163 
as the lapse of several ages, and many repeated efforts of 
invention, were required to produce." 
The treatises on geometry are pronounced to be inferior in 
excellence to those on algebra ; but they contain the cele- 
brated proposition, that the square on the hypothenuse of 
a right-angled triangle, is equal to the squares on the sides 
containing the right angle; and others which form part 
of the system of modern geometry. Among these, that 
which discovers the area of a triangle when its three 
sides are known, is remarkable, as it does not appear to 
have been known to the ancient Greeks. 
The division of the circle among the Hindoos, and their 
correspondence in this respect with the Greeks, is a subject 
which has attracted attention ; and deservedly so, as it is 
purely conventional, having no dependence on the nature 
of the circle. Of this the circumference is divided by the 
ancient Hindoos into 360 equal parts, each of which was 
subdivided into sixty, and these into an equal number 
of smaller parts, similar to our present division into 
degrees, minutes, and seconds. The Hindoos, moreover, 
express the radius of a circle in parts of the circumference, 
and have but one measure (the minute of a degree) for 
both. Of these, the circumference is said to contain 21,600, 
and the radius 3438, which is pronounced by mathe- 
maticians as great a degree of accuracy as can be obtained ; 
without taking in smaller divisions than minutes, as it is true 
to the nearest minute; and this is all the exactness aimed 
at in their trigonometrical tables. The Bramins, however, 
knew to greater exactness the ratio of the diameter to 
the circumference, as they supposed it to be as 1 to 
3.1416. 
" The tables employed in their trigonometrical calcu- 
lations are two, — one of sines, and the other of versed 
sines : the sine of an arc they call cramajya or jyapind-a, 
