Page:Aryabhatiya of Aryabhata, English translation.djvu/32

2 present the evidence is too scanty to allow us to specify the sources from which Aryabhata drew.

The stanza has been translated by Fleet. As pointed out first by Bhau Daji, a passage of Brahmagupta (XII, 43), janaty ekam api yato naryabhato ganitakalagolanam, seems to refer to the Ganitapada, the Kalakriyapada, and the Golapada of our Aryabhatiya (see also Bibhutibhusan Datta). Since Brahmagupta (XI, 8) names the Dasagitika and the Aryastasata (108 stanzas) as works of Aryabhata, and since the three words of XI, 43 refer in order to the last three sections of the Aryabhatiya (which contain exactly 108 stanzas), their occurrence there in this order seems to be due to more than mere coincidence. As Fleet remarks, Aryabhata here claims specifically as his work only three chapters. But Brahmagupta (628 A.D.) actually quotes at least three passages of our Dasagitika and ascribes it to Aryabhata. There is no good reason for refusing to accept it as part of Aryabhata's treatise.

B. Beginning with ka the varga letters (are to be used) in the varga places, and the avarga letters (are to be used) in the avarga places. Ya is equal to the sum of na and ma. The nine vowels (are to be used) in two nines of places varga and avarga. Navantyavarge va.

Aryabhata's system of expressing numbers by means of letters has been discussed by Whish, by