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History of Mathematics: Fifth Edition
Florian Cajori
cover
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AMS Chelsea Publishing
1991; 524 pp; hardcover
Volume: 303
Reprint/Revision History:
second AMS printing 2000
ISBN-10: 0-8218-2102-4
ISBN-13: 978-0-8218-2102-2
List Price: US$61
Member Price: US$54.90
Order Code: CHEL/303.H
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Originally issued in 1893, this popular Fifth Edition (1991) covers the period from antiquity to the close of World War I, with major emphasis on advanced mathematics and, in particular, the advanced mathematics of the nineteenth and early twentieth centuries. In one concise volume this unique book presents an interesting and reliable account of mathematics history for those who cannot devote themselves to an intensive study. The book is a must for personal and departmental libraries alike.

Cajori has mastered the art of incorporating an enormous amount of specific detail into a smooth-flowing narrative. The Index--for example--contains not just the 300 to 400 names one would expect to find, but over 1,600. And, for example, one will not only find John Pell, but will learn who he was and some specifics of what he did (and that the Pell equation was named erroneously after him). In addition, one will come across Anna J. Pell and learn of her work on biorthogonal systems; one will find not only H. Lebesgue but the not unimportant (even if not major) V.A. Lebesgue. Of the Bernoullis one will find not three or four but all eight. One will find R. Sturm as well as C. Sturm; M. Ricci as well as G. Ricci; V. Riccati as well as J.F. Riccati; Wolfgang Bolyai as well as J. Bolyai; the mathematician Martin Ohm as well as the physicist G.S. Ohm; M. Riesz as well as F. Riesz; H.G. Grassmann as well as H. Grassmann; H.P. Babbage who continued the work of his father C. Babbage; R. Fuchs as well as the more famous L. Fuchs; A. Quetelet as well as L.A.J. Quetelet; P.M. Hahn and Hans Hahn; E. Blaschke and W. Blaschke; J. Picard as well as the more famous C.E. Picard; B. Pascal (of course) and also Ernesto Pascal and Etienne Pascal; and the historically important V.J. Bouniakovski and W.A. Steklov, seldom mentioned at the time outside the Soviet literature.

Reviews

"This title belongs in every math library."

-- E-STREAMS

"This book is an astonishing synthesis (astonishing by the author's exact judgement of the historical facts to be left aside, yet without presenting an incomplete version) of the essential contributions brought by dedicated minds--starting from Antiquity up to the end of World War I--to the settlement and development of what is now the powerful, indubitable and marvelous science of mathematics. Thus, the first chapters deal with the development of mathematics in the Babylonian, Egyptian, Greek (the Ionic school, the school of Pythagoras, the Sophist, Platonic and Alexandrian schools), Roman, Chinese, Maya, Japanese, Hindus and Arabian antic societies--a fascinating survey of the main moments of mankind's mathematical inspiration. There follow two chapters "Europe during the Middle Ages" and "Europe during the Sixteenth, Seventeenth and Eighteenth centuries", opening the way to the most dense chapter of the book: the nineteenth and twentieth centuries, divided into the following subtitles: synthetic geometry, analytic geometry, algebra, analysis, theory of functions, theory of numbers, applied mathematics. It is an all-inclusive book, an impressively human approach of the conjugated efforts made by long ranks of generations for the rounding off of a faultless science, a book with a perfectly chosen motto: "No subject loses more than mathematics by any attempt to dissociate it from its history.""

-- Zentralblatt MATH

Table of Contents

  • Introduction
  • The Babylonians
  • The Egyptians
  • The Greeks
  • The Romans
  • The Maya
  • The Chinese
  • The Japanese
  • The Hindus
  • The Arabs
Europe During the Middle Ages
  • Introduction of Roman mathematics
  • Translation of Arabic manuscripts
  • The first awakening and its sequel
Europe During the Sixteenth, Seventeenth and Eighteenth Centuries
  • The Renaissance
  • Vieta to Descartes
  • Descartes to Newton
  • Newton to Euler
  • Euler, Lagrange and Laplace
The Nineteenth and Twentieth Centuries. Introduction
  • Definition of mathematics
Synthetic Geometry
  • Elementary geometry of the triangle and circle
  • Link-motion
  • Parallel lines, non-Euclidean geometry and geometry of \(n\) dimensions
Analytic Geometry
  • Analysis Situs
  • Intrinsic co-ordinates
  • Definition of a curve
  • Fundamental postulates
  • Geometric models
Algebra
  • Theory of equations and theory of groups
  • Solution of numerical equations
  • Magic squares and combinatory analysis
Analysis
  • Calculus of variations
  • Convergence of series
  • Probability and statistics
  • Differential equations. Difference equations
  • Integral equations, integro-differential equations, general analysis, functional calculus
  • Theories of irrationals and theory of aggregates
  • Mathematical logic
Theory of Functions
  • Elliptic functions
  • General theory of functions
  • Uniformization
Theory of Numbers
  • Fermat's "Last Theorem," Waring's theorem
  • Other recent researches. Number fields
  • Transcendental numbers. The infinite
Applied Mathematics
  • Celestial mechanics
  • Problem of three bodies
  • General mechanics
  • Fluid motion
  • Sound. Elasticity
  • Light, electricity, heat, potential
  • Relativity
  • Nomography
  • Mathematical tables
  • Calculating machines, planimeters, integraphs
  • Editor's notes
  • Alphabetical index
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