Vol, IV, No. 3.] Notes on Indian Mathematics. 135 
LS 
translate into pent dees mathematical language ; nevertheless 
its general aim is obvious. It is a rule for ns solution of inde- 
ba or equations of some such form as (Ag+ Bay; 
not our business here to give an pent of the general 
‘ean vt indeterminate equations, but rather to attempt to 
trace their history up to the time of Aryabhata. Even a cursory 
of the method under consideration ; and a closer investigation estab- 
lishes this conclusion beyond all doubt. At one time, indeed, i 
was thought that this special treatment of indeterminate equa- 
tions was of Indian origin. Colebrooke, Woepcke, Chasles and 
Rodet seemed to think so; and the conclusions of such eminent 
scholars cannot be altogether ignored. But Colebrooke, Woepcke 
and Chasles attributed the discovery to Brahmagupta and in this 
Rodet was misled by the later commentators. Now vy 
position to give at least a more correct version of this partion, of 
the history of mathematics, Still there are difficulties in the way, 
and it must not be expected that the conclusions here set forth 
are quite fina 
diligent search through Hindu works has failed to bring to 
light any of those orderly processes by which such a complicated 
theorem as this is bound to be prece but we do find the 
cect preliminary notions apaniualy set forth by Greek 
writer 
The fundamental process involved in the method given by 
Aryabhata is contained in the first and second propositions of the 
seventh book, and the second and third of the tenth book of Euclid. 
The results of these propositions translated into Algebraic nota- 
tion! give us the following indeterminate equations : AL — M=1 
d AL’—BM’ 
an =g. The process by which the former of these 
is arrived at may be exhibited thus :— 
B) A (a, 
a,B a 1 i on ae 
r, ) B (ag ks Ba, t at. Gek: OF 
Ag") 
tT) t, (az 
At 
a 

bstitute for 
1 The question has often been asked, had Bucl lid any su 
Algebra ? tf not, his skill, as shown particularly in the tenth book, was 
