Diophantus of Alexandria: A Study in the History of Greek AlgebraUniversity Press, 1910 - 387 páginas |
Dentro del libro
Resultados 1-5 de 25
Página 10
... greatest error , in any case in which a 1 Dioph . II . p . xix . ' Thus Tannery holds ( loc . cit . ) that the solution of the complete quadratic was given in the form of corollaries to I. 27 , 30 ; and he refers the three " porisms ...
... greatest error , in any case in which a 1 Dioph . II . p . xix . ' Thus Tannery holds ( loc . cit . ) that the solution of the complete quadratic was given in the form of corollaries to I. 27 , 30 ; and he refers the three " porisms ...
Página 100
... greatest of three numbers such that the product of any pair of them added to either the sum of that pair or the remaining number gives a square . ” That is , the three numbers m3 , ( m + 1 ) 3 , 4 ( m2 + m + 1 ) " " " Euler has a paper ...
... greatest of three numbers such that the product of any pair of them added to either the sum of that pair or the remaining number gives a square . ” That is , the three numbers m3 , ( m + 1 ) 3 , 4 ( m2 + m + 1 ) " " " Euler has a paper ...
Página 107
... greatest square which measures it , must not be divisible by a prime number of the form 4n - 1 . " ( Note upon v . 9 ; also in a letter to Roberval ' . ) There is room for any number of conjectures as to what may have been Diophantus ...
... greatest square which measures it , must not be divisible by a prime number of the form 4n - 1 . " ( Note upon v . 9 ; also in a letter to Roberval ' . ) There is room for any number of conjectures as to what may have been Diophantus ...
Página 137
... greatest exceeds the middle number by a given fraction of the least , the middle exceeds the least by a given fraction of the greatest , but the least exceeds a given fraction of the middle number by a given number . Necessary condition ...
... greatest exceeds the middle number by a given fraction of the least , the middle exceeds the least by a given fraction of the greatest , but the least exceeds a given fraction of the middle number by a given number . Necessary condition ...
Página 138
... greatest must be such that , when it is added to the least , the coefficient of x in the sum is less than the coefficient of x in the expression for the middle number resulting from the assumptions made1 . Let the least number be x + 10 ...
... greatest must be such that , when it is added to the least , the coefficient of x in the sum is less than the coefficient of x in the expression for the middle number resulting from the assumptions made1 . Let the least number be x + 10 ...
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