Davies, Charles, 1798-1876 · New York and Chicago, A. S. Barnes and company · leaf 192
angle, and AD perpendicular to the base;then will BC: CA + AB :: CA — AB: CD — DB For, ~A1? = ~Bl?+~AD* (Bk. IV, Th. xii) ; and AC* = IK? + ~KI) by subtraction AC —AB — CD —BlP. But since the difference of the squaresof two lines is equivalent to the rectangle contained by their sumand difference… … 192 TRIGONOMETRY T h e o r e m a. THEOREM IV. In any right-angled plane triangle, radius is to the tan-gent of either of the acute angles, as the side adjacent to Ontide opposite. Let CAB be the proposed triangle,and denote the radius by R : then willR: tan C::AC : AB.For, with any radius as CD…
Geometry · Plane trigonometry
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