Diophantus of Alexandria: A Study in the History of Greek AlgebraUniversity Press, 1910 - 387 páginas |
Dentro del libro
Resultados 1-5 de 71
Página 6
... find that Diophantus moves in a rigidly defined and limited circle of methods and artifices , and that any attempts ... right- angled triangles in rational numbers such that the sides and area satisfy given conditions , the geometrical ...
... find that Diophantus moves in a rigidly defined and limited circle of methods and artifices , and that any attempts ... right- angled triangles in rational numbers such that the sides and area satisfy given conditions , the geometrical ...
Página 71
... find a square [ to replace 4 ] such that 18 times ( this square + 1 ) + ( § ) may be a square . " Diophantus then solves the auxiliary equation 18 ( m2 + 1 ) + f = ya , finding ... right - angled triangle 4x2 + 6x + 2 , which has to be a cube ...
... find a square [ to replace 4 ] such that 18 times ( this square + 1 ) + ( § ) may be a square . " Diophantus then solves the auxiliary equation 18 ( m2 + 1 ) + f = ya , finding ... right - angled triangle 4x2 + 6x + 2 , which has to be a cube ...
Página 93
... find only a few examples under conditions favourable for solution by his method . 6. Diophantus ' treatment of ... right - angled triangle , ” all that can be said of a general character is that only “ rational ” right- angled triangles ...
... find only a few examples under conditions favourable for solution by his method . 6. Diophantus ' treatment of ... right - angled triangle , ” all that can be said of a general character is that only “ rational ” right- angled triangles ...
Página 94
... right - angled triangle with sides ( 7a + 2a ) , ( 7a — 2o ) , 2.7.2 , or 53 , 45 , 28 . II . METHOD OF LIMITS . • As Diophantus often has to find ... find solutions which lie within certain limits in place of those rejected . • 1. A very ...
... right - angled triangle with sides ( 7a + 2a ) , ( 7a — 2o ) , 2.7.2 , or 53 , 45 , 28 . II . METHOD OF LIMITS . • As Diophantus often has to find ... find solutions which lie within certain limits in place of those rejected . • 1. A very ...
Página 105
... find four rational right - angled triangles having the same hypotenuse . The method is this . Form two right - angled triangles from ( a , b ) and ( c , d ) respectively , ie . let the sides of the triangles be respectively and a2 + b3 ...
... find four rational right - angled triangles having the same hypotenuse . The method is this . Form two right - angled triangles from ( a , b ) and ( c , d ) respectively , ie . let the sides of the triangles be respectively and a2 + b3 ...
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