The History of Mathematical Proof in Ancient Traditions

502 agathe keller

hypotenuse of AHC. Bhāskara explains how to compute the upright side by

using the Pythagorean Th eorem and the Rule of Th ree. Th e determination

of CH, from which the upright side AH may be computed, rests upon the

proportional properties of similar triangles, illustrated in Figure 14.8. Th e

triangles BB ′ C and B ′ CH are similar:

BB :CB=CB :CH.′′

From this relationship it is known that:

CH CB CB

BB

.

′

′

Bhāskara expressed this relationship as the Rule of Th ree. Th e text does

not give a precise argument, but it alludes to the properties as being clear

from a diagram. It is in this context that the word upapatti appears: 31

Figure 14.7 An equilateral pyramid with a triangular base.

B

H

A

C

D

31 trairāśikopapattipradarśanārtham. ks. etranyāsah. – (Shukla 1976 : 59).