The Pythagorean Proposition: Algebraic Proofs, Proof #36

Thirty-Six

Fig. 34

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.