Diophantus of Alexandria: A Study in the History of Greek AlgebraUniversity Press, 1910 - 387 páginas |
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Página 27
... numbers , and even the rest of his work was not very successful , as he himself admits that he did not thoroughly understand a number ... given us demonstra- tions , such as they are , of the theorems in the problem : but in the first ...
... numbers , and even the rest of his work was not very successful , as he himself admits that he did not thoroughly understand a number ... given us demonstra- tions , such as they are , of the theorems in the problem : but in the first ...
Página 95
... numbers the sum of which is a given number , while each of them approximates as closely as possible to one and the same number . This method can be best exhibited by giving Diophantus ' two instances , in the first of which two such ...
... numbers the sum of which is a given number , while each of them approximates as closely as possible to one and the same number . This method can be best exhibited by giving Diophantus ' two instances , in the first of which two such ...
Página 98
... given number ( 10 , say ) , sometimes the squares lie respectively between different pairs of numbers , some- times they are respectively greater than different numbers , while they are always subject to the condition that their sum is a ...
... given number ( 10 , say ) , sometimes the squares lie respectively between different pairs of numbers , some- times they are respectively greater than different numbers , while they are always subject to the condition that their sum is a ...
Página 99
... numbers and their product when severally added to the same given number produce squares , the squares with which they are so connected are squares of two consecutive numbers1 . " That is to say , if x + a = m2 , y + a = n2 , and if xy + ...
... numbers and their product when severally added to the same given number produce squares , the squares with which they are so connected are squares of two consecutive numbers1 . " That is to say , if x + a = m2 , y + a = n2 , and if xy + ...
Página 100
... numbers are required , such that each of them , and the product of each pair , when severally added to a given number , produce squares . Thus if the third number be z , three additional conditions have to be satisfied , namely z + a ...
... numbers are required , such that each of them , and the product of each pair , when severally added to a given number , produce squares . Thus if the third number be z , three additional conditions have to be satisfied , namely z + a ...
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
a²-b² absolute term added Algebra Archimedes arithm Arithmetica Assume assumption auxiliary triangle Ax² 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 form 4n fraction Frénicle given number given ratio gives a square Greek hypotenuse Iamblichus indeterminate equations infinite number integral Lagrange Lemma letter Maximus Planudes method minus multiplied Nesselmann obtain Oeuvres de Fermat pair polygonal number Porisms prime number problem proposition quadratic rational numbers required numbers required squares required triangle result 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 ἀριθμός καὶ