A Source Book in Mathematics, 1200-1800

446 Pages·1986·26.408 MB·English

by  D. J. Struik

DIRK JAN STRUIK
A Source Book in
Mathelllatics, 1200-1800
PRI CETO LEGA Y LIBRARY
A SOURCJ<; BOOK l!S' MATHl!:MATICS, 1200-1800

A SOURCE BOOK IN MATHEMATICS, 1200-1800
EDITED BY D. J. STRUIK
PRINCETON UNIVERSITY PRESS, PRINCETON, NEW JERSEY
Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540
In the United Kingdom: Princeton University Press, Guildford, Surrey
Copyright!!;; 1969 by the President and Fellows of Harvard College
Copyright© 1986 by Princeton University Press
All rights reserved
First Princeton Paperback printing, 1986
LCC 85-43381
ISBN 0-691-08404-1
ISBN 0-691-02397-2 (pbk.)
Clothbound editions of Princeton University Press books are printed on acid-free paper,
and binding materials are chosen for strength and durability. Paperbacks, while
satisfactory for personal collections, are not usually suitable for library rebinding.
Printed in the United States of America by Princeton University Press,
Princeton, New Jersey
TO THE MEMORY 0}' GEORGE SARTON

ERRATA ET ADDENDA
Page Line
f.b. ~
from
below
12 3 Macdonald's book was reprinted in 1966.
69 note The Witmer translation was published in 1968, title: The
Great Art.
75 14 H. Guericke and K. Reich published a German translation
(Mtinchen, 1973).
152 10 f. b. Between "diminished by" and "the square of z" add·
"a multiplied by z, or the cube of z is equal to a
multiplied.''
168 11 For "it was written ... after 1676" read "it was first written
in 1667 or 1668 and rewritten later."
189 19 After "179-388" add "and Margaret E. Baron, The origins of
the infinitesimal calculus (Oxford etc., 1969)."
215 14 of note Read· :lxy = :l(V.a2-z2) = 11,La2-.2z2.
217 note A Read CD =a
223 9 f.b. For "2ae+e" read "2ae+e 2 . "
236 9 f.b. Read: DS2 =sin (quartare-FR2).
246 2, 3 of For "and maybe medieval," read "and are medieval, e.g.
note 2 Bradwardine. ''
253 12 f .b. For "His most famous disciple was," read "Among the
attendants at his lectures may have been."
255 note 3 Read: "The theorem that FT is tangent to the curve VIF."
262 note 10 Re::id in the fust formula y d x dy
J y d~ dx for J y dx dx
0 0
270 5 f.b. It is J. 0. Fleckenstein.
271 19 f.b. For "111(1863" read "1(1858)"; for "Band VII" read "Band V."
vii
Page Line
280 end text After "213-222," add "and H.J. M. Bos, Differentials, higher
order differentials and the derivative in the Leibnizian calculus,
Arch. Hist. Exact Sc. 14 (1974), 1-90.
281 13 For "Band III" read "Band I."
284 15 f.b. Omit "under Barrow."
285 14 f.b. For "(1959) vol l," read "(1960) vol. 2."
291 8, 9 f.b. Hofmann's book now exists in a (revised) English translation,
Leibniz in Paris 1672-1676 (Cambridge University Press, 1974).
a
See also Leibniz Paris, a symposrnm of 1976 reported in
Historia Mathematica 9 (1982), 113-123.
311 16 For "1930" read "(1938)."
317 18 For nn-n read nn-n
n 2
note 7 For 1+2+··+n read 1+2+--+(n-1).
After "before" read "the then well-known fact."
324 8 For "305-558" read "385-558."
329 10 For "Lix+2Lix+Li3x" read "Lix+2Li2x+Li3x ."
For "3Li2x+Li4x" read "3Li3x+Li4x ."
348 3 f.b. For (sin)2 read (sin 7)3.
349 10 f.b. For "infinitely small" read "infinitely large."
351 13 After "vol 6" add "(1809)."
355 15 For "'l'(s) is an even" read "'l'(s) is an odd."
368 On the history of the function concept consult also sections of
M. Kline, Mathematical thought from ancient to modern times
(Oxford University Press, 1972).
Furthermore.
English translations have appeared
1) Of W1telonis Perspect1vae Liber Primus Perspectiva Book I by W1telo
(ca. 1230/35 - after ca. 1275), Stud1a Coperrucana 15 (1977), ed. S. Unguru
(Pohsh Academy of Sciences).
2) Of a sectio~ on divergent series by Euler, part of De seriebus
d1vergent1bus, NoVl Comm. Acad. Sc. Petrop. 5 (1754/55), 205-237,
Opera Omnia (1) 14, 585-617, see H1storia Matematica 3 (1976), 141-160,
Some work of Lagrange, Legendre, and Laplace belonging to our per10d
1200-1800 is found m Engllsh translation m the Source book m class1cal
analysis (Harvard University Press, 1973), ed. G. Birkhoff, with Uta
Merzbach.
On the authors of the selections included m our book we can fmd usually
excellent articles on life and work m the Dictionary of scientific
biography, 16 vols. (Scribner, New York, 1970-1980),
viii
PREFACE
This Source Book contains selections from mathematical writings of authors in the Latin
world, authors who lived in the period between the thirteenth and the end of the eighteenth
century. By Latin world I mean that there are no selections taken from Arabic or other
Oriental authors, unless, as in the case of Al-Khwarizmi, a much-used Latin translation
was available. The choice was made from books and from shorter writings. Usually only a
significant part of the document has been taken, although occasionally it was possible to in
clude a complete text. All selections are presented in English translation. Reproductions
of the original text, desirable from a scientific point of view, would have either increased
the size of the book far too much, or made it necessary to select fewer documents in a
field where even so there was an embarras du choix. I have indicated in all cases where the
original text can be consulted, and in most cases this can be done in editions of collected
works available in many university libraries and in some public libraries as well.
It has not often been easy to decide to which selections preference should be given. Some
are fairly obvious; parts of Cardan's ArB magna, Descartes's Geometrie, Euler's MethodUB in
veniendi, and some of the seminal work of Newton and Leibniz. In the selection of other
material the editor's decision whether to take or not to take was partly guided by his per
sonal understanding or feelings, partly by the advice of his colleagues. It stands to reason
that there will be readers who miss some favorites or who doubt the wisdom of a particular
choice. However, I hope that the final pattern does give a fairly honest picture of the mathe
matics typical of that period in which the foundations were laid for the theory of numbers,
analytic geometry, and the calculus.
The selection has been confined to pure mathematics or to those fields of applied mathe
matics that had a direct bearing on the development of pure mathematics, such as the
theory of the vibrating string. The works of scholastic authors are omitted, except where,
as in the case of Oresme, they have a direct connection with writings of the period of our
survey. Laplace is represented in the Source Book on nineteenth-century calculus.
Some knowledge of Greek mathematics will be necessary for a better understanding1 of
the selections: Diophantus for Chapters I and II, Euclid for Chapter III, and Archimedes
for Chapter IV. Sufficient reference material for this purpose is found in M. R. Cohen and
I. E. Drabkin, A Bource book in Greek Bcience (Harvard University Press, Cambridge, Massa
chusetts, 1948). Many of the classical authors are also easily available in English editions,
such as those of Thomas Little Heath.
ix