Extend GA making AP
= AG; extend DB making BN
= BD = CP. Tri. CKP = tri. ANB = ½ sq. HD = ½ rect. LK.
Tri. APB = ½ sq. HG = ½ rect. AM. Sq. AK = rect. AM
+ rect. LK.
∴ sq. upon AB = sq. upon HB + sq. upon AH. ∴ h² = a² + b². Q.E.D.
a. This is Huygens' proof (1657); see also Versluys, p. 25, fig. 22.