Sources page biographical material

6.BF.5. TRAVELLING ON SIDES OF A RIGHT TRIANGLE.
New section. See also the Mittenzwey example in 10.A.6.
Brahmagupta. Brahma sphuta siddhanta. 628. Chap. XII, sect. IV, v. 39. In Colebrooke, p. 308. Rule for the problem illustrated by Chaturveda.

Mahavira. 850. Chap. VII, v. 210-211, pp. 251-252. A slower traveller goes due east at rate v. A faster traveller goes at rate V and starts going north. After time t, he decides to meet the other traveller and turns so as to go directly to their meeting point. How long, T, do they travel? This gives us a right triangle with sides vT, Vt, V(T-t) leading to a quadratic in T whose constant term drops out, yielding T = 2t V²/(V²-v²). If we set r = v/V, then T = 2t/(1-r²), so we can determine T from t and r without actually knowing V or v. Indeed, if we let ρ = d/D, we get 2ρ = 1 - r². v, V, t = 2, 3, 5.

Chaturveda. 860. Commentary to the Brahma sphuta siddhanta, chap. XII, section IV, v. 39. In Colebrooke, p. 308. Two ascetics are at the top of a (vertical!) mountain of height A. One, being a wizard, ascends a distance X and then flies directly to a town which is distance D from the foot of the mountain. The other walks straight down the mountain and to the town. They travel at the same speeds and reach the town at the same time. Example with A, D = 12, 48.

Bhaskara II. Lilavati. 1150. Chap. VI, v. 154-155. In Colebrooke, pp. 66-67. Similar to Chaturveda. Two apes on top of a tower of height A and they move to a point D away. A, D = 100, 200.

Bhaskara II. Bijaganita. 1150. Chap. IV, v. 126. In Colebrooke, pp. 204-205. Same as Lilavati.