History of Hindu Mathematics: A Source Book v2.c17.s19.t2.18

v2.c17.s19.t2.18

The dimensions of a rational inscribed quadrilateral, as stated by Mahâvîra, have been noted before (p. 236). The diameter of its circum-circle is $(p² + q²)(m² + n²)².$ Then, according to Mahâvîra, the sides of a rational quadrilateral inscribed in a circle of diameter D, are $D(2mn/(m² + n²)), D((m² - n²)/(m² + n²)), D(2pq/(p² + q²)), D((p² - q²)/(p² + q²));$ its diagonals are $2pq (m² - n²) + 2mn (p² - q²) D/((p² + q²)(m² + n²)),$ $(m² - n²)(p² - q²) + 4mnpq D/((p² + q²)(m² + n²));$ and its area is $(D²)/(2 (p² + q²)(m² + n²)) 2pq(m² - n²) + 2mn(p² - q²)$ $× (m² - n²)(p² - q²) + 4mnpq;$ so that the sides, diagonals and area are all rational.