it may be proved that sq. BG = |[» BM. But ||»^« AM, BM make up the whole sq. AE. Hence sq. CK + sq. BG = sq. AE; i.e., the square on AB is equal to the sum of the squares on AC, CB. Additional Propositions. 237 Prop. 12. In any triangle, the square on theside opposite any angle, according as the… … Let ABC be the A ; and from C let CN be drawn ±r to BA, so that AN is the projection of AC on AB. Represent BC by «, CA by h, AB by c, and AN by x. Then a-={c±x)^-^C^\ (III, 13.)= (e±a:)2 + 7;2 _^2^ = cr±2cx + x ^h~ -J7% (5 c% 7, Add. Props.)= h+ c,^ ±2cx. Prop. 14, Bk. III., is also a…
Geometry · Geometry, Plane
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