Diophantus of Alexandria: A Study in the History of Greek AlgebraDover Publications, 1964 - 387 páginas |
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Página 177
... whence y = 4 . Thus we must assume x , 64- for the numbers . Therefore - 128x3 + 4096 + x = a square = ( x3 +64 ) 3 , say ; whence 2563 = x , and x = = 18 . The numbers are I 262143 16 ' 4096 19. To find three numbers indeterminately1 ...
... whence y = 4 . Thus we must assume x , 64- for the numbers . Therefore - 128x3 + 4096 + x = a square = ( x3 +64 ) 3 , say ; whence 2563 = x , and x = = 18 . The numbers are I 262143 16 ' 4096 19. To find three numbers indeterminately1 ...
Página 351
... whence A = 40 , whence A = 88 , B = 8 , C = 1 , D = 23 , m = 1 } . B = 16 , C = 1 , D = 51 , m = 4 . If ƒ = 5 , g = 1 , we can obtain integral solutions , thus . A = 20a , B = 20b , C = 30b + 2a , D = 8a - 20b , m = 30 ( a + b ) ( 25b ...
... whence A = 40 , whence A = 88 , B = 8 , C = 1 , D = 23 , m = 1 } . B = 16 , C = 1 , D = 51 , m = 4 . If ƒ = 5 , g = 1 , we can obtain integral solutions , thus . A = 20a , B = 20b , C = 30b + 2a , D = 8a - 20b , m = 30 ( a + b ) ( 25b ...
Página 370
... whence p + q = 12mn — 10n2 — 13m2 , − p + q = 12mn — 26n2 — 5m2 , while % = 8 + 63 ( p ± 9 ) 2 شد Thus there are any number of values of z from which triangles may be obtained satisfying the conditions . The simplest value is found by ...
... whence p + q = 12mn — 10n2 — 13m2 , − p + q = 12mn — 26n2 — 5m2 , while % = 8 + 63 ( p ± 9 ) 2 شد Thus there are any number of values of z from which triangles may be obtained satisfying the conditions . The simplest value is found by ...
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The MSS of and writers on Diophantus | 14 |
3253 | 32 |
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Diophantus of Alexandria: A Study in the History of Greek Algebra Thomas L. Heath Vista previa restringida - 1910 |
Términos y frases comunes
absolute term added Algebra Arithmetica Assume auxiliary triangle Ax² Bachet Books coefficient cube difference differential equations Dioph Diophantus divide double-equation equal Euler expression factors Fermat find a right-angled find three numbers find two numbers formula four numbers fraction functions geometry given number given ratio gives a square Greek hypotenuse Iamblichus indeterminate indeterminate equations Index integral Konrad Knopp Lagrange Lemma letter linear mathematics method minus multiplied Nesselmann obtain Oeuvres de Fermat Paperbound perpendicular polygonal number Porisms prime number problem propositions quadratic rational numbers required numbers required squares right-angled triangle satisfy the conditions sides solution solved square number substitute subtract Suppose symbol Tannery theorem theory third number triple-equation whence whole numbers Xylander