490 



Journal of the Asiatic Society of BengaL [Ju-ly, 1907. 



in the time of Firdausi the two words were used with totally 

 different meanings — with meanings between which there was no 

 alliance. M. Woepcte quotes another instance of the use of the 

 word ^^^<viA from Ibn Sina, the great philosopher (b. 980 A.D,). 

 This "example is interesting from several points of view, but 

 primarily because it helps to disprove the conclusions of the 

 Indianists. Tn a rule Ibn Sina gives relating to the properties of 



square numbers the phrase ^^ *^^\ i^j^^ u* occurs and in a 

 corresponding rule for cubes the phrase ^s^^H^t wL-»»J t Now, if 



either of these rules could be traced to an Indian source one might 

 be pardoned for translating <*»iywk by the term " Indian " ; but 

 there is not the remotest reference to any such rules or any- 

 thing akin to them in any of the known writings of the Hindu 

 mathematicians prior to Avicenna. Further, M. Woepcke says, 

 *' Si nous considerons que ce mot ne pent ici en aucnne fa9on 

 fiignifier ' geometrique,' sens qu'il a ordinairement, et si nous 

 rappelons que le meme mot hindact designe aussi chez les 

 Arabes, d'apre§ M. Taylor, * I'echelle decimale de I'arithmetique/ 

 nous devons etre portes a admettre que le sens primitif du mot 



^j^^3Jk qui se prononce Mndigah et handagah est * methode 



indienne ' ou * art indien ' ; et que, si ce mot designe en arabe 

 ordinairement, la geometrie, c'est parce que les premieres notions 

 de cette science arrivees aux Arabes sont venues de I'lnde*' 

 (p. 505). 



M. Woepcke's conclusion depends upon the following (sup- 

 posed) facts : (i) the word ^jmAi/k cannot by any possible means 



imply geometry in the passage referred to ; (ii) a statement by 

 Mr. Taylor ; (iii) the Arabs owe their knowledge of geometry to 

 the Hindus. It is only necessary to refer to the firat of these 

 points here. Of all the problems relating to numbers this very 



one is most likely 

 of geometric origin, 

 as a glance at the 

 accompanying 



figure will show. 

 AB is any square 

 of which the sides 



divided into 



parts. 

 larger 

 which 

 AB the 



are 



nine equal 

 Of the 



squares 



surround 



dotted parts show 

 the remainders on 

 division by nine 

 and Avicenna's 

 proposition is at 

 once seen to be 



Fig. L 



true, 



VIZ, 



that 



