161 
on the subject of arithmetic (Lilavati), algebra (Vija 
Ganita), geometry, and mensuration, by the astronomers 
Bramagupta, Bhascara, and Aryabhatta. " The Lilavati 
treats of arithmetic, and contains not only the common rules 
of that science, — there reckoned, eight in number, — but the 
application of these rules to various questions on interest, 
barter, mixtures, combinations, permutations, the science of 
progressions, indeterminate problems, and, lastly, of the 
mensuration of surfaces and solids." " The rules are 
found to be exact, and nearly as simple as in the present 
state of analytical investigation. The numeral results are 
readily deduced ; and if they be compared with the earliest 
specimens of Greek calculation, the advantages of the 
decimal notation are placed in a stinking light. 11 (Wallace.) 
" It appears from the Hindoo treatises on algebra, that 
they understood well the arithmetic of surd roots ; that 
they knew the general resolution of equations of the second 
degree, and had touched on those of higher denomination, 
resolving them in the simplest cases ; that they had 
attained a general solution of indeterminate problems of 
the first degree, and a method of deriving a multitude of 
answers to problems in the second degree, when one solution 
was discovered by trials. This is as near an approach to a 
general solution, as was made, until the time of Lagrange. 
The Hindoos had also attempted equations of higher 
orders : they not only applied algebra both to astronomy 
and geometry, but conversely applied geometry to the de- 
monstration of algebraic rules." Mr. Colebrooke has, by a 
variety of arguments, shown that the astronomer and alge- 
braist, Aryabhatta (the oldest of those they consider their 
uninspired and merely human writers), wrote as far back as 
the fifth century of the Christian era, and probably at a 
much earlier period : he was therefore, even on this compu- 
tation, almost as old as the Greek algebraist, Diophantus, 
