologne<br />
Publisher: Johann Gymnich<br />
Edition: 1st<br />
Language: Latin<br />
Binding: contemporary limp vellum; boxed<br />
Pagination: pp. [76], 236, 239–269, [2], 353–614, 619–798<br />
Collation: … 6 …… 4 ……… 4 à 4 è 4 ì 4 ò 4 ù 4 & 4 A–T 4 V 2 a–o 4 2A–4I 4 4K 2<br />
Size: 238x170 mm<br />
Reference: Smi Rara, p. 396; Ada CBCE, #B–3153<br />
Reiner Budel was director <strong>of</strong> the Bavarian mint.<br />
This is the first edition <strong>of</strong> a well-known massive work<br />
in the history <strong>of</strong> economics with particular emphasis<br />
on the history <strong>of</strong> money and coinage. It consists <strong>of</strong><br />
two significant <strong>chapter</strong>s written by Budelius followed<br />
by <strong>chapter</strong>s written by Albertus Brunus, Johannes<br />
Aquila, Bilibaldus Pirkheymer, Martinus Laudensis and<br />
several others. The work is difficult to understand and<br />
illustrations are few. There is a striking bookplate in the<br />
front cover from Arthur Hugh Smith Barry (with a label<br />
<strong>of</strong> Marbury Library at the Barry estates near Cheshire,<br />
England) and the book label <strong>of</strong> Robert Honeyman.<br />
Illustrations available:<br />
Title page<br />
B 287<br />
Bull, Ludlow, editor<br />
See Chace, Arnold Buffum; The Rhind mathematical<br />
papyrus, 1929.<br />
B 288
Erwin Tomash Library<br />
Bullet, Pierre Burkhardt, Heinrich Friedrich Karl Ludwig<br />
B 288<br />
Bullet, Pierre (1639–1716)<br />
Traite de l’usage du pantometre, instrument<br />
geometrique, propre à prendre toutes sortes d’angles,<br />
mezurer les distances accessibles & inaccessibles,<br />
arpenter & diviser toutes sortes de figures, & c.<br />
Year: 1675<br />
Place: Paris<br />
Publisher: André Pralard<br />
Edition: 1st<br />
Language: French<br />
Figures: engraved half title; woodcut device on title; woodcut<br />
initials and headpieces; engraved coat <strong>of</strong> arms printed<br />
on verso <strong>of</strong> title; 25 full-page engraved illustrations<br />
printed in text.<br />
Binding: contemporary sprinkled leather; gilt spine with raised<br />
bands<br />
Pagination: pp. [xxii], 26,187, [5]<br />
Collation: a 8 e 4 i 8 o 4 AB–PQ 8,4<br />
Size: 157x185 mm<br />
Pierre Bullet was a prominent architect and engineer. He<br />
was responsible for a number <strong>of</strong> works in Paris, including<br />
the rebuilding <strong>of</strong> the Quay le Peletier in 1673. In 1676,<br />
he published, with Nicolas-François Blondel, a plan <strong>of</strong><br />
Paris showing all <strong>of</strong> its buildings.<br />
It seems likely that during his survey <strong>of</strong> Paris, Bullet<br />
created the pantometre instrument described in this<br />
work. It was not unlike many such devices <strong>of</strong> its day—<br />
basically three rods hinged together or, like this one,<br />
one rod capable <strong>of</strong> sliding on another (see entries for<br />
Pantometre, B 288<br />
Danfree, 1597, and Bürgi, 1684). Bullet indicates that<br />
this version could be purchased from the stock <strong>of</strong> the<br />
instrument maker Lemaire in Paris. The work is well<br />
illustrated, showing the instrument in use for the usual<br />
types <strong>of</strong> problems: finding heights <strong>of</strong> towers, depths <strong>of</strong><br />
wells, breadths <strong>of</strong> rivers, etc.<br />
The unusual collation results from the original printed<br />
sheets having been cut in two unequal portions that were<br />
separately signed before being bound.<br />
Illustrations available:<br />
Title page<br />
Pantometre instrument<br />
Instrument in use<br />
[Burgi, Joost (1552–1632)]<br />
See Bramer, Benjamin; Dritter Theil oder Anhang<br />
eines Berichts von M. Johsten Burgi, 1684.<br />
Journal cover, B 289<br />
B 289<br />
Burkhardt, Heinrich Friedrich Karl Ludwig (1861–<br />
1914)<br />
Wie man vor Zeiten rechnete<br />
Year: 1905<br />
Place: Leipzig<br />
Publisher: B. G. Teubner<br />
Edition: <strong>of</strong>fprint<br />
Language: German<br />
Binding: original paper wrappers<br />
Pagination: pp. 9–20<br />
Size: 247x162 mm<br />
Burkhardt was a major figure in the manufacture<br />
<strong>of</strong> mechanical calculating machines. His factory in<br />
225
226<br />
Erwin Tomash Library<br />
Burks, Arthur Walter Burks, Arthur Walter<br />
Glashütte was a major supplier <strong>of</strong> calculating machines<br />
worldwide.<br />
This paper describing the early history <strong>of</strong> calculating<br />
does not go into any depth but does give examples <strong>of</strong><br />
Greek, Chinese and other numerals as well as illustrating<br />
a few methods <strong>of</strong> calculating.<br />
A four-page 1893 manuscript letter by Burkhardt is laid<br />
in.<br />
Illustrations available:<br />
Front cover<br />
B 290<br />
Burks, Arthur Walter (1915–)<br />
Electronic computing circuits <strong>of</strong> the ENIAC. In<br />
Proceedings <strong>of</strong> the I.R.E., vol. 35, #8, August 1947.<br />
Year: 1947<br />
Place: New York<br />
Publisher: <strong>Institute</strong> <strong>of</strong> Radio Engineers<br />
Edition: 1st<br />
Language: English<br />
Binding: original journal paper wrappers<br />
Pagination: pp. 756–767<br />
