Sq. AE = sq. KD - 4ABH
= (a + b)² - 2ab; and h² = sq.
NH + 4ABH = (b - a)² + 2ab.
Adding, 2h² = (a + b)²
+ (b - a)² = 2a² + 2b². ∴ h² = a² + b². Q.E.D.
a. See Versluys, p. 72, fig. 78; also given by Saunderson (1682-1750); also see Fourrey, p. 92, and A. Marre. Also assigned to Bhaskara, the Hindu Mathematician, 12th century A.D. Also said to have been known in China 1000 years before the time of Christ.