AMS Chelsea Publishing 1991; 524 pp; hardcover Volume: 303 Reprint/Revision History: second AMS printing 2000 ISBN10: 0821821024 ISBN13: 9780821821022 List Price: US$61 Member Price: US$54.90 Order Code: CHEL/303.H
 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 smoothflowing narrative. The Indexfor examplecontains 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."  ESTREAMS "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 mindsstarting from Antiquity up to the end of World War Ito 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 societiesa 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 allinclusive 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 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
 Linkmotion
 Parallel lines, nonEuclidean geometry and geometry of \(n\) dimensions
Analytic Geometry  Analysis Situs
 Intrinsic coordinates
 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, integrodifferential 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
