Diophantus of Alexandria: A Study in the History of Greek AlgebraUniversity Press, 1910 - 387 páginas |
Dentro del libro
Resultados 1-5 de 11
Página 1
... καὶ δὴ καὶ τοῦ παρόντος θεωρή paros , " Your soul to perdition , Diophantus , for the difficulty of your problems in general and of this one in particular " ) ; John of Jerusalem ( 10th c . ) alone ( Vita Ioannis Damas- ceni XI . Dioph ...
... καὶ δὴ καὶ τοῦ παρόντος θεωρή paros , " Your soul to perdition , Diophantus , for the difficulty of your problems in general and of this one in particular " ) ; John of Jerusalem ( 10th c . ) alone ( Vita Ioannis Damas- ceni XI . Dioph ...
Página 2
... καὶ Διόφαντός φησι · τῆς γὰρ μονάδος ἀμεταθέτου οὔσης καὶ ἑστώσης πάντοτε , τὸ πολλαπλασιαζόμενον εἶδος ἐπ ̓ αὐτὴν αὐτὸ τὸ εἶδος ἔσται κ.τ.έ. 3 * Dioph . II . p . 38-9 : περὶ δὲ τῆς αἰγυπτιακῆς μεθόδου ταύτης Διόφαντος μὲν διέλαβεν ...
... καὶ Διόφαντός φησι · τῆς γὰρ μονάδος ἀμεταθέτου οὔσης καὶ ἑστώσης πάντοτε , τὸ πολλαπλασιαζόμενον εἶδος ἐπ ̓ αὐτὴν αὐτὸ τὸ εἶδος ἔσται κ.τ.έ. 3 * Dioph . II . p . 38-9 : περὶ δὲ τῆς αἰγυπτιακῆς μεθόδου ταύτης Διόφαντος μὲν διέλαβεν ...
Página 4
... καὶ πρὸς αὐτὰ καὶ πρὸς ἄλληλα πῶς ἔχει πλήθους ἐπισκοπεῖ τὸ περιττὸν καὶ τὸ ἄρτιον ἡ λογιστική . Proclus , Comment . on Euclid 1. , p . 39 , 14-40 , 7 . ♢ Cf. Plato , Laws 819 B , C , on the advantage of combining amusement with ...
... καὶ πρὸς αὐτὰ καὶ πρὸς ἄλληλα πῶς ἔχει πλήθους ἐπισκοπεῖ τὸ περιττὸν καὶ τὸ ἄρτιον ἡ λογιστική . Proclus , Comment . on Euclid 1. , p . 39 , 14-40 , 7 . ♢ Cf. Plato , Laws 819 B , C , on the advantage of combining amusement with ...
Página 13
... καὶ Ἰνδικῆς ψηφιφορίας ( i.e. ψηφοφορίας ) , written in 1252 and raided about half a century later by Maximus Planudes . The second fragment ' is the work edited by C. Henry in 1879 as Opusculum de multiplicatione et divisione ...
... καὶ Ἰνδικῆς ψηφιφορίας ( i.e. ψηφοφορίας ) , written in 1252 and raided about half a century later by Maximus Planudes . The second fragment ' is the work edited by C. Henry in 1879 as Opusculum de multiplicatione et divisione ...
Página 47
... καὶ μυριάδων πρώτων ηψμζ καὶ Μ δφξ , and the fraction 131299224/1629586560 would be written deurépa μvpiàs ā πpúraι ( μυριάδες ) γρκθ Μ θσκδ μορίου δευτέρων μυριάδων 15 πρώτων ( μυριάδων ) βλνη Μ εφξι But there is another kind of ...
... καὶ μυριάδων πρώτων ηψμζ καὶ Μ δφξ , and the fraction 131299224/1629586560 would be written deurépa μvpiàs ā πpúraι ( μυριάδες ) γρκθ Μ θσκδ μορίου δευτέρων μυριάδων 15 πρώτων ( μυριάδων ) βλνη Μ εφξι But there is another kind of ...
Otras ediciones - Ver todo
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
absolute term added Algebra Archimedes Arithmetica Assume auxiliary triangle Ax² Bachet Books coefficient commentary cube difference Dioph Diophantus divide double-equation equal Euler expression factors find a right-angled find three numbers find three squares find two numbers four numbers fraction Frénicle given number given ratio gives a square Greek hypotenuse Iamblichus indeterminate equations integral Lagrange Lemma letter Maximus Planudes method minus multiplied Nesselmann obtain Oeuvres de Fermat polygonal number Porisms prime number problem proposition quadratic rational numbers required numbers required squares result right-angled triangle satisfy the conditions solution solved square number substitute subtract Suppose Tannery theorem third number triple-equation unknown quantity whence whole numbers Xylander καὶ
Pasajes populares
Página 75 - 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 267 - Now every number is either a square or the sum, of two, three or four squares...
Página 145 - 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 20 - 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 293 - 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 158 - To find three numbers such that their sum is a square and the sum of any pair is also a square.
Página 187 - 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 376 - To find three numbers such that the product of any two added to the sum of those two gives a square (III.