Diophantos of AlexandriaCambridge University Press, 2014 M03 20 - 266 pages The Greek mathematician Diophantos of Alexandria lived during the third century CE. Apart from his age (he reached eighty-four), very little else is known about his life. Even the exact form of his name is uncertain, and only a few incomplete manuscripts of his greatest work, Arithmetica, have survived. In this impressive scholarly investigation, first published in 1885, Thomas Little Heath (1861-1940) meticulously presents what can be gleaned from Greek, Latin and Arabic sources, and guides the reader through the algebraist's idiosyncratic style of mathematics, discussing his notation and originality. This was the first thorough survey of Diophantos' work to appear in English. Also reissued in this series are Heath's two-volume History of Greek Mathematics, his treatment of Greek astronomy through the work of Aristarchus of Samos, and his edition in modern notation of the Treatise on Conic Sections by Apollonius of Perga. |
Contents
CHAPTER | 1 |
w Results of the preceding investigation 1617 | 16 |
What portion of the Arithmetics is lost? The contents of | 26 |
CHAPTER III | 38 |
NOTATION AND DEFINITIONS OF DIOPHANTOS | 57 |
gs Notation for powers of the unknown 6769 | 67 |
ga General remarks on the historical development of algebraic | 76 |
DIOPHANTOS METHODS OF SOLUTION | 83 |
g3 Summary of the preceding investigation 113114 | 113 |
The Porisms of Diophantos 121125 | 121 |
HOW FAR WAS DIOPHANTOS ORIGINAL | 133 |
É Comparison of Diophantos with his Greek predecessors 139142 | 139 |
CHAPTER VIII | 148 |
Diophantos and AbulWafà | 155 |
Arithmetics Book I 163171 | 163 |
Polygonal Numbers 238244 | 238 |
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Common terms and phrases
abbreviation Abu’l-Wafa Algebra Alkarkhi Arithmetics Bachet Bombelli coefficient condition Cossali cube definite difference difficult difi'erence Diophantos divide a given double-equation equal exceeds expression Fermat final sigma find a right-angled find three numbers find three squares find two numbers finding first and second first degree first number given number Given number 20 given ratio Greek Greek Mathematics Hence hypotenuse Hypsikles indeterminate equations indeterminate problems ka‘b Let the first let the number letters Maximus Planudes mentioned minus multiplied Nesselmann Nikomachos notation Pappos phantos Polygonal Numbers Porisms problem quadratic equations question Rafael Bombelli rational numbers Regiomontanus remark required number required squares result right-angled triangle Rodet roots satisfied side solved square number subtract sufficient Suidas suppose symbol T0 find Tannery Theon Theon of Alexandria theorems third thirteen books tion translation unknown quantity whence words write Xylander Xylander’s