Diophantus of Alexandria: A Study in the History of Greek AlgebraUniversity Press, 1910 - 387 páginas |
Dentro del libro
Resultados 1-5 de 96
Página 3
... equal to half the age at which his father died . In that case 8x + 1'2x + x + 3 + 1 ( x − 4 ) + 4 = x , or 3x = 196 and x = 65j . This would substitute 108 for 14 , 161 for 21 , 251 for 33 , 301 for 43 , 611 for 80 , and 65 for 84 ...
... equal to half the age at which his father died . In that case 8x + 1'2x + x + 3 + 1 ( x − 4 ) + 4 = x , or 3x = 196 and x = 65j . This would substitute 108 for 14 , 161 for 21 , 251 for 33 , 301 for 43 , 611 for 80 , and 65 for 84 ...
Página 7
... equal to another . If there are on both sides , or on either side , any terms with negative coefficients ( ἐν ἐλλείψεσί τινα είδη ) , the defects must be added on both sides until the terms on both sides have none but positive ...
... equal to another . If there are on both sides , or on either side , any terms with negative coefficients ( ἐν ἐλλείψεσί τινα είδη ) , the defects must be added on both sides until the terms on both sides have none but positive ...
Página 8
... equal to one term , such an equation is solved . " That is to say , reduce the quadratic , if possible , to one of the forms ax3- bx , ax1 - c , or bx = c ; I will show later how to solve the equation when three terms are left of which ...
... equal to one term , such an equation is solved . " That is to say , reduce the quadratic , if possible , to one of the forms ax3- bx , ax1 - c , or bx = c ; I will show later how to solve the equation when three terms are left of which ...
Página 47
... equal , connecting the two sides of an equation , the sign in the archetype seems to have been ; but copyists intro- 1 Hultsch , loc . cit . duced a sign which was sometimes confused with the sign NOTATION AND DEFINITIONS OF DIOPHANTUS 47.
... equal , connecting the two sides of an equation , the sign in the archetype seems to have been ; but copyists intro- 1 Hultsch , loc . cit . duced a sign which was sometimes confused with the sign NOTATION AND DEFINITIONS OF DIOPHANTUS 47.
Página 50
... equal to nine and thirty dirhems , that is , if you add ten roots to one square , the sum is equal to nine and thirty . The solution is as follows . Take half the number of roots , that is in this case five ; then multiply this by ...
... equal to nine and thirty dirhems , that is , if you add ten roots to one square , the sum is equal to nine and thirty . The solution is as follows . Take half the number of roots , that is in this case five ; then multiply this by ...
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 arithm Assume auxiliary triangle 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 four numbers fraction Frénicle given number given ratio gives a square Greek hypotenuse Iamblichus indeterminate 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 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 καὶ