The Blackwell Companion to Hinduism

negative number. A fraction was expressed, just like our fractions, by placing the
numerator above the denominator (without a bar between them), and the frac-
tional part of a number was put below its integer part. Thus, for example, the
diameter of the reference circle of A ̄ryabhat.a’s sine table whose circumference
is 21600 is

6875

625

1309

since A ̄ryabhat.a’s value of pis 62832/20000, and the circumference of the
earth, whose diameter is 1050 yojanas according to A ̄ryabhat.a, is

3299

8°

25

(= 3299 - 25 –^8 )yojanas. The value of the linear measure, yojanas, varies from time
to time and from place to place. A ̄ryabhat.a equates it with 8000 nr.s(“men”),
where 1 nr.= 4 hastas(cubits)= 96 an.gulas(“fingers”).
In geometry, Bha ̄skara I probably knew a proof of the Pythagorean Theorem,
because he provides a square figure (figure 17.1) divided into 8 equal right-

370 takao hayashi

34

5

5

5

5

4

3

4 3

8

3

4

8

Figure 17.1: Diagram by Bha ̄ skara I, probably used for a proof of the Pythagorean
Theorem.