Size: 278x217 mm<br />
Reference: Ran ODC, p. 409<br />
Burks was a member <strong>of</strong> the ENIAC computer team.<br />
After the war, he joined John von Neumann at the<br />
<strong>Institute</strong> for Advanced Study, then became a pr<strong>of</strong>essor,<br />
and later chairman, <strong>of</strong> the Department <strong>of</strong> Computer and<br />
Communication Sciences at the <strong>University</strong> <strong>of</strong> Michigan.<br />
He is also known for his work in logic and the philosophy<br />
<strong>of</strong> science.<br />
This paper describes the circuit elements <strong>of</strong> the ENIAC.<br />
It indicates that the rate <strong>of</strong> circuit failure has only been<br />
about two or three per week, usually resulting from a<br />
failure <strong>of</strong> the heaters in the vacuum tubes. With an<br />
operator thoroughly familiar with all the details <strong>of</strong><br />
ENIAC design and with the particular problem being<br />
solved … only a few hours per week are lost on account<br />
<strong>of</strong> failures.<br />
Illustrations available:<br />
None<br />
B 291<br />
Burks, Arthur Walter (1915–) and Jesse B. Wright<br />
Theory <strong>of</strong> logical nets. In Proceedings <strong>of</strong> the I.R.E., vol.<br />
41, #10, October 1953<br />
Year: 1953<br />
Place: New York<br />
Publisher: <strong>Institute</strong> <strong>of</strong> Radio Engineers<br />
Edition: <strong>of</strong>fprint<br />
Language: English<br />
Binding: unbound<br />
Pagination: pp. 1357–1365, [3]<br />
Size: 278x217 mm<br />
This is an extract from the Proceedings <strong>of</strong> the I.R.E. It<br />
is a technical paper on the design <strong>of</strong> computer circuits<br />
using the concept <strong>of</strong> logical nets. It requires some<br />
mathematical sophistication to follow the development<br />
<strong>of</strong> the theorems.<br />
Illustrations available:<br />
First page<br />
B 292<br />
B 292<br />
Burks, Arthur Walter (1915–); Herman Heine<br />
Goldstine (1913–) and John Von Neumann (1903–1957)<br />
Preliminary discussion <strong>of</strong> the logical design <strong>of</strong> an<br />
electronic computing instrument. Part I, Volume I<br />
Year: 1947<br />
Place: Princeton<br />
Publisher: <strong>Institute</strong> for Advanced Study<br />
Edition: 2nd<br />
Language: English<br />
Binding: original printed paper wrappers; back wrapper torn<br />
Pagination: ff. [6], 42<br />
Size: 279x213 mm<br />
Reference: Ran ODC, p. 409<br />
This series <strong>of</strong> reports prepared by Burks, Goldstine and<br />
von Neumann were some <strong>of</strong> the most detailed available<br />
on the construction <strong>of</strong> a stored program computer and<br />
were widely circulated among the early computing<br />
community. This report discusses the general nature <strong>of</strong><br />
the IAS computer; it is divided into sections discussing<br />
the memory, control, and arithmetic organs <strong>of</strong> the<br />
machine. At this time they were still planning to use the<br />
RCA Selectron memory tube (with 4,000 40-bit words<br />
<strong>of</strong> memory); that idea ultimately proved impractical, and<br />
they switched to the use <strong>of</strong> a Williams’ tube memory.
Erwin Tomash Library<br />
Burks, Arthur Walter Burroughs Adding Machine Company<br />
Illustrations available:<br />
Title page<br />
B 293<br />
Burks, Arthur Walter (1915–); Don B. Warren and<br />
Jesse B. Wright<br />
An analysis <strong>of</strong> a logical machine using parenthesis-free<br />
notation. In MTAC, April 1954, vol. VIII, No. 46<br />
Year: 1954<br />
Place: Lancaster, PA<br />
Publisher: National Research Council<br />
Edition: 1st<br />
Language: English<br />
Binding: library buckram<br />
Pagination: pp. 53–58<br />
Size: 227x149 mm<br />
In this paper Burks and his co-authors report on the<br />
use <strong>of</strong> Lukasiewicz notation (a notation that allows the<br />
writing <strong>of</strong> mathematical and logical formulas without<br />
the use <strong>of</strong> brackets – <strong>of</strong>ten called Polish notation) to use<br />
as input to a machine for calculating truth values. The<br />
machine, built by Burroughs, is reported as constructed<br />
from relays and copes with formulas <strong>of</strong> ten variables.<br />
The machine is illustrated by a photograph.<br />
Illustrations available:<br />
Photograph <strong>of</strong> the Burroughs machine<br />
B 294<br />
Burroughs Adding Machine Company<br />
Instructions for operating the Burroughs calculator<br />
Year: 1941<br />
Place: Detroit<br />
Publisher: Burroughs<br />
Edition: 1st<br />
Language: English<br />
Binding: original paper wrappers<br />
Pagination: pp. 35<br />
Size: 277x214 mm<br />
This instruction book gives tips on how to make more<br />
efficient use <strong>of</strong> the Burroughs calculating machines.<br />
Illustrations available:<br />
Title page<br />
B 295<br />
Burroughs Adding Machine Company<br />
The story <strong>of</strong> figures<br />
Year: 1950<br />
Place: Detroit<br />
Publisher: Burroughs<br />
Edition: 3rd<br />
Language: English<br />
Binding: original paper wrappers<br />
Pagination: pp. 36<br />
Size: 191x138 mm<br />
This is a short history <strong>of</strong> the development <strong>of</strong> numbers<br />
