Diophantus of Alexandria: A Study in the History of Greek AlgebraUniversity Press, 1910 - 387 páginas |
Dentro del libro
Resultados 1-5 de 40
Página 105
... hypotenuse . The method is this . Form two right - angled triangles from ( a , b ) and ( c , d ) respectively , ie ... hypotenuse of the other , we have two triangles with the same hypotenuse , namely and ( a2 + b3 ) ( c2 + d3 ) , ( a2 ...
... hypotenuse . The method is this . Form two right - angled triangles from ( a , b ) and ( c , d ) respectively , ie ... hypotenuse of the other , we have two triangles with the same hypotenuse , namely and ( a2 + b3 ) ( c2 + d3 ) , ( a2 ...
Página 106
... hypotenuse of a right - angled triangle in one way only , its square is so in two ways , its cube in three , its biquadrate in four . ways , and so on ad infinitum . " [ 2 ] The same prime number 4n + 1 and its square are the sum of two ...
... hypotenuse of a right - angled triangle in one way only , its square is so in two ways , its cube in three , its biquadrate in four . ways , and so on ad infinitum . " [ 2 ] The same prime number 4n + 1 and its square are the sum of two ...
Página 107
... hypotenuse of other right - angled triangles , that product having precisely the property of being , as in Fermat's [ 3 ] , the sum of two squares in two ways . Diophantus may therefore have had an inkling , whether obtained empirically ...
... hypotenuse of other right - angled triangles , that product having precisely the property of being , as in Fermat's [ 3 ] , the sum of two squares in two ways . Diophantus may therefore have had an inkling , whether obtained empirically ...
Página 120
... hypotenuse , of a right - angled triangle , S its area , the radius of its inscribed circle , and s = } ( a + b + c ) : S = rs = tab , r + s = a + b , c = s - r . ( The proof of these formulae by means of the usual figure , that used by ...
... hypotenuse , of a right - angled triangle , S its area , the radius of its inscribed circle , and s = } ( a + b + c ) : S = rs = tab , r + s = a + b , c = s - r . ( The proof of these formulae by means of the usual figure , that used by ...
Página 166
... hypotenuse ) ± ( twice product of perps . ) = a square , we must seek four right - angled triangles [ in rational numbers ] having the same hypotenuse , or we must find a square which is divisible into two squares in four different ways ...
... hypotenuse ) ± ( twice product of perps . ) = a square , we must seek four right - angled triangles [ in rational numbers ] having the same hypotenuse , or we must find a square which is divisible into two squares in four different ways ...
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