History of Hindu Mathematics: A Source Book v2.c17.s19.t1.24

v2.c17.s19.t1.24

If the rectangle generated from *m*, *n* be smaller than that from *p*, *q*, then, according to Mahâvîra, we obtain the rational inscribed quadrilateral of which the sides are $(m² - n²)(p² + q²)(m² + n²), (p² - q²)(m² + n²)²,$ $2mn(p² + q²)(m² + n²), 2pq(m² + n²)² ;$ whose diagonals are $2pq(m² - n²) + 2mn(p² - q²)(m² + n²),$ $(m² - n²)(p² - q²) + 4mnpq(m² + n²);$ whose altitudes are $2pq(m² - n²) + 2mn(p² - q²) 2mn,$ $(m² - n²)(p² - q²) + 4mnpq (m² - n²);$ whose segments are $2pq(m² - n²) + 2mn(p² - q²) (m² - n²),$ $(m² - n²)(p² - q²) + 4mnpq 2mn;$ and whose area is $½ 2pq(m² - n²) + 2mn(p² - q²) (m² - n²)(p² - q²)$ $+ 4mnpq (m² + n²)².$