596 COSMOS. 



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 mathema- 

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

 command of the Caliph Al-Mamun, was not based on Dio- 

 phantus, but on Indian science, as has been shown by my 

 lamented and too- early deceased friend, the learned Friedrich 

 Rosen ;* and it would even appear that Indian astronomers 

 had been called to the brilliant court of the Abassides, as 

 early as the close of the eighth century under Almansor. 

 Diophantus was, according to Castri and Colebrooke, first 

 translated into Arabic by Abul-Wefa Buzjani, towards the 

 close of the tenth century. The process of establishing a 

 conclusion by a progressive advance 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 inheritance, enriched by their 

 additions, passed in the twelfth century, through Johannes 

 Hispalensis and Gerhard of Cremona, into the European 

 literature of the middle ages.f " In the algebraic works of 

 the Indians, we find the general solution 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 philosophers; 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 bene- 

 ficially in favouring the development of modern analysis." 

 The same channels and the same relations which led the 



Sanscrit of Brahmegupta and Bhascara, Lond. 1817. Chasles, Aper$u 

 liistorique sur Vorigine et le developpement des methodes en Geo- 

 metrie, 1837, pp. 416-502; Kesselmann, Versuch einer Jcritischen 

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



* Algebra of Mohammed Ben Musa, edited and translated by F. 

 Kosen, 1831, pp. 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 Chinese 

 cities. Eeinaud, Relation des Voyages fails par lesArabes dans I'lnde 

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



t Chasles, Histoire de I'Algebre, in the Comptes rendus,\>, xiii. 1841, 

 pp. 497-524, 601-626; compare also Libri, in the same volume, 

 pp, 559-563. 



