Elements of geometry and trigonometry. Revised and adapted to the course of mathematical instruction in the United States (1856)
Legendre, A. M. (Adrien Marie), 1752-1833, Davies, Charles, 1798-1876 · New York : A.S. Barnes · leaf 224
le CAB, has for its measure irrX{All--BX)xCD. To this expression another form may be given. From ijthe middle