Diophantus of Alexandria: A Study in the History of Greek AlgebraUniversity Press, 1910 - 387 páginas |
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Página 12
... square number in the Cattle - Problem stretches , as Tannery says , a wide domain which was certainly not unknown to Diophantus , but was his hunting - ground for the most various problems . Whether Diophantus dealt with plane numbers ...
... square number in the Cattle - Problem stretches , as Tannery says , a wide domain which was certainly not unknown to Diophantus , but was his hunting - ground for the most various problems . Whether Diophantus dealt with plane numbers ...
Página 38
A Study in the History of Greek Algebra Sir Thomas Little Heath. square ' . With Diophantus , however , it is not any square , but only the square of the unknown ; where he speaks of any particular square number , it is Terρáy∞vos ápuós ...
A Study in the History of Greek Algebra Sir Thomas Little Heath. square ' . With Diophantus , however , it is not any square , but only the square of the unknown ; where he speaks of any particular square number , it is Terρáy∞vos ápuós ...
Página 50
... square root , or eight , and subtract from it half the number of roots , namely five , and there remain three : this is the root of the square which was required , and the square itself is nine1 " Here we observe that not even are ...
... square root , or eight , and subtract from it half the number of roots , namely five , and there remain three : this is the root of the square which was required , and the square itself is nine1 " Here we observe that not even are ...
Página 51
... ( Square ) for 4o ( dúvaμış ) , N ( Number ) for s , U . ( Units ) for M ( μονάδες ) . " To divide the proposed square into two squares . Let it be proposed then to divide 16 into two squares . And let the first be supposed to be 1S ...
... ( Square ) for 4o ( dúvaμış ) , N ( Number ) for s , U . ( Units ) for M ( μονάδες ) . " To divide the proposed square into two squares . Let it be proposed then to divide 16 into two squares . And let the first be supposed to be 1S ...
Página 65
... square number ; but it is not , " ie . tp + mg , or in this case ( † ) ' + 42 , must be a square in order that the root may be . rational , which in this case it is not . Case 2. Form mx2 = px + q . Diophantus takes x = } p + √ ( { p2 ...
... square number ; but it is not , " ie . tp + mg , or in this case ( † ) ' + 42 , must be a square in order that the root may be . rational , which in this case it is not . Case 2. Form mx2 = px + q . Diophantus takes x = } p + √ ( { p2 ...
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