Diophantos of Alexandria: A Study in the History of Greek Algebra |
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Page 79
... multiply this by itself , and the result is five and twenty . Add this to the nine and thirty , which gives sixty - four ; take the square root , or eight , and subtract from it half the number of roots , namely five , and there remain ...
... multiply this by itself , and the result is five and twenty . Add this to the nine and thirty , which gives sixty - four ; take the square root , or eight , and subtract from it half the number of roots , namely five , and there remain ...
Page 91
... multiplied by a so as to bring the equation into the form a2x2 + abx + ac = 0 ; then solving he found ax = - 1b ± √1 b2 — ac , and regarded the result in the1 form x = { b ± √ 4 b2 - ac a Whether the inter- mediate procedure was as we ...
... multiplied by a so as to bring the equation into the form a2x2 + abx + ac = 0 ; then solving he found ax = - 1b ± √1 b2 — ac , and regarded the result in the1 form x = { b ± √ 4 b2 - ac a Whether the inter- mediate procedure was as we ...
Page 93
... Multiply half the coeffi- cient of x into itself and we have 1296 : subtract the product of the coefficient of x2 and the absolute term , or 289. The remainder is 1007 , the square root of which is not * > 31. Add half the coefficient ...
... Multiply half the coeffi- cient of x into itself and we have 1296 : subtract the product of the coefficient of x2 and the absolute term , or 289. The remainder is 1007 , the square root of which is not * > 31. Add half the coefficient ...
Page 96
... multiplied by some square , and the other is subtracted from the product , the result is a square number ; another square also can be found , greater than the first taken square , which will have the same effect . " It is curious that ...
... multiplied by some square , and the other is subtracted from the product , the result is a square number ; another square also can be found , greater than the first taken square , which will have the same effect . " It is curious that ...
Page 100
... multiplying either equation or both by a square number , an operation which does not affect the problem , for a square multi- plied by a square is still a square . Thus if B = m2 n2 or an2 = 6m2 100 DIOPHANTOS OF ALEXANDRIA .
... multiplying either equation or both by a square number , an operation which does not affect the problem , for a square multi- plied by a square is still a square . Thus if B = m2 n2 or an2 = 6m2 100 DIOPHANTOS OF ALEXANDRIA .
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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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