and mechanical machines to process them. It begins<br />
with early systems <strong>of</strong> numeration, continues through<br />
individuals such as Blaise Pascal and <strong>Charles</strong> <strong>Babbage</strong>,<br />
and ends, not surprisingly, with several sections on Mr.<br />
Burroughs and company he founded.<br />
Illustrations available:<br />
Title page<br />
Burroughs logic machine, B 293 B 295<br />
227
228<br />
Erwin Tomash Library<br />
Bush, Vannevar Bush, Vannevar<br />
B 296<br />
Bush, Vannevar E. (1890–1974)<br />
As we may think. In Atlantic Monthly vol. 176, no. 1,<br />
July 1945<br />
Year: 1945<br />
Place: Boston<br />
Publisher: The Atlantic Monthly Co.<br />
Edition: 1st<br />
Language: English<br />
Binding: library buckram<br />
Pagination: pp. 101–108<br />
Size: 297x182 mm<br />
Vannevar Bush was one <strong>of</strong> the most important scientists<br />
<strong>of</strong> World War II. He began his career as a pr<strong>of</strong>essor at<br />
MIT and eventually became president <strong>of</strong> that institution.<br />
While still a pr<strong>of</strong>essor, he developed the Bush<br />
Differential Analyzer and was later responsible for the<br />
creation <strong>of</strong> the Rockefeller Differential Analyzer (RDA-<br />
2). During Word War II, he was called upon to head the<br />
Office <strong>of</strong> Scientific Research and Development. He was<br />
responsible for the coordination <strong>of</strong> over 6,000 scientists<br />
on war-related projects.<br />
At the end <strong>of</strong> the war, with electronic computers and other<br />
such devices on the horizon, Bush wrote this article on<br />
the relationship <strong>of</strong> technology to human activity. It was<br />
one <strong>of</strong> the most farsighted statements <strong>of</strong> what wartime<br />
developments might bring. In it he proposes a device he<br />
calls a memex, which would be much like a desk with<br />
attached information storage and retrieval equipment.<br />
Initially, Bush suggests that it might be based on a library<br />
<strong>of</strong> micr<strong>of</strong>ilm, but his vision quickly expands to include<br />
the indexing <strong>of</strong> information that could be retrieved at the<br />
touch <strong>of</strong> a button. He concludes:<br />
Wholly new forms <strong>of</strong> encyclopedias will appear,<br />
ready-made with a mesh <strong>of</strong> associative trails<br />
running through them, ready to be dropped into<br />
the memex and there amplified.<br />
This statement, and others like it, reveal that he was<br />
thinking <strong>of</strong> things like modern hypertext documents<br />
with the links that are so common on personal computers<br />
today.<br />
Douglas Engelbert, the inventor <strong>of</strong> the mouse and modern<br />
graphical interface to computers, has said that Bush’s<br />
article inspired him and that it was this publication that<br />
shaped the rest <strong>of</strong> his life.<br />
Illustrations available:<br />
Start <strong>of</strong> section 8<br />
B 297<br />
Bush, Vannevar E. (1890–1974)<br />
The differential analyzer. In Journal <strong>of</strong> the Franklin<br />
<strong>Institute</strong>, Philadelphia, PA., vol. 212, No. 4, October<br />
1931<br />
Year: 1931<br />
Place: Philadelphia<br />
Publisher: Franklin <strong>Institute</strong><br />
Edition: 1st<br />
Language: English<br />
Binding: contemporary black buckram<br />
Pagination: pp. 447–488<br />
Size: 234x150 mm<br />
While still a pr<strong>of</strong>essor at MIT, Bush was responsible for<br />
the development <strong>of</strong> the torque amplifier, the mechanism<br />
that made it possible to construct an accurate differential<br />
analyzer. His machine was ready for use in 1931, and this<br />
paper not only gives construction details but also shows<br />
how it might be set up to solve differential equations.<br />
Torque amplifier, B 297 Differential analyzer, B 297
Erwin Tomash Library<br />
Bush, Vannevar Bush, Vannevar<br />
The Bush differential analyzer (in particular the torque<br />
amplifier) was copied in many places before World War<br />
II. The electronic ENIAC was designed as a replacement<br />
machine when mechanical differential analyzers proved<br />
too slow to speedily produce ballistic tables for the U.S.<br />
Army.<br />
Illustrations available:<br />
Diagram <strong>of</strong> torque amplifier<br />
Photograph <strong>of</strong> torque amplifier.<br />
Photograph and diagram <strong>of</strong> the differential analyzer<br />
B 298<br />
Bush, Vannevar E. (1890–1974)<br />
Instrumental analysis. In Bulletin <strong>of</strong> the American<br />
Mathematical Society Vol. XLII, No. 10, October 1936<br />
Year: 1936<br />
Place: Menasha, WI<br />
Publisher: American Mathematical Society<br />
Edition: 1st<br />
Language: English<br />
Binding: original gray paper wrappers<br />
Pagination: pp. 649–669<br />
Size: 239x146 mm<br />
Reference: Ran ODC, p. 409<br />
This is the text <strong>of</strong> the twelfth Josiah Willard Gibbs Lecture<br />
<strong>of</strong> the American Mathematical Association, which Bush<br />
was invited to give. He describes various tools for<br />
calculation, a majority being analog instruments such as<br />
