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A History of Mathematics

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556 pages
The Project Gutenberg EBook of A History of Mathematics, by Florian CajoriThis eBook is for the use of anyone anywhere at no cost and withalmost no restrictions whatsoever. You may copy it, give it away orre-use it under the terms of the Project Gutenberg License includedwith this eBook or online at www.gutenberg.orgTitle: A History of MathematicsAuthor: Florian CajoriRelease Date: January 24, 2010 [EBook #31061]Language: EnglishCharacter set encoding: ISO-8859-1*** START OF THIS PROJECT GUTENBERG EBOOK A HISTORY OF MATHEMATICS ***Produced by Andrew D. Hwang, Peter Vachuska, Carl Hudkinsand the Online Distributed Proofreading Team athttp://www.pgdp.nettranscriber’s noteFigures may have been moved with respect to thesurrounding text. Minor typographical correctionsand presentational changes have been made withoutcomment.This PDF le is formatted for screen viewing, butmay be easily for printing. Please consultAthe preamble of the LT X source le for instructions.EA HISTORY OF MATHEMATICSA HISTORY OFMATHEMATICSBYFLORIAN CAJORI, Ph.D.Formerly Professor of Applied Mathematics in the Tulane Universityof Louisiana; now Professor of Physicsin Colorado College\I am sure that no subject loses more than mathematicsby any attempt to dissociate it from its history."|J. W. L.GlaisherNew YorkTHE MACMILLAN COMPANYLONDON: MA & CO., Ltd.1909All rights reservedCopyright, 1893,By MACMILLAN AND CO.Set up and electrotyped January, 1894. Reprinted March ...
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The Project Gutenberg EBook of A History of Mathematics, by Florian Cajori
This eBook is for the use of anyone anywhere at no cost and with
almost no restrictions whatsoever. You may copy it, give it away or
re-use it under the terms of the Project Gutenberg License included
with this eBook or online at www.gutenberg.org
Title: A History of Mathematics
Author: Florian Cajori
Release Date: January 24, 2010 [EBook #31061]
Language: English
Character set encoding: ISO-8859-1
*** START OF THIS PROJECT GUTENBERG EBOOK A HISTORY OF MATHEMATICS ***Produced by Andrew D. Hwang, Peter Vachuska, Carl Hudkins
and the Online Distributed Proofreading Team at
http://www.pgdp.net
transcriber’s note
Figures may have been moved with respect to the
surrounding text. Minor typographical corrections
and presentational changes have been made without
comment.
This PDF le is formatted for screen viewing, but
may be easily for printing. Please consult
Athe preamble of the LT X source le for instructions.EA HISTORY OF MATHEMATICSA HISTORY OF
MATHEMATICS
BY
FLORIAN CAJORI, Ph.D.
Formerly Professor of Applied Mathematics in the Tulane University
of Louisiana; now Professor of Physics
in Colorado College
\I am sure that no subject loses more than mathematics
by any attempt to dissociate it from its history."|J. W. L.
Glaisher
New York
THE MACMILLAN COMPANY
LONDON: MA & CO., Ltd.
1909
All rights reservedCopyright, 1893,
By MACMILLAN AND CO.
Set up and electrotyped January, 1894. Reprinted March,
1895; October, 1897; November, 1901; January, 1906; July, 1909.
Norwood Pre&:
J. S. Cushing & Co.|Berwick & Smith.
Norwood, Mass., U.S.A.PREFACE.
An increased interest in the history of the exact sciences
manifested in recent years by teachers everywhere, and the
attention given to historical inquiry in the mathematical
class-rooms and seminaries of our leading universities, cause
me to believe that a brief general History of Mathematics will
be found acceptable to teachers and students.
The pages treating|necessarily in a very condensed form|
of the progress made during the present century, are put forth
with great di dence, although I have spent much time in
the e ort to render them accurate and reasonably complete.
Many valuable suggestions and criticisms on the chapter on
\Recent Times" have been made by Dr. E. W. Davis, of the
University of Nebraska. The proof-sheets of this chapter have
also been submitted to Dr. J. E. Davies and Professor C. A.
Van Velzer, both of the University of Wisconsin; to Dr. G. B.
Halsted, of the University of Texas; Professor L. M. Hoskins, of
the Leland Stanford Jr. University; and Professor G. D. Olds,
of Amherst College,|all of whom have a orded valuable
assistance. I am specially indebted to Professor F. H. Loud, of
Colorado College, who has read the proof-sheets throughout.
To all the gentlemen above named, as well as to Dr. Carlo
Veneziani of Salt Lake City, who read the rst part of my work
in manuscript, I desire to express my hearty thanks. But in
acknowledging their kindness, I trust that I shall not seem to
vlay upon them any share in the responsibility for errors which
I may have introduced in subsequent revision of the text.
FLORIAN CAJORI.
Colorado College, December, 1893.TABLE OF CONTENTS
Page
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . 1
ANTIQUITY . . . . . . . . . . . . . . . . . . . . . . . . . . 5
The Babylonians . . . . . . . . . . . . . . . . . . . . . 5
The Egyptians . . . . . . . . . . . . . . . . . . . . . . 10
The Greeks . . . . . . . . . . . . . . . . . . . . . . . . 17
Greek Geometry . . . . . . . . . . . . . . . . . . . . . 17
The Ionic School . . . . . . . . . . . . . . . . . . . 19
The School of Pythagoras . . . . . . . . . . . . . . 22
The Sophist School . . . . . . . . . . . . . . . . . . 26
The Platonic School . . . . . . . . . . . . . . . . . 33
The First Alexandrian School . . . . . . . . . . . . 39
The Second Alexandrian School . . . . . . . . . . . 62
Greek Arithmetic . . . . . . . . . . . . . . . . . . . . . 72
The Romans . . . . . . . . . . . . . . . . . . . . . . . . 89
MIDDLE AGES . . . . . . . . . . . . . . . . . . . . . . . . 97
The Hindoos . . . . . . . . . . . . . . . . . . . . . . . 97
The Arabs . . . . . . . . . . . . . . . . . . . . . . . . . 116
Europe During the Middle Ages . . . . . . . . . . . 135
Introduction of Roman Mathematics . . . . . . . . 136
Translation of Arabic Manuscripts . . . . . . . . . . 144
The First Awakening and its Sequel . . . . . . . . . 148
MODERN EUROPE . . . . . . . . . . . . . . . . . . . . . . 160
The Renaissance . . . . . . . . . . . . . . . . . . . . . 161
Vieta to Descartes . . . . . . . . . . . . . . . . . . . 181
Descartes to Newton . . . . . . . . . . . . . . . . . 213
Newton to Euler . . . . . . . . . . . . . . . . . . . . 231
viiTABLE OF CONTENTS. viii
Page
Euler, Lagrange, and Laplace . . . . . . . . . . . . 286
The Origin of Modern Geometry . . . . . . . . . . . 332
RECENT TIMES . . . . . . . . . . . . . . . . . . . . . . . 339
Synthetic Geometry . . . . . . . . . . . . . . . . . . 341
Analyticy . . . . . . . . . . . . . . . . . . . 358
Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . 367
Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 386
Theory of Functions . . . . . . . . . . . . . . . . . . 405y of Numbers . . . . . . . . . . . . . . . . . . . 422
Applied Mathematics . . . . . . . . . . . . . . . . . . 435

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