Diophantus of Alexandria: A Study in the History of Greek AlgebraUniversity Press, 1910 - 387 páginas |
Dentro del libro
Resultados 1-5 de 64
Página 67
... factor on both sides of the equation . The result of dividing by it is x4 , which is Diophantus ' solution . Of the other two roots x = ± √ ( 1 ) no account is taken , for the reason stated above . It is not possible to judge from this ...
... factor on both sides of the equation . The result of dividing by it is x4 , which is Diophantus ' solution . Of the other two roots x = ± √ ( 1 ) no account is taken , for the reason stated above . It is not possible to judge from this ...
Página 68
... factor x disappearing and the root x = 0 being neglected as usual . Thus x = Exx . II . 21 : 4x2 + 3x = y2 = ( 3x ) 3 , say , and x = = + . II . 33 : 16x2 + 7x = y2 = ( 5x ) 2 , say , and r = f . Bn m2 — An2 ' 2. Equations which can ...
... factor x disappearing and the root x = 0 being neglected as usual . Thus x = Exx . II . 21 : 4x2 + 3x = y2 = ( 3x ) 3 , say , and x = = + . II . 33 : 16x2 + 7x = y2 = ( 5x ) 2 , say , and r = f . Bn m2 — An2 ' 2. Equations which can ...
Página 71
... factors . ( Curiously enough Diophantus does not separate quadratic expressions into their factors except in one case , VI . 19 , where however his purpose is quite different : he has made the sum of three sides of a right - angled ...
... factors . ( Curiously enough Diophantus does not separate quadratic expressions into their factors except in one case , VI . 19 , where however his purpose is quite different : he has made the sum of three sides of a right - angled ...
Página 73
... factors p , q , the expressions themselves are equated to ( 9 ) } respectively . Diophantus himself ( II . 11 ) states his rule thus . " Observing the difference [ between the two expressions ] , seek two numbers such that their product ...
... factors p , q , the expressions themselves are equated to ( 9 ) } respectively . Diophantus himself ( II . 11 ) states his rule thus . " Observing the difference [ between the two expressions ] , seek two numbers such that their product ...
Página 74
... factors ; let these bep , { ( a− B ) x + ( a − b ) } / p . We write accordingly 24 ± 2 = ( a − B ) x + a − b ̧ P u = w = p . Thus therefore ! - - W = ax + a = { ( a − B ) x + a = b + " ) } " ; 4 p { ( a − B ) x + a − b + p2 } 3 ...
... factors ; let these bep , { ( a− B ) x + ( a − b ) } / p . We write accordingly 24 ± 2 = ( a − B ) x + a − b ̧ P u = w = p . Thus therefore ! - - W = ax + a = { ( a − B ) x + a = b + " ) } " ; 4 p { ( a − B ) x + a − b + p2 } 3 ...
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