Diophantus of Alexandria: A Study in the History of Greek AlgebraUniversity Press, 1910 - 387 páginas |
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Página 10
... lemmas to what follows , " Anupa eis Tò ¿ Es ( cf. lemmas before IV . 34 , 35 , 36 , V. 7 , 8 , VI . 12 , 15 ) . On the other hand , there is nothing improbable in the supposition that Diophantus was induced by the difficulty of his ...
... lemmas to what follows , " Anupa eis Tò ¿ Es ( cf. lemmas before IV . 34 , 35 , 36 , V. 7 , 8 , VI . 12 , 15 ) . On the other hand , there is nothing improbable in the supposition that Diophantus was induced by the difficulty of his ...
Página 11
... lemmas to help him , undertook a more difficult task than he would have undertaken if he had attempted to fill up seven Diophantine Books with numerical problems which the Greeks may reasonably be supposed to have solved . " On the ...
... lemmas to help him , undertook a more difficult task than he would have undertaken if he had attempted to fill up seven Diophantine Books with numerical problems which the Greeks may reasonably be supposed to have solved . " On the ...
Página 46
... Lemma to v . 8 we have BL's ' = 2 or 2 } , where is decomposed into submultiples as in Heron . Cf. also ( III . 11 ) TOL ' is * = 370 + √6 . • Before leaving the subject of numerical notation , it may be convenient to refer to the ...
... Lemma to v . 8 we have BL's ' = 2 or 2 } , where is decomposed into submultiples as in Heron . Cf. also ( III . 11 ) TOL ' is * = 370 + √6 . • Before leaving the subject of numerical notation , it may be convenient to refer to the ...
Página 69
... Lemma to VI . 15 thus , though only for the case in which C is negative : " Given two numbers , if , when one is multiplied by some square and the other is subtracted from the product , the result is a square , then another square also ...
... Lemma to VI . 15 thus , though only for the case in which C is negative : " Given two numbers , if , when one is multiplied by some square and the other is subtracted from the product , the result is a square , then another square also ...
Página 117
... ( Lemma following x . 28 ) . Starting with numbers u = c + b and v = c − b , so that uv = c − b3 , - Euclid points out that , in order that wv may be a square , and v must be " similar plane numbers " or numbers of the form mnp3 , mnq ...
... ( Lemma following x . 28 ) . Starting with numbers u = c + b and v = c − b , so that uv = c − b3 , - Euclid points out that , in order that wv may be a square , and v must be " similar plane numbers " or numbers of the form mnp3 , mnq ...
Otras ediciones - Ver todo
Diophantus of Alexandria: A Study in the History of Greek Algebra Thomas L. Heath Vista previa restringida - 1910 |
Diophantus of Alexandria: A Study in the History of Greek Algebra Sir Thomas Little Heath,Leonhard Euler Vista de fragmentos - 1964 |
Términos y frases comunes
absolute term added Algebra arithm Assume auxiliary triangle Bachet Books coefficient commentary cube difference Dioph Diophantus double-equation equal Euler expression factors find a right-angled find three numbers find three squares find two numbers four numbers fraction Frénicle given number given ratio gives a square Greek hypotenuse Iamblichus indeterminate indeterminate equations integral Lagrange Lemma letter Maximus Planudes method minus multiplied Nesselmann obtain Oeuvres de Fermat polygonal number Porisms prime number problem proposition quadratic rational numbers required numbers required squares right-angled triangle satisfy the conditions solution square number substitute subtract Suppose Tannery Theon of Smyrna theorem third number triple-equation unknown quantity whence whole numbers Xylander καὶ