A History of Mathematics

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American Mathematical Soc., 1991 - Mathematics - 524 pages
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Originally published in 1893, this book was significantly revised and extended by the author (second edition, 1919) to cover the history of mathematics from antiquity to the end of World War I. Since then, three more editions were published, and the current volume is a reproduction of the fifth edition (1991). The book covers the history of ancient mathematics (Babylonian, Egyptian, Roman, Chinese, Japanese, Mayan, Hindu, and Arabic, with a major emphasis on ancient Greek mathematics). The chapters that follow explore European mathematics in the Middle Ages and the mathematics of the sixteenth, seventeenth, and eighteenth centuries (Vieta, Decartes, Newton, Euler, and Lagrange). The last and longest chapter discusses major mathematics events of the nineteenth and early twentieth centuries. Topics discussed in this chapter include synthetic and analytic geometry, algebra, analysis, the theory of functions, the theory of numbers, and others. In one concise volume, the author presents an interesting and reliable account of mathematics history. Cajori has mastered the art of incorporating an enormous amount of material into a smoothly flowing narrative. The review of the volume's third edition in Mathematical Reviews ends with the following words: "Chaque mathematicien devrait lire ce livre!"
 

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Contents

THE BABYLONIANS
1
THE EGYPTIANS
9
THE GREEKS
15
Greek Arithmetic and Algebra
52
THE ROMANS
63
THE MAYA
69
THE CHINESE
71
THE JAPANESE
78
Descartes to Newton
173
Newton to Euler
190
Euler Lagrange and Laplace
231
THE NINETEENTH AND EARLY TWENTIETH CENTURIES
278
Synthetic Geometry
286
Analytic Geometry
309
Algebra
329
Analysis
367

THE HINDUS
83
THE ARABS
99
EUROPE DURING THE MIDDLE AGES
113
Translation of Arabic Manuscripts
118
The First Awakening and its Sequel
120
EUROPE DURING THE SIXTEENTH SEVENTEENTH AND EIGHTEENTH CENTURIES
130
Vieta to Descartes
145
Theory of Functions
411
Theory of Numbers
434
Applied Mathematics
447
EDITORS NOTES
487
INDEX
497
Copyright

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