Serrurier Marseille E-books > Ancient > Download e-book for iPad: Abu Kamil Algèbre et analyse diophantienne. Édition, by Roshdi Rashed

Download e-book for iPad: Abu Kamil Algèbre et analyse diophantienne. Édition, by Roshdi Rashed

By Roshdi Rashed

ISBN-10: 3110295679

ISBN-13: 9783110295672

The mathematical works of Ab? K?mil (floruit circa 880) have been produced generations after the works of Al-Khwarizm?, the founding father of algebra. They unfolded fields of analysis that proved fertile up till the 17th century, and have been quickly to turn into either a reference and a version. Their impression used to be decisive at the improvement of algebra in Arabic a minimum of in Latin and Hebrew. there'll be present in the current book the 1st conscientiously severe version of Ab? K?mil s works, in addition to the 1st ever translation right into a glossy language. textual content and translation are preceded through an exhaustive remark, without delay mathematical and historical."

Show description

Read Online or Download Abu Kamil Algèbre et analyse diophantienne. Édition, traduction et commentaire PDF

Best ancient books

New PDF release: Apollo (Gods and Heroes of the Ancient World)

Put up yr be aware: First released in 2000
------------------------

Fritz Graf right here provides a survey of a god as soon as regarded as the main strong of gods, and in a position to nice wrath should still he be crossed: Apollo the sunlight god.

From his first attestations in Homer, throughout the complicated query of pre-Homeric Apollo, to the competition among Apollo and Dionysos in 19th and twentieth-century pondering, Graf examines Greek faith and delusion to supply an entire account of Apollo within the historical world.

For scholars of Greek faith and tradition, of fantasy and legend, and within the fields of artwork and literature, Apollo will supply an informative and enlightening advent to this strong determine from the previous.

Get The Story of the Roman Amphitheatre PDF

The Roman amphitheatre was once a website either one of bloody wrestle and marvellous spectacle, symbolic of the could of Empire; to appreciate the significance of the amphitheatre is to appreciate a key point within the social and political lifetime of the Roman ruling sessions. Generously illustrated with 141 plans and images, the tale of the Roman Amphitheatre bargains a entire photo of the origins, improvement, and eventual decline of the commonest and evocative of Roman monuments.

Get The Reign of Adad-nīrārī III: An Historical and Ideological PDF

Within the Reign of Adad-nīrārī III, Luis Siddall examines the facts and edits new inscriptions from the king’s reign to enquire the chronology, campaigns, imperial management and royal ideology of the interval. whereas historians have ordinarily considered this era as one in every of turmoil, imperial recession, political weak spot and decentralisation, Siddall indicates that Adad-nīrārī’s reign marked a interval of imperial balance, mainly via alterations to the management.

Additional info for Abu Kamil Algèbre et analyse diophantienne. Édition, traduction et commentaire

Example text

Alors V5ÔÔÔÔ - 200-f-x' = lOx jc = 5±V 225-V 5Ô æO . Abü Kâmil pouvait sûrement vérifier cette égalité au moyen de la théorie du livre X des Éléments d’Euclide. Autre méthode ; On pose >' = 10-X Si X est l’une des deux racines, (10 - x) est l’autre. yx = 10 - X Autre méthode : On pose u = —- et v = —- — X 10-X + V= V5 ^ 10 - X = V5- En multipliant la seconde équation par (10 - x), puis en y remplaçant yx par sa valeur (10 - x), on obtient [mv = 1 fyx = 1 0 - X Alors V5m- [x + 10y = (1 0 -x ) + V M - x 4 5 =1 La deuxième équation donne alors une valeur de y linéaire en x.

Mais AH = EH = OM. D’autre part, on a MI = NI, d’où MI • OM = KD ■ND, d’où Algorithme pour déterminer le carré de l ’inconnue : aire {MS) + aire {EK) = aire (7D) + aire {EK) = aire {ED) - c. b -> b ^ -^b ^c , Il est aussi évident que HB - EB = EH = lE - MI - ME, d’où b ^ y ^ 7 , b ^ Ÿ ,2 ,2 — + b^c-^ Jb c + \ ^J —^ 2 J + b^c. + C+ 2 \ ^J Dans le cas général, pour a ^ 1, on divise par a pour normaliser l’équation. aire {HM) = HE^ ~ I 2 ' On a alors aire {HK) = aire {ED) + aire {HM) = c + 1- 1 , Démonstration de l ’algorithme : Démonstration 1 : Soit l’aire carrée (ABCD) = et l’aire rectangulaire {AN) = bx {et Fig.

PROBLÈMES DIVERS Alors 10 = 5x et X = 2 ; - 7 - On considère le système (type ax = b). flO = X + y | y ^ - x ^ = 8 0 - 4 - On considère le système JlO = X + y l9y = x^ Alors 100 - 20x = 80, d’où x = 1. Abu Kâmil calcule aussi l’équation en y : 2 0 y - 100 = 80. 58 Chapitre II Le calcul algébrique et ses applications 59 Il indique enfin une autre méthode X X-5-U Il ajoute que cette méthode n’est pas connue des algébristes et qu’elle est particulièrement utile pour résoudre les équations quadratiques trinômes (elle permet de les réduire à des équations binômes par élimination du terme de degré 1 en x).

Download PDF sample

Abu Kamil Algèbre et analyse diophantienne. Édition, traduction et commentaire by Roshdi Rashed


by Edward
4.5

Rated 4.14 of 5 – based on 41 votes