Legendre, A. M. (Adrien Marie), 1752-1833, Brewster, David, Sir, 1781-1868, Davies, Charles, 1798-1876 · New York, Wiley & Long · leaf 44
ter thanthe arc AD ; then will the chord AHbe greater than the chord AD. For, draw the radii CD, CH. Thetwo sides AC, CH, of the triangleACH are equal to the two AC, CD,of the triangle ACD, and the angleACH is greater than ACD ; hence, the third side AH is greater than the third side AD (Book I.… … BOOK III. 45 greater than ACD (Bk. I. Prop. IX. Sch.) ; and hence thatthe arc AH is greater than AD ; since the whole is greaterthan its part. Scholium. The arcs here treated of are each less than thesemicircumference. If they were greater, the reverse pro-perty would have place ; for, as the arcs…
Trigonometry · Geometry
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