Diophantos of Alexandria: A Study in the History of Greek Algebra |
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Page 35
... square and any other number to be again a square number by finding a suitable value of the first square ; these methods , argues Bombelli , of Diophantos must have been given for the reason that the author intended to use them for the ...
... square and any other number to be again a square number by finding a suitable value of the first square ; these methods , argues Bombelli , of Diophantos must have been given for the reason that the author intended to use them for the ...
Page 67
... square of the unknown . is called by Diophantos dúvaus and denoted by the abbrevia- tion ' . Now the word Sivapis ( " power " ) is commonly used in Greek to express a square number . The first occurrence of the word in its technical ...
... square of the unknown . is called by Diophantos dúvaus and denoted by the abbrevia- tion ' . Now the word Sivapis ( " power " ) is commonly used in Greek to express a square number . The first occurrence of the word in its technical ...
Page 68
... square " , there is only one word for a third power , namely Kúßos . It is important , however , to observe that the abbreviations κι , δδ ' , δκύ , και are , like δύναμις and δ ' , only used to denote powers of the unknown . It is ...
... square " , there is only one word for a third power , namely Kúßos . It is important , however , to observe that the abbreviations κι , δδ ' , δκύ , και are , like δύναμις and δ ' , only used to denote powers of the unknown . It is ...
Page 79
... square root , or eight , and subtract from it half the number of roots , namely five , and there remain three : this is the root of the square which was required and the square itself is nine1 . " Here we observe that not even are ...
... square root , or eight , and subtract from it half the number of roots , namely five , and there remain three : this is the root of the square which was required and the square itself is nine1 . " Here we observe that not even are ...
Page 80
... Square . Thus 16 minus One Square must be equal to a square . I form the square from any number of N's minus as many U's as there are in the side of 16 U's . Suppose this to be 2 N's minus 4 U's . Thus the square itself will be 4 ...
... Square . Thus 16 minus One Square must be equal to a square . I form the square from any number of N's minus as many U's as there are in the side of 16 U's . Suppose this to be 2 N's minus 4 U's . Thus the square itself will be 4 ...
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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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