Diophantus of Alexandria: A Study in the History of Greek AlgebraUniversity Press, 1910 - 387 páginas |
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Página 50
... required , and the square itself is nine1 " Here we observe that not even are symbols used for numbers , so that this example is even more " rhetorical " than the work of Iamblichus who does use the Greek symbols for his numbers . - as ...
... required , and the square itself is nine1 " Here we observe that not even are symbols used for numbers , so that this example is even more " rhetorical " than the work of Iamblichus who does use the Greek symbols for his numbers . - as ...
Página 67
... required numbers , converted into determinate equations . Nor is it likely that indeterminate equations of the first degree were treated of in the lost Books . For , as Nesselmann observes , while with indeterminate quadratic equations ...
... required numbers , converted into determinate equations . Nor is it likely that indeterminate equations of the first degree were treated of in the lost Books . For , as Nesselmann observes , while with indeterminate quadratic equations ...
Página 87
... requires the solution in rational numbers of Ax " + Bx " + ... + Kx + L = y , the second the solution of Ax " + Bx " 1 + ... + Kx + L = y , for Diophantus does not go beyond making a certain function of x a cube . In no instance ...
... requires the solution in rational numbers of Ax " + Bx " + ... + Kx + L = y , the second the solution of Ax " + Bx " 1 + ... + Kx + L = y , for Diophantus does not go beyond making a certain function of x a cube . In no instance ...
Página 94
... Required to find a value of x such that some power of it , x " , shall lie between two given numbers . Let the given numbers be a , b . Then Diophantus ' method is to multiply both a and b by 2 " , 3 ′′ , and so on , successively ...
... Required to find a value of x such that some power of it , x " , shall lie between two given numbers . Let the given numbers be a , b . Then Diophantus ' method is to multiply both a and b by 2 " , 3 ′′ , and so on , successively ...
Página 95
... numbers the sum of which is a given number , while each of them approximates as closely as possible to one and the ... required . In cases like this the principles cannot be so well indicated with general symbols as with concrete numbers ...
... numbers the sum of which is a given number , while each of them approximates as closely as possible to one and the ... required . In cases like this the principles cannot be so well indicated with general symbols as with concrete numbers ...
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