the harmonic analyzer and optical masks for integrating.<br />
He begins, however, with a description <strong>of</strong> punched card<br />
machinery and the possibilities for calculating using<br />
tabulating equipment.<br />
Illustrations available:<br />
Cover page<br />
B 299<br />
Bush, Vannevar E. (1890–1974)<br />
Operational circuit analysis<br />
Year: 1929<br />
Place: New York<br />
Publisher: John Wiley & Sons<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards<br />
Pagination: pp. x, 392<br />
Size: 195x131 mm<br />
This is a highly technical book on the analysis <strong>of</strong><br />
electrical circuits. The material is not only applicable<br />
to electrical circuits but also, by analogy, to acoustics,<br />
mechanics, hydraulics, etc.<br />
This work includes an appendix by Norbert Wiener<br />
(who was then an assistant pr<strong>of</strong>essor at MIT) on<br />
Fourier analysis—a system that can be used to break<br />
down a complex curve into its simple trigonometric<br />
components.<br />
Illustrations available:<br />
Title page<br />
B 300<br />
Bush, Vannevar E. (1890–1974)<br />
Recent progress in analysing machines. In Proceedings<br />
<strong>of</strong> the Fourth International Congress for Applied<br />
Mechanics, Cambridge, England, July 3rd–9th, 1934<br />
Year: 1935<br />
Place: Cambridge<br />
Publisher: Cambridge <strong>University</strong> Press<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards<br />
Pagination: pp. xx, 282, [2]<br />
Collation: π 10 1–17 8 18 6<br />
Size: 266x187 mm<br />
B 299<br />
By 1935, Bush was well known for his differential<br />
analyzer and a recognized expert on machines for solving<br />
complex mathematical systems. In this lecture Bush<br />
surveys machines used for producing specific types <strong>of</strong><br />
mathematical results. While mentioning mechanical<br />
calculation, the main topic is really the machines used for<br />
solving differential equations and other similar systems.<br />
229
230<br />
Erwin Tomash Library<br />
Bush, Vannevar Bush, Vannevar<br />
Bush covers mechanical (including his own differential<br />
analyzer), electrical and optical devices.<br />
Illustrations available:<br />
None<br />
B 301<br />
Bush, Vannevar E. (1890–1974)<br />
Science. The endless frontier. A report to the President<br />
Year: 1945<br />
Place: Washington, D.C.<br />
Publisher: USGPO<br />
Edition: 1st<br />
Language: English<br />
Binding: original paper wrappers<br />
Pagination: pp. x, 184<br />
Size: 230x150 mm<br />
This report was produced by Vannevar Bush, director <strong>of</strong><br />
the Office <strong>of</strong> Scientific Research and Development, at<br />
the end <strong>of</strong> the war. World War II had stimulated a huge<br />
leap forward in science and technology, and President<br />
Roosevelt had asked Bush to prepare a report on how<br />
best to release scientific information developed as part<br />
<strong>of</strong> secret military programs. In addition, he was to<br />
make recommendations about medical research, how to<br />
further research in the private sector, and how to develop<br />
a program to find and train the best scientific talent<br />
among American youth. One <strong>of</strong> Bush’s most influential<br />
recommendations was to establish a National Research<br />
Foundation to fund research in American universities<br />
and other institutions.<br />
Illustrations available:<br />
Title page<br />
[Bush, Vannevar E.]<br />
See Zernike, F.; De differentiaal-analysator als<br />
vorbeeld van een continue machine, 1949.<br />
B 302<br />
Bush, Vannevar E. (1890–1974) and Harold Locke<br />
Hazen (1901–1980)<br />
Integraph solution <strong>of</strong> differential equations. In Journal<br />
<strong>of</strong> the Franklin <strong>Institute</strong>, Vol. 204, No. 5, November<br />
1927<br />
Year: 1927<br />
Place: Philadelphia<br />
Publisher: Franklin <strong>Institute</strong><br />
Edition: 1st<br />
Language: English<br />
Binding: entire volume<br />
Pagination: pp. 575–615<br />
Size: 234x156 mm<br />
The Bush integraph was the precursor to his much more<br />
famous differential analyzer, announced in the pages<br />
<strong>of</strong> this same journal in 1931 (see entry for Bush, The<br />
differential analyzer, 1931). This integraph contained<br />
two stages <strong>of</strong> integration, allowing the solution <strong>of</strong><br />
second-order differential equations: the first integrator<br />
is a Thompson direct-current integrating watt-hour<br />
meter; the second the more familiar Kelvin, wheel-disk,<br />
mechanical integrating device. Having not yet developed<br />
his torque amplifier (used in the Differential Analyzer),<br />
Bush used servo-motors controlled by relays actuated<br />
by contacts on the integrators to power the rest <strong>of</strong> the<br />
system.<br />
Illustrations available:<br />
First page<br />
General view <strong>of</strong> the integraph<br />
Disk-Wheel integrator<br />
B 301 Disk-wheel integrator, B 302
Erwin Tomash Library<br />
Bush, Vannevar Buteo, Jean<br />
B 303<br />
Bush, Vannevar E. (1890–1974); F. D. Gage and H. R.<br />
Stewart<br />
A continuous integraph. In Journal <strong>of</strong> the Franklin<br />
