Diophantus of Alexandria: A Study in the History of Greek AlgebraUniversity Press, 1910 - 387 páginas |
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Página 50
... 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 nine . " 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 nine . " Here we observe that not even are ...
Página 87
... square , = a square . a2 + ba ( m2 - a ) ( m2 - a ) We have therefore to solve the equation abm2 + a ( aß - ab ) ... required to make a function of x , of a degree higher than the second , a square ; the second comprises those in ...
... square , = a square . a2 + ba ( m2 - a ) ( m2 - a ) We have therefore to solve the equation abm2 + a ( aß - ab ) ... required to make a function of x , of a degree higher than the second , a square ; the second comprises those in ...
Página 94
... Required to find a value of x such that some power of it , x , shall lie between two given numbers . Let the given ... square between 1 and 2. He multiplies both by a square , 64 ; this gives 80 and 128 , and 100 is clearly a ...
... Required to find a value of x such that some power of it , x , shall lie between two given numbers . Let the given ... square between 1 and 2. He multiplies both by a square , 64 ; this gives 80 and 128 , and 100 is clearly a ...
Página 95
... requires that -60 shall be a square . Assume then that and we have x2 - 60 = ( x - m ) , x = ( m3 +60 ) / 2m ... squares , and in the second three , are required . In cases like this the principles cannot be so well indicated ...
... requires that -60 shall be a square . Assume then that and we have x2 - 60 = ( x - m ) , x = ( m3 +60 ) / 2m ... squares , and in the second three , are required . In cases like this the principles cannot be so well indicated ...
Página 96
... squares each of which > 6 ( v . 9 ) . Take half of 13 , or 61 , and find what small fraction 1 / x added to it will ... required squares , where therefore x is not exactly but near it . Thus ( 3-9x ) + ( 2 + 11x ) = 13 , and ...
... squares each of which > 6 ( v . 9 ) . Take half of 13 , or 61 , and find what small fraction 1 / x added to it will ... required squares , where therefore x is not exactly but near it . Thus ( 3-9x ) + ( 2 + 11x ) = 13 , and ...
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
a²-b² absolute term added Algebra Archimedes arithm Arithmetica Assume assumption auxiliary triangle Ax² Bachet Books coefficient commentary cube difference Dioph Diophantus double-equation equal Euler expression factors find a right-angled find three numbers find three squares find two numbers form 4n fraction Frénicle given number given ratio gives a square Greek hypotenuse Iamblichus indeterminate equations infinite number integral Lagrange Lemma letter Maximus Planudes method minus multiplied Nesselmann obtain Oeuvres de Fermat pair polygonal number Porisms prime number problem proposition quadratic rational numbers required numbers required squares required triangle result right-angled triangle satisfy the conditions solution square number substitute subtract Suppose Tannery Theon of Smyrna theorem third number triple-equation unknown quantity whence whole numbers Xylander ἀριθμός καὶ