B chapter.indd - Charles Babbage Institute - University of Minnesota

Erwin Tomash Library
Bernoulli, John III Beutel, Tobias
While making contributions in many areas of mathematics
and mechanics, this volume contains Jacob’s most
famous work. It is considered as the foundation of the
mathematical theory of probability and, indeed, has
been termed the foundation of the field of mathematical
statistics. The editing of the manuscript was incomplete
when Jacob died and his nephew Nicolas (the son of
Jacob’s brother of the same name) saw it through the
press. This work, whose title means casting, as in the
casting of dice (not counters), is divided into four parts.
The first is a discussion of Huygens’ De ratiociniis in
alae ludo, and the second deals with permutations in
which Bernoulli derives a number of fundamental notions
about series. The third applies the theory developed in
Part II to twenty-four examples of games of chance for
which Bernoulli calculates the odds. The final section
is more philosophical in nature and makes reference to
moral as opposed to mathematical expectation and the
law of large numbers (the fundamental underpinning of
most simulations). This last section also contains some
comments on jeu de paume—a game similar to modern
tennis having little to do with the major topic of the
work. This is Jacob’s thinly disguised satirical response
to some caustic criticisms made earlier of his views on
scholarly logic.
Illustrations available:
Title page
B 144
Bernoulli, John III (1744–1807)
A sexcentenary table; exhibiting at sight, the result of
any proportion, where the terms do not exceed 600
seconds or 10 minutes with precepts and examples.
b/w: Taylor, Michael S.; A sexagesimal table …, 1780
Year: 1779
Place: London
Publisher: William Richardson
Edition: 1st
Language: English
Binding: contemporary half-bound leather, marbled boards;
rebacked; red leather label
Pagination: pp. viii, 165, [1]
Collation: a–b 2 A–2S 2 T 1
Size: 284x229 mm
See the entry for Taylor, Michael S.A.; A sexagesimal
table…,1780.
John (Johann) Bernoulli, a member of the famous Swiss
mathematical family—the grandson of Johann and
grandnephew of Jacob Bernoulli, was a child prodigy,
obtaining a master of jurisprudence degree at age
fourteen. By the age of twenty, he was asked by Frederick
II to reorganize the observatory in Berlin. While his
mathematical works are not of great importance today,
he wrote many papers on diverse subjects and eventually
became the trustee of the family documents.
Illustrations available:
Title page
B 145
Beutel, Tobias
B 144
Neu auffgelegte Arithmetica, Oder sehr nützliche
und schöne Rechen-Kunst mit kurtzen Regulen und
Exemplis, Nach der Practica, welche ausführlich
hierinnen beschriben ist, nebenst der Coss oder
Algebra.
Year: 1670
Place: Leipzig
Publisher: Printed by Johann Wittigau for Philip Fuhrman
Edition: 4th
Language: German
Figures: engraved frontispiece; title in red and black
Binding: Contemporary vellum; with ties
Pagination: pp. [24], 502, [2] (interleaved from p. 1 to p. 475)
Collation: ):( 12 A–X 12
Size: 127x75 mm
Reference: Pogg Vol. I, p. 181
This copy is interleaved with contemporary inscriptions
in finely penned handwriting in brown ink.
This arithmetic book begins with numeration (including
an example of Roman numerals using some of the
alternate forms for “M”) and continues with the four
basic operations and rule of three, multiplication being
illustrated with an unusual triangular table. The same
material is repeated in the next section, this time dealing
137