<strong>Institute</strong>, Vol. 203, No. 1, January 1927<br />
Year: 1927<br />
Place: Philadelphia<br />
Publisher: Franklin <strong>Institute</strong><br />
Edition: 1st<br />
Language: English<br />
Binding: black library buckram<br />
Pagination: pp. 63–84<br />
Size: 234x156 mm<br />
Integraph, B 302<br />
This integrating machine was Bush’s first effort at<br />
producing what would become his Differential Analyzer<br />
(see Bush, Integraph solution <strong>of</strong> differential equations,<br />
1927, and Bush, The differential analyzer, 1931). It<br />
used a Thompson integrating watt-hour meter as the<br />
integrating device and had a mechanical multiplier as<br />
part <strong>of</strong> the system.<br />
Mechanical multiplier, B 303<br />
Illustrations available:<br />
First page<br />
Mechanical multiplier photograph<br />
Mechanical multiplier diagram<br />
B 304<br />
Buteo, Jean (1492–CA.1564–1572)<br />
De quadratura circuli libri duo, ubi multorum<br />
quadraturæ confutantur, & ab omniium impugnatione<br />
defenditur Archimedes. Eiusdem, annotationum<br />
opuscula in errores Campani, Zamberti, Orontij,<br />
Peletarij, Io. Penæ interpretum Euclidis.<br />
Year: 1559<br />
Place: Lyon<br />
Publisher: Gulielmum Rouillium<br />
Edition: 1st<br />
Language: Latin<br />
Binding: modern leather<br />
Pagination: pp. 284<br />
Collation: a–r 8 s 6<br />
Size: 165x107 mm<br />
Reference: Ada CBCE, 3358; DSB II, p. 618<br />
Buteo (also known as Borrel, Boteo, Butéon, or<br />
Bateon) was a French monk whose main interest was in<br />
mathematics and languages. Before he was twenty, he<br />
was able to read and understand Euclid in the original<br />
Greek. After studying in Paris under Oronce Fine, he<br />
returned to the Abbey at St. Antoine, where he wrote<br />
on scientific subjects but, as far as is known, never<br />
took pupils. He reputedly calculated, then disputed, the<br />
ability <strong>of</strong> Noah’s ark to hold all the animals and stores<br />
that would have been required.<br />
In this, an account <strong>of</strong> the quadrature <strong>of</strong> the circle, Buteo<br />
criticizes those who believed that they had found a<br />
solution, even having harsh words for his teacher,<br />
Oronce Fine. In the second half, he pointed out errors<br />
in earlier translations <strong>of</strong> the works <strong>of</strong> Euclid and argued<br />
that it was Euclid himself, and not Theon, who created<br />
the pro<strong>of</strong>s.<br />
Illustrations available:<br />
Title page<br />
Mechanical multiplier, B 303<br />
231
B 305<br />
Butte, Wilhelm<br />
Grundlinien der Arithmetik des menschlichen Lebens,<br />
nebst Winken für deren Anwendung auf Geographie,<br />
Staats - und Natur - Wissenschaft<br />
232<br />
Year: 1811<br />
Place: Landshut<br />
Publisher: Philipp Krüll<br />
Edition: 1st<br />
Language: German<br />
Figures: 9 folding plates<br />
Binding: half bound, marbled paper boards<br />
Pagination: pp. xxxiv, [4], 420<br />
Collation: * 8 ** 8 *** 3 (-***4) 1–26 8 27 2<br />
Size: 201x123 mm<br />
Butte was the pr<strong>of</strong>essor <strong>of</strong> economics at the Ludwig<br />
Maximilians <strong>University</strong> in Landshut, Bavaria. He begins<br />
by acknowledging earlier authors such as Graunt,<br />
Malthus, Kersseboom and others, but then claims that<br />
he is the first to really apply arithmetic and mathematics<br />
to the study <strong>of</strong> human life. The work is divided into two<br />
sections: the first theoretical, the second practical. In<br />
the first he creates a typology <strong>of</strong> human development<br />
(different for males and females), and in the second<br />
he attempts to apply this to support practical policy<br />
proposals. He attempts to develop a correlation between<br />
different world areas, climates, and peoples and proposes<br />
correct ages for voting, majority, schooling, etc.<br />
Illustrations available:<br />
Title page<br />
Erwin Tomash Library<br />
Butte, Wilhelm Butterworth, Edmond<br />
B 304<br />
B 306<br />
Butterworth, Edmond (ca.1755–1819)<br />
B 305<br />
Butterworth’s young arithmeticians instructor<br />
containing specimens <strong>of</strong> writing. With directions for<br />
attaining in the shortest time a current-hand. Designed<br />
for the use <strong>of</strong> schools & private families.<br />
Year: 1815<br />
Place: Edinburgh<br />
Publisher: Oliver & Boyd<br />
Edition: 2nd<br />
Language: English<br />
Figures: engraved plates, 2 folding<br />
Binding: contemporary marbled paper boards; recently<br />
recornered and rebacked<br />
Pagination: pp. 52, [52]<br />
Collation: 1–6 4 7 2 γ 26<br />
Size: 258x210 mm<br />
There were two Edmond Butterworths, a father and<br />
son. They are difficult to separate, but one or the other<br />
(perhaps both) was a writing master at Dumfrees<br />
Academy and Edinburgh High School. It is likely they<br />
both participated in the production <strong>of</strong> this work because<br />
the title page mentions the authors.<br />
This is a fully engraved textbook on arithmetic and<br />
commercial practice. It teaches penmanship at the<br />
same time as arithmetic with examples <strong>of</strong> simple and<br />
compound arithmetic, English and Scottish weights and<br />
measures, and bookkeeping.
