116 Journal of the Asiatic Society of Bengal. {| March, 1908. 
proceeds at once to involution, evolution (3-5), areas and volumes 
(6-9). Next comes an astronomical-mathematical section in 
which he deals with the circle (10-12), shadow problems (13-16), 
eclipse problems (17-18). Then comes a set of propositions deal- 
ing with progressions (19-22), which are followed by some algebraic 
ae a (23-24). ee remaining rules (25-23) may be classed 
as practical application 
am inclined to think that Aryabhata intended his mathe- 
matical work to be supplementary to what was ordinarily known 
to Hindu scholars. This hypothesis eliminates many difficulties 
and, in page it explains why Aryabhata made the rather 
incongruous selection of mathematical oki given in the ues: 
of reer rules deal with the elements of the subjec 
evidently takes for granted that his readers are cal with 
the easier problems of mathematics and only gives certain more 
difficult problems which were, probably, not found in other Hindu 
ween in his time. 
‘yabhata’s selection must have been determined by the works 
that were available. What those works were it is now difficult to 
say, but it is pretty certain that their original source was the later 
Alexandrian school. The content and form of the Ganita remind 
one of the works of Heron and of Sextus Julius Africanus, Parts 
of it can be traced indirectly to Ptolemy, to Diophantus, to Theon 
and others, and no portion of it deals with matter that had not 
_ been pretty fully dealt with by the Alexandrians. While there is 
no evidence which contradicts an ultimate Egyptian! origin, there 
are many points in detail which support this hypothesis. 
Aryabhata’s work is of interest, principally because it appears 
to form a connecting link with Alexandria. Asa mathematical 
treatise it ranks neither with the works of the Greeks nor with those 
of the Muhammadans of the middle ages. In India itself Arvabhata 
became renowned as an astronomer rather than as a mathemati- 
cian, and the Ganita is seldom directly referred to by Hindu 
writers. Brahmagupta’s work contains very nearly all the matter 
given in the Ganita, but, as it is much fuller, we must conclude that 
it was not a mere copy. ‘The evidence all points to a common 
origin of the two works, and the identification of this common 
origin would not be difficult if we had it before us. As the case 
at present stands, we cannot come to any very definite conclu- 
sion, Possibly Pulisa was the connecting lin 
A translation of the Ganita together with a commentary is 
given below. 
Tue Ganita. 
1. Aryabhata having rendered homage to Brahma, the Earth, 
the Moon, Mercury, the Sun, Mars, Jupiter, Saturn and the constel- 
lations sets forth his knowledge which was well appreciated in the city 
of Kusumapura.* 

1 Damascius (circ A.D. 500) tells us how ‘‘ There came Bra 
to plectnds to Severus.” (Quoted by T. Kennedy, Journ, Roy. tabi oo ss 
19%, p. 95 
2 The cecil of the text is printed in italics. 
