224 COSMOS. 



eral mass of mathematical science. According to the most 

 recent works which have appeared in England, France, and 

 Germany* on the history of mathematics, we learn that " 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-Mamun, was not based on Diophantus, 

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

 too-early deceased friend, the learned Friedrich Rosen ;f 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 unknoAvn 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, arid were 

 not now first made known to Europeans, they might have 

 acted very beneficially in favoring the development of modern 

 analysis." 



The same channels and the same relations which led the 



* Colebrooke, Algebra with Arithmetic and Mensuration, from the 

 Sanscrit of Brahmagupta and Bhascara, Load., 1817. Chasles, Apercu 

 Hisl&rique sitr V Origins et le D&veloppement des Methodes en Gtometrie, 

 1837, p. 416-502 ; Nesselmann, Ver&ich einer krilischen Geschichte der 

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



t Algebra of Mohammed 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 

 nese cities. Reiuaud, Relation des Voyages faifs par les Arabet dunt 

 I'Inde et a la Chine, t. i., p. cix. ; t. ii., p. 36. 



J Chasles, Histoire de T Algebre, in the Comptes Rendus, t. xiii., 1841, 

 p. 497-524, 601-626. Compare, also, Libri, in the same volume, p. 

 559-5R3. 