Erwin Tomash Library<br />
Butterworth, Edmond Buxton, Leonard Halford Dudley<br />
The title shown above is actually from page three, while<br />
page one states:<br />
In the following engraved system <strong>of</strong> arithmetic<br />
the authors have endeavour’d to combine<br />
accurate writing, correct figures, and judiscious<br />
arrangements. They have studied to make the<br />
rules clear & concise and have given a variety <strong>of</strong><br />
questions calculated to enable the pupil to apply<br />
them; they have also inserted a sufficient number<br />
<strong>of</strong> examples in full under each rule, to save the<br />
pupil, if thought proper, the trouble <strong>of</strong> writing<br />
an account book. The answers to the questions<br />
will be found correct, it is therefore hoped it will<br />
inspire a taste for writing, and prove a useful text<br />
book.<br />
Illustrations available:<br />
Title page 1<br />
Title page 2<br />
Weights and measures<br />
Compound addition<br />
Writing practice<br />
Business documents<br />
Title 1, B 306<br />
B 307<br />
Buxton, Leonard Halford Dudley (1889–1939)<br />
<strong>Charles</strong> <strong>Babbage</strong> and his difference engines. In<br />
Transactions <strong>of</strong> the Newcomen Society, Vol XIV, 1933–<br />
1934<br />
Year: 1933<br />
Place: London<br />
Publisher: Newcomen<br />
Edition: 1st<br />
Language: English<br />
Binding: original printed gray wrappers<br />
Pagination: pp. 43–65<br />
Size: 247x195 mm<br />
Reference: Ran ODC, p. 410<br />
Buxton’s grandfather, Harry Wilmot Buxton, had been<br />
a friend <strong>of</strong> <strong>Charles</strong> <strong>Babbage</strong>. Late in life <strong>Babbage</strong><br />
had entrusted H. W. Buxton with the job <strong>of</strong> writing his<br />
biography, and Buxton had accumulated a number <strong>of</strong><br />
papers and artifacts with that end in mind. L. H. Dudley<br />
Buxton, a reader in physical anthropology at Oxford, had<br />
inherited those papers and used them to prepare this talk<br />
to the Newcomen Society. In the course <strong>of</strong> the talk, he<br />
mentioned that his grandfather had actually written the<br />
requested biography <strong>of</strong> <strong>Babbage</strong> but that it had never<br />
been published and that the manuscript was still in<br />
the old cowhide trunk with all the other papers. It was<br />
another fifty years before this manuscript was published<br />
as Memoir <strong>of</strong> the life and labours <strong>of</strong> the late <strong>Charles</strong><br />
<strong>Babbage</strong> Esq. F.R.S., Volume 13 in the <strong>Charles</strong> <strong>Babbage</strong><br />
<strong>Institute</strong> Reprint Series for the History <strong>of</strong> Computing.<br />
This talk to the Newcomen Society describes <strong>Babbage</strong>’s<br />
work on the Difference Engine, with an occasional<br />
Title 2, B 306 Journal cover, B 307<br />
233
234<br />
Erwin Tomash Library<br />
Byrne, Oliver Byrne, Oliver<br />
mention <strong>of</strong> the Analytical Engine. Leslie Comrie was<br />
in the audience and remarked that it was now possible<br />
to obtain commercial machines that would do the job <strong>of</strong><br />
<strong>Babbage</strong>’s Difference Engine. He had recently ordered a<br />
National Cash Register Company National accounting<br />
machine that could be used in that manner. Comrie was<br />
to use that machine to produce and check many different<br />
sets <strong>of</strong> tables.<br />
Illustrations available:<br />
First page<br />
B 308<br />
Byrne, Oliver (1810–1880)<br />
B 308<br />
Byrne’s timber and log book, ready reckoner and price<br />
book, for lumber dealers and ship builders, merchants<br />
and traders, farmers and drovers, and all others<br />
engaged in buying or selling at either wholesale or<br />
retail.<br />
Year: 1878<br />
Place: New York<br />
Publisher: The American News Company, Orange Judd<br />
Company<br />
Edition: 1st<br />
Language: English<br />
Binding: printed paper boards<br />
Pagination: pp. [5], 5–178, [1]<br />
Size: 153x93 mm<br />
Little factual information seems to be available on<br />
Oliver Byrne’s life, though he published more than<br />
twenty volumes and is described variously in them.<br />
According to one or another <strong>of</strong> his publications, Byrne<br />
was Surveyor-General <strong>of</strong> the Falkland Islands, Pr<strong>of</strong>essor<br />
<strong>of</strong> Mathematics in the College for Civil Engineers,<br />
Consulting Actuary to the Philanthropic Life Assurance<br />
Society etc. etc. etc. DeMorgan (A Budget <strong>of</strong> Paradoxes,<br />
1872, pp. 199–200) is scathing about an item written by<br />
Byrne in which he attempts to use mathematical symbols<br />
to prove statements in the creed <strong>of</strong> St. Athanasius.<br />
This volume, unlike several <strong>of</strong> Byrne’s other works, has<br />
nothing to do with dual arithmetic but is a standard ready<br />
reckoner for the timber trade. One unusual item, not<br />
encountered in other ready reckoners, is a table listing the<br />
statutes <strong>of</strong> limitations for assaults, slanders, judgements,<br />
etc. for each state in the U.S. and for Ontario and Quebec<br />
in Canada. Perhaps, given his somewhat checkered<br />
career, Byrne had experience in such matters.<br />
Illustrations available:<br />
Title page<br />
B 309<br />
Byrne, Oliver (1810–1880)<br />
B 309<br />
Byrne’s treatise on navigation and nautical astronomy<br />
Year: 1877<br />
Place: London<br />
Publisher: Richard Bentley & Son<br />
Edition: 2nd
Erwin Tomash Library<br />
Byrne, Oliver Byrne, Oliver<br />
Language: English<br />
Binding: original cloth boards<br />
Pagination: pp. Iii–xvi, iii–vi, 5–218, 464, [4 adverts]<br />
Collation: π 9 A–L 4 a–p 4 q 3 A–Z 8 2A–2F 8 γ 2<br />
Size: 248x172 mm<br />
Reference: Hend BTM, #209.3, p. 188<br />
In this volume Byrne continues to stress his dual<br />
arithmetic system (see Byrne; Dual Arithmetic, 1867),<br />
but this time it is couched in terms <strong>of</strong> navigation. The<br />
