11. Ancient Hindu Spherical Astronomy. 
By G. R. Kaye. 
1. The following notes are the result of an ais to 
summarise, with the aid of modern mathematical formulae, the 
fundamental sib ge of the classical Sanskrit astronomical 
texts. The results achieved, even though they may not be 
perfectly polapliae: are, it is thought, worthy of publication. 
exts dealt with are the Aryabhatiya (4.D. 498), the 
(A.D. 628), and the later Surya Siddhanta (circa a.p. 1000). 
The period covered, it will be noticed, corresponds pretty 
closely with the period that was characterised by a remarkable 
rennaissance of literature, art and science in India; and the 
following paragraphs indicate in a somewhat forcible manner, 
but, of course, only in part, the scope of intellectual activity 
in India in that early time. This summary may, indeed, be 
looked upon as an aid to the study of a particular intellectual 
phase of that period; and this ancillary function has largely 
determined the form of presentation of the material. 
Spherical Trigonometry. 
though no formal spherical trigonometry is exhibited 
Hindu as re obvi - 
triangles. This statement, however, requires some qualifica- 
tion. The Hindu school of mathematicians preferred to dea 
cient astronomers were chiefly interested in results it is pos- 
sible, if we assume that they obtained these results from 
outside sources and were not interested in the mathematical 
principles involved, to conceive that they were not acquainted 
with those principles ; but the assumption is rather a strain, as 
there are too rege formulae based cur the spherical triangle 
e 
indications which point to some lack of a knowledge of the 
* See also A. v. BRaUNMUBL Vorlesungen iiber Geschichte der Poiseno- 
metrie, p. 41. 
