Diophantus of Alexandria: A Study in the History of Greek AlgebraUniversity Press, 1910 - 387 páginas |
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Página 7
... coefficients ( μn óμomλnon dé ) , we must take like from like until we have one single expression equal to another . If there are on both sides , or on either side , any terms with negative coefficients ( ἐν ἐλλείψεσί τινα εἴδη ) , the ...
... coefficients ( μn óμomλnon dé ) , we must take like from like until we have one single expression equal to another . If there are on both sides , or on either side , any terms with negative coefficients ( ἐν ἐλλείψεσί τινα εἴδη ) , the ...
Página 33
... coefficient is expressed by putting the required Greek numeral immediately after it , thus soi a corresponds to IIx , s ' a to x and so on . Tannery discusses the question whether in the archetype ( a ) of the MSS . this duplication of ...
... coefficient is expressed by putting the required Greek numeral immediately after it , thus soi a corresponds to IIx , s ' a to x and so on . Tannery discusses the question whether in the archetype ( a ) of the MSS . this duplication of ...
Página 38
... coefficients of the different powers of the unknown , like that of the unknown itself , are expressed by the addition of the Greek letters denoting numerals , e.g. , 4K 5 cor- responds to 263 . Thus in Diophantus ' system of notation ...
... coefficients of the different powers of the unknown , like that of the unknown itself , are expressed by the addition of the Greek letters denoting numerals , e.g. , 4K 5 cor- responds to 263 . Thus in Diophantus ' system of notation ...
Página 39
... coefficient of s , would cause confusion . This fact makes it necessary to have some expression to distinguish the absolute term from the variable terms . For this purpose Diophantus uses the word μovádes , or units , and denotes them ...
... coefficient of s , would cause confusion . This fact makes it necessary to have some expression to distinguish the absolute term from the variable terms . For this purpose Diophantus uses the word μovádes , or units , and denotes them ...
Página 52
... coefficients etc. in the functions of s which express the numbers to be found , the unknown quantity which it is the object of the new subsidiary problem to find is also in its turn denoted by the same symbol s ; hence we often have in ...
... coefficients etc. in the functions of s which express the numbers to be found , the unknown quantity which it is the object of the new subsidiary problem to find is also in its turn denoted by the same symbol s ; hence we often have in ...
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.