Diophantus of Alexandria: A Study in the History of Greek Algebra

University Press, 1910 - 387 páginas

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Página 65 - But the squares on straight lines incommensurable in length have not to one another the ratio which a square number has to a square number...
Página 257 - Now every number is either a square or the sum, of two, three or four squares...
Página 135 - On the other hand it is impossible to separate a cube into two cubes, or a biquadrate into two biquadrates, or generally any power except a square into two powers with the tame exponent. I have discovered a truly marvellous proof of this, which however the margin is not large enough to contain.
Página 10 - To Regiomontanus belongs the credit of being the first to call attention to the work of Diophantus as being extant in Greek. We find two notices by him during his sojourn in Italy, whither he journeyed after the death of his teacher Georg von Peurbach, which took place on the 8th April, 1461. In connexion with lectures on the astronomy of Alfraganus which he gave at Padua he delivered an Oratio introductoria in omnes scientias mat/tematicas*.
Página 283 - The area of a right-angled triangle the sides of which are rational numbers cannot be a square number. This proposition, which is my own discovery, I have at length succeeded in proving, though not without much labour and hard thinking. I give the proof here, as this method will enable extraordinary developments to be made in the theory of numbers.
Página 148 - To find three numbers such that their sum is a square and the sum of any pair is also a square.
Página 177 - Therefore y = ^-, and the numbers are ^, ^. 64 64 30. To find two numbers such that their product + their sum gives a square. Now >«* + «J ± 2w
Página 366 - To find three numbers such that the product of any two added to the sum of those two gives a square (III.

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