first half <strong>of</strong> the text presents his dual arithmetic, while<br />
the second is an elementary work on navigation showing<br />
the examples demonstrating its use. He includes two<br />
large tables <strong>of</strong> Byrne’s Numbers as well as several other<br />
trigonometric tables.<br />
Illustrations available:<br />
Title page<br />
B 310<br />
Byrne, Oliver (1810–1880)<br />
Dual arithmetic. A new art.<br />
B 310<br />
Year: 1863<br />
Place: London<br />
Publisher: Bell and Daldy<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards, faded<br />
Pagination: pp. xl, 246 (misnumbered 246 as 244), 22<br />
Size: 215x135 mm<br />
Collation: π 4 a 2 b–d 4 e 2 B–2H 4 2I 3 A 11<br />
In this work, Byrne proposes a new method <strong>of</strong> performing<br />
mental arithmetic that involves breaking numbers down<br />
into the form a1.1 b 1.01 c 1.001 d …and then operating on<br />
the quantities a, b, c, d, etc. to find the answer. DeMorgan<br />
is anything but complimentary in his judgment <strong>of</strong> the<br />
dual arithmetic proposal. It does, however, indicate the<br />
lengths to which some practitioners will go in attempting<br />
to ease the labor inherent in doing arithmetic.<br />
Illustrations available:<br />
Title page<br />
B 311<br />
Byrne, Oliver (1810–1880)<br />
B 311<br />
The essential elements <strong>of</strong> practical mechanics, based<br />
on the principle <strong>of</strong> work; designed for engineering<br />
students..<br />
Year: 1867<br />
Place: London<br />
Publisher: E. & F. N. Spon<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards<br />
Pagination: pp.xii, 360<br />
Collation: π 4 a 2 B–Z 8 2A 4<br />
Size: 183x120 mm<br />
While this work does deal with mechanics, it is little<br />
more than a tract promoting Byrne’s dual arithmetic.<br />
Illustrations available:<br />
Title page<br />
B 312<br />
Byrne, Oliver (1810–1880)<br />
The geometry <strong>of</strong> compasses or problems resolved by<br />
235
236<br />
Erwin Tomash Library<br />
Byrne, Oliver Byrne, Oliver<br />
the mere description <strong>of</strong> circles, and the use <strong>of</strong> coloured<br />
diagrams and symbols..<br />
Year: 1877<br />
Place: London<br />
Publisher: Crosby, Lockwood, and Co.<br />
Edition: 1st<br />
Language: English<br />
Figures: frontispiece figure in red and black, 36 full-page<br />
figures (19 in color)<br />
Binding: original cloth boards<br />
Pagination: pp. iv, [74]<br />
Collation: A–D 8 E 7<br />
Size: 186x123 mm<br />
In this work Byrne demonstrates the solution <strong>of</strong> several<br />
geometric problems by the use <strong>of</strong> the compass. Of major<br />
interest is the use <strong>of</strong> color to illustrate the different<br />
compass radii and movements. This may be regarded<br />
as an extension <strong>of</strong> Byrne’s most successful book, The<br />
first six books <strong>of</strong> the elements <strong>of</strong> Euclid, in which colored<br />
diagrams and symbols are used instead <strong>of</strong> letters for<br />
the greater ease <strong>of</strong> learners. London, 1847 (not in the<br />
collection).<br />
Illustrations available:<br />
Title page<br />
Frontispiece<br />
B 312<br />
B 313<br />
Byrne, Oliver (1810–1880)<br />
Mechanics: Their principles and practical applications<br />
Year: 1853<br />
Place: New York<br />
Publisher: De Witt & Davenport<br />
Edition: 1st<br />
Language: English<br />
Binding: original gilt-pictorial cloth boards; gilt spine faded<br />
Pagination: pp. 182<br />
Collation: 1 4 1* 8 -7 4 7* 8 8 4 8* 3<br />
Size: 185x122 mm<br />
In this work Byrne describes himself as a civil, military,<br />
and mechanical engineer. He points out that there are<br />
already a great many books describing mechanical<br />
devices; his has the advantage that it stands in the same<br />
relation to the execution <strong>of</strong> works, and the construction<br />
<strong>of</strong> machines, as Descriptive Geometry stands to the<br />
drawing <strong>of</strong> machines. Once the reader has attempted<br />
to digest that boast, he or she is treated to a complex<br />
jumble <strong>of</strong> physical principles in the rest <strong>of</strong> the volume.<br />
While Byrne certainly does describe simple mechanical<br />
devices such as the lever, pulley and gears, the examples<br />
given are seldom the practical applications <strong>of</strong> the title.<br />
They <strong>of</strong>ten refer to hypothetical falling balls, balancing<br />
<strong>of</strong> eggs, etc. When Byrne does consider more practical<br />
problems, he assumes idealized conditions. For example,<br />
he notes that the inclined plane must be considered to be<br />
a perfectly hard, smooth, inflexible surface … and other<br />
such less than realistic considerations.<br />
Illustrations available:<br />
Title page<br />
Book binding, front gilt<br />
Frontispiece, B 312
Erwin Tomash Library<br />
Byrne, Oliver Byrne, Oliver<br />
B 314<br />
Byrne, Oliver (1810–1880)<br />
The pocket companion for machinists, mechanics, and<br />
engineers.<br />
Year: 1851<br />
Place: New York<br />
Publisher: Dewitt & Davenport<br />
Edition: 1st<br />
Language: English<br />
Figures: 2 large folding tables; 3 engraved folding plates<br />
Binding: contemporary morocco leather wallet with inscribed<br />
flap; gilt edges; marbled endpapers<br />
Pagination: pp. 144<br />
Collation: 1 4 1* 8 -6 4 6* 8<br />
Size: 150 x 98 mm<br />
Oliver Byrne was certainly an unusual personality. It is<br />
<strong>of</strong> interest to note the different ways he describes himself<br />
on the title pages <strong>of</strong> his books. In this one he lists himself<br />
as Pr<strong>of</strong>essor <strong>of</strong> Mathematics, College <strong>of</strong> Civil Engineers,<br />
London, Surveyor-General <strong>of</strong> Her Majesty’s Settlements<br />
in the Falkland Islands and the author <strong>of</strong> several books.<br />
This pocket companion appears to be another <strong>of</strong> Byrne’s<br />
eclectic collections <strong>of</strong> information. It contains items such<br />
as a description <strong>of</strong> what a plus sign indicates, the values<br />
<strong>of</strong> various Roman numerals, the first five hundred prime<br />
numbers, weights <strong>of</strong> malleable iron, tables <strong>of</strong> expansion<br />
<strong>of</strong> liquids at various temperatures and the dimensions <strong>of</strong><br />
the rings <strong>of</strong> Saturn.<br />
Illustrations available:<br />
Title page<br />
B 313<br />
B 315<br />
Byrne, Oliver (1810–1880)<br />
The practical model calculator, for the engineer,<br />
mechanic, machinist, manufacturer <strong>of</strong> engine-work,<br />
naval architect, miner, and millwright.<br />
Year: 1866<br />
Place: Philadelphia<br />
Publisher: Henry Carey Baird<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards; gilt spine<br />
Pagination: pp. 3–494, 85, [1], 583–591, [3], 24 pp. catalogue<br />
Collation: A 6 (-A6) B–V 6 W 6 X–Z 6 2A–2G 6 25–37 8<br />
Size: 228x140 mm<br />
Reference: Hend BTM, #152.0, p. 121<br />
This is Byrne’s largest collection <strong>of</strong> miscellaneous<br />
tables <strong>of</strong> information. He had been developing tables <strong>of</strong><br />
this nature for nearly forty years. There is no table <strong>of</strong><br />
contents, but the work does have an index through which<br />
one could access the hundreds <strong>of</strong> different tables and<br />
formulae it contains. There is also a very large section<br />
on the steam engine and another on ship building and<br />
naval architecture.<br />
Illustrations available:<br />
Title page<br />
B 316<br />
Byrne, Oliver (1810–1880)<br />
B 314<br />
Practical, short, and direct method <strong>of</strong> calculating<br />
the logarithm <strong>of</strong> any number, and the number<br />
corresponding to any given logarithm.<br />
237
238<br />
Erwin Tomash Library<br />
Byrne, Oliver Byrne, Oliver<br />
Year: 1849<br />
Place: New York<br />
Publisher: D. Appleton & Co<br />
Edition: 1st<br />
Language: English<br />
Binding: original cloth boards; embossed cover; gilt spine<br />
Pagination: pp. xxiv, 13–82, [2]<br />
Size: 186x120 mm<br />
Collation: [A] 12 B 4 B* 8 -D 4 D* 8<br />
Like other publications by Byrne, this is a work carried<br />
to the extreme. In it he shows a method <strong>of</strong> calculating<br />
any logarithm for any number. While Byrne’s innovation<br />
is correct, the approach is completely impractical,<br />
particularly when a standard table <strong>of</strong> logarithms is so<br />
easy to use. In the introduction Byrne points out, as a<br />
curiosity, eight numbers that have the same digits as their<br />
logarithms.<br />
A second copy <strong>of</strong> this item is available in the collection.<br />
Illustrations available:<br />
Title page<br />
8 numbers and their logarithms<br />
B 316<br />
B 317<br />
Byrne, Oliver (1810–1880)<br />
Tables <strong>of</strong> dual logarithms, dual numbers, and<br />
corresponding natural numbers; with proportional<br />
parts <strong>of</strong> differences for single digits and eight<br />
places <strong>of</strong> decimals. Tables <strong>of</strong> angular magnitudes,<br />
trigonometrical lines, and differences graded to the<br />
hundredth part <strong>of</strong> a second for single digits.<br />
Year: 1867<br />
Place: London<br />
Publisher: Bell and Daldy<br />
Edition: 1st<br />
Language: English<br />
Figures: ff.1–54 printed in red<br />
Binding: contemporary green crushed morocco; blind and<br />
gilt fillets round sides and in spine compartments; gilt<br />
edges; marbled end papers<br />
Pagination: pp. vi, 7–40, [2], 74, [2], 38, [2], 90<br />
Collation: A–D 4 E 5 B–K 4 L 1 1–5 4 a 1 b–m 4 n 1<br />
Size: 241x179 mm<br />
These tables were designed to accompany Byrne’s<br />
system <strong>of</strong> Dual Arithmetic (see entry for Byrne, 1863).<br />
An unusual characteristic <strong>of</strong> the tables (other than their<br />
odd, impractical, nature) is that some tables have been<br />
printed in red to ensure that the user will consult the<br />
correct one.<br />
Illustrations available:<br />
Title page<br />
Red table page<br />
Logarithm table, B 316 B 317
Erwin Tomash Library<br />
Byrne, Oliver Byron, Augusta Ada, Lady Lovelace<br />
B 318<br />
Byrne, Oliver (1810–1880)<br />
The young dual arithmetician: Or, dual arithmetic. A<br />
new art, designed for elementary instruction and the<br />
use <strong>of</strong> schools. To which are added, tables <strong>of</strong> ascending<br />
and descending dual logarithms, dual numbers and<br />
corresponding natural numbers.<br />
Year: 1871<br />
Place: London<br />
Publisher: E. & F. N. Spon<br />
Edition: 2nd<br />
Language: English<br />
Binding: original cloth boards; silt stamped front cover<br />
Pagination: pp. [iii–xii], 144, [2], 32, [2], [33–58]<br />
Collation: π 5 B–H 12 I 6 c 12<br />
Size: 185x106 mm<br />
Reference: Hend BTM, #209, p. 187<br />
See entry for Byrne, Dual arithmetic, 1863. In the<br />
preface, Byrne immodestly describes his system <strong>of</strong> dual<br />
arithmetic as a branch <strong>of</strong> greater importance has not<br />
been contributed to mathematical science. This work, a<br />
promotional item for dual arithmetic, would have been<br />
most difficult for anyone to use, let alone the young<br />
students <strong>of</strong> different capacities to which this book was<br />
addressed. A table <strong>of</strong> ascending and descending dual<br />
logarithms is printed at the end <strong>of</strong> the work—ascending<br />
logarithms in black and descending ones in red.<br />
Illustrations available:<br />
Title page<br />
B 318<br />
Byron, Augusta Ada, Lady Lovelace (1815–1852),<br />
translator<br />
See Menabrea, Luigi Federico; Sketch <strong>of</strong> the<br />
Analytical Engine invented by <strong>Charles</strong> <strong>Babbage</strong>,<br />
Esq.… with notes by the translator. Extract from<br />
the ‘Scientific Memoirs’ vol. iii<br />
From Boissiere; L’ art d’arythmetique, 1554<br />
239
240<br />
Erwin Tomash Library<br />
Blundeville; Exercises, 1594