History of Hindu Mathematics: A Source Book v2.c17.s19.t1.5
History of Hindu Mathematics: A Source Book v2.c17.s19.t1.5
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v2.c17.s19.t1.5
If ABCD be a rational trapezium whose sides AB, BC, AD are equal, then $AB = BC = AD = (m² + n²)²,$ $CD = 3(2mn)² - (m² - n²)² = 14m²n² - m⁴ - n⁴,$ or CD = 3(m² - n²)² - (2mn)² = 3m⁴ + 3n⁴ - 10m²n².