Diophantos of Alexandria: A Study in the History of Greek Algebra |
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Page 106
... of x's and x becomes some number multiplied by 6 together with 12 and divided by the difference by which the square of the number exceeds three . " ditions under which more general cases might be solved in 106 DIOPHANTOS OF ALEXANDRIA .
... of x's and x becomes some number multiplied by 6 together with 12 and divided by the difference by which the square of the number exceeds three . " ditions under which more general cases might be solved in 106 DIOPHANTOS OF ALEXANDRIA .
Page 108
... exceed 6 , nor in the second class ( except in a special case or two ) exceed 3 . First class . Equation Ax " + Bx - 1 + ...... + Kx + L = y3 . We give now the forms found in Diophantos . 1. Equation Ax + Bx + Сx + d2 = y3 . Here we ...
... exceed 6 , nor in the second class ( except in a special case or two ) exceed 3 . First class . Equation Ax " + Bx - 1 + ...... + Kx + L = y3 . We give now the forms found in Diophantos . 1. Equation Ax + Bx + Сx + d2 = y3 . Here we ...
Page 111
... exceeds a square by 2. Diophantos assumes ( x - 1 ) for the cube , and ( x + 1 ) for the square , obtaining x3 - 3x2 + 3x - 1 = x2 + 2x + 3 , or the equation x3 + x = 4x2 + 4 , previously mentioned ( pp . 36 , 93 ) , which is satisfied ...
... exceeds a square by 2. Diophantos assumes ( x - 1 ) for the cube , and ( x + 1 ) for the square , obtaining x3 - 3x2 + 3x - 1 = x2 + 2x + 3 , or the equation x3 + x = 4x2 + 4 , previously mentioned ( pp . 36 , 93 ) , which is satisfied ...
Page 164
... exceeds a given fraction of the other by a given difference . Necessary condition . The latter number must be less than that which arises when that fraction of the first number is taken which exceeds the other fraction . 1 4 1 6 Given ...
... exceeds a given fraction of the other by a given difference . Necessary condition . The latter number must be less than that which arises when that fraction of the first number is taken which exceeds the other fraction . 1 4 1 6 Given ...
Page 172
... exceeds the difference of the numbers themselves by a given number . Condition . The square of their difference must ... exceed a given proportion or fraction of it by a given number . " Given number 10 , difference of numbers required 2 ...
... exceeds the difference of the numbers themselves by a given number . Condition . The square of their difference must ... exceed a given proportion or fraction of it by a given number . " Given number 10 , difference of numbers required 2 ...
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Common terms and phrases
Abu'l-Wafa Algebra Alkarkhi Arabian Arithmetics Assume Ave Maria Lane Ax² Bachet Bombelli C. J. CLAY Cambridge University Press CLAY & SONS coefficients College commentary condition Cossali Crown 8vo cube Demy 8vo difference Diophantos edition Editor English equal Fellow Fermat final sigma find a right-angled find three numbers find two numbers fraction given number given ratio gives Greek Hence hypotenuse Hypsikles indeterminate equations LL.D Maximus Planudes mentioned method Mohammed ibn Mūsā multiplied Nesselmann Nikomachos notation Notes phantos Polygonal Numbers Porisms problem Professor quadratic Regiomontanus remark required number result right-angled triangle roots side solution solved square number St John's College subtract Suidas symbol Tannery term Theon of Alexandria third translation treatise Trinity College University of Cambridge University Press Warehouse unknown quantity whence words write Xylander δὲ εἰς ἐν καὶ τὰ τὸ τοῦ τῶν
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