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A History of Mathematics: Fifth Edition
 
Florian Cajori
A History of Mathematics
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
eBook ISBN:  978-1-4704-7059-3
Product Code:  CHEL/303.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Add to cart
A History of Mathematics
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A History of Mathematics: Fifth Edition
Florian Cajori
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
eBook ISBN:  978-1-4704-7059-3
Product Code:  CHEL/303.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Add to cart
  • Book Details
     
     
    AMS Chelsea Publishing
    Volume: 303; 1991; 524 pp
    MSC: Primary 01

    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.
  • Table of Contents
     
     
    • Front Cover
    • Preafce to the Third Edition
    • Preface to the Fourth Edition
    • Preface to the Fifth Edition
    • Preface to the Second Edition
    • Table of Contents
    • Introduction
    • The Babylonians
    • The Egyptians
    • The Greeks
    • Greek Geometry
    • The Ionic School
    • The School of Pythagoras
    • The Sophist School
    • The Platonic School
    • The First Alexandrian School
    • The Second Alexandrian School
    • Greek Arithmetic and Algebra
    • The Romans
    • The Maya
    • The Chinese
    • The Japanese
    • The Hindus
    • The Arabs
    • Europe During the Middle Ages
    • Introduction of Romam 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 Early Twentieth Centuries
    • Introduction
    • Definitions of Mathematics
    • Synthetic Geometry
    • Elementary Geometry of the Triangle and Circle
    • Link-motion
    • Parallel Lines, Non-euclidean Geometry on 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
    • General Theory of Functions
    • Uniformization
    • Theory of Numbers
    • Fermat's "Last Theorem," waring's Theorem
    • Other 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
    • Index
    • Back Cover
  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
AMS Chelsea Publishing
Volume: 303; 1991; 524 pp
MSC: Primary 01

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.
  • Front Cover
  • Preafce to the Third Edition
  • Preface to the Fourth Edition
  • Preface to the Fifth Edition
  • Preface to the Second Edition
  • Table of Contents
  • Introduction
  • The Babylonians
  • The Egyptians
  • The Greeks
  • Greek Geometry
  • The Ionic School
  • The School of Pythagoras
  • The Sophist School
  • The Platonic School
  • The First Alexandrian School
  • The Second Alexandrian School
  • Greek Arithmetic and Algebra
  • The Romans
  • The Maya
  • The Chinese
  • The Japanese
  • The Hindus
  • The Arabs
  • Europe During the Middle Ages
  • Introduction of Romam 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 Early Twentieth Centuries
  • Introduction
  • Definitions of Mathematics
  • Synthetic Geometry
  • Elementary Geometry of the Triangle and Circle
  • Link-motion
  • Parallel Lines, Non-euclidean Geometry on 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
  • General Theory of Functions
  • Uniformization
  • Theory of Numbers
  • Fermat's "Last Theorem," waring's Theorem
  • Other 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
  • Index
  • Back Cover

  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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