224 c 0SMO3. 



eral mass of matheii.atical science. According to the mwst 

 recent works which have appeared in England, France, and 

 Germany* on the history of mathematics, we learn tliat " the 

 algebra of the Arabs originated from an Indian and a Greek 

 source, which long flowed independently of one another." The 

 Compendium of Algebra which the Arabian mathematician 

 Mohammed Ben-Musa (the Chorowazneir), framed by com 

 mand of the Calif Al-Mamnn, was not based on Diophantus, 

 but on Indian science, as has been shown by my lamented and 

 too-early deceased friend, the learned Friedrich Hosen ;t and 

 it would even appear that Indian astronomers had been called 

 to the brilliant court of the Abbassides as early as the close 

 of the eighth century, under Almansur. Diophantus was, ac 

 cording to Castri and Colebrooke, first translated into Arabic 

 by Abul-Wefa Buzjani, toward the close of the tenth century. 

 The process of establishing a conclusion by a progressive ad 

 vance from one proposition to another, which seems to have 

 been unknown to the ancient Indian algebraists, was acquired 

 by the Arabs from the Alexandrian school. This noble in- 

 heritance, enriched by their additions, passed in the twelfth 

 century, through Johannes Hispalensis and Gerhard of Cre- 

 mona, into the European literature of the Middle Ages.$^ " In 

 the algebraic works of the Indians, we find the general solu- 

 tion of indeterminate equations of the first degree, and a far 

 more elaborate mode of treating those of the second, than has 

 been transmitted to us in the writings of the Alexandrian phi- 

 losophers ; there is, therefore, no doubt, that if the works of the 

 Indians had reached us two hundred years earlier, and were 

 not now first made known to Europeans, they might have 

 acted very beneficially in favoring the development of modem 

 analysis." 



The same channels and the same relations which led the 



* Colebrooke, Algebra with Arithmetic and Mensuration, from the 

 Sanscrit of Bralimagapta and Bhascara, Lond., 1817. Chasles, Apcr^tt 

 Historique sur VOrigine et le Developpcment des Methodes en Giom6trie, 

 1837, p. 416-502 ; Nesselmann, Versuch einer krilisclien Geschichte der 

 Algebra, th. i., s. 30-61, 273-276, 302-306. 



t Algebra of Moliammed Ben-Musa, edited and translated by F. Rosen, 

 1831, p. viii., 72, and 196-199. The mathematical knowledge of India 

 was extended to China about the year 720 ; but this was at a period 

 when many Arabians were already settled in Canton and other Chi 

 ne?e cities. Reinaud, Relation des Voyages fails par les Arabes dam 

 VInde et a la Chine, t. i., p. cix. ;.t. ii., p. 36. 



X Chasles, Hlstoire de VAlgebrc, in the Comptts Rendus. t. xiii., 184' 

 p. 497-.'i24. 601-620. Compare, also, L'bri, in the same volume, f 

 5o9-0C3. 



