Diophantus of Alexandria: A Study in the History of Greek Algebra |
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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
accordingly added Algebra Arithmetica Assume assumption Bachet becomes beginning Books coefficient common condition containing corresponding cube difference Dioph Diophantus divide double double-equation equal equation Euler expression fact factors Fermat find a right-angled find three numbers four fourth fraction given number given ratio gives a square greater Greek half Hence hypotenuse integral least Lemma less letter means method middle minus multiplied namely necessary negative observes obtain original pair particular perpendicular polygonal Porisms positive possible powers prime number problem proof propositions proved ratio remains respectively result right-angled triangle root rule satisfied shows sides solution solved square number substitute subtract Suppose symbol taken Tannery theorem third three squares unknown whence whole
Pasajes populares
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.
Información bibliográfica
| Título | Diophantus of Alexandria: A Study in the History of Greek Algebra Nineteenth Century Collections Online (NCCO): Science, Technology, and Medicine: 1780-1925 |
| Autor | Sir Thomas Little Heath |
| Editor | Leonhard Euler |
| Edición | 2 |
| Editor | University Press, 1910 |
| Procedencia del original | Universidad de Harvard |
| Digitalizado | 30 Sep 2005 |
| N.º de páginas | 387 páginas |
| Exportar cita | BiBTeX EndNote RefMan |