we 


Vol. IV, No. 3.] Notes on Indian Mathematics. 113 
[N.S.] 
astronomers; but there is no evidence! for Aryabhata having 
been acqu uainted with those views; nor, indeed, is this generally 
credit for ‘ originality,’ i schouete sense that he had the mat and 
refer to it only to reject it; and Aryabhata’s originality in this 
or aie. hence stands out all the brighter.” (Indian Thought, 
1907, 215.) 
Bhau Daji reproduces nearly all the passages in the Arya- 
bhata Satra that have been controverted by Brahmagnupta. These 
are all astronomical as-are, strangely enough, all those quoted by 
Albiruni. The first purely mathematical niga! we find is by 
Chaturvéda-Prithidaga Swami who, in his comment n Brahma- 
gupta, says: ‘‘ What is leet by us ‘ diameter son arrow,’ 
is by Aryabhata denominated the greater arrow.” He then quotes 
direct from the Ganita (see below § 17), and this is possibly the 
earliest direct reference to it known, According to Colebrooke 
Chaturvéda was anterior to Bhaskara, being more than once quoted 
by him. Albiruni (I., 158) also mentions a Prithidaka-svamin 
repeatedly adverts to preceding writers and refers to Him in 
general terms, where his commentators understand him to allude 
to Aryabhatta, to Brahmagupta, ete. 
II. 
That the Aryabhata we are dealing with was born about 476 
A.D. is now generally accepted as a fact (Journ. Roy. Asiatic yee 2 
1864, 392; Kern, Brhat Sanhita, 57 ; Journ. Asiatique, 1878) : 
still there is an element of doubt about it, and the whole runes is 
a by the question of iden iMeition: There were at least 
two® astronomers of the name of Aryabhata, prior to Albiruni, who 
clearly distinguishes between them. e younger of these he 
always designates as Aryabhata of Kusumapura (India, I., 176 ; 


l Plenty of eae indirect sae it may be, is given belo 
® The abe of the Maha Aryasiddhanta also calls himself ‘Arrabbata 
but according to Kern (irhat Sahita, p. 60) this was only a nomme de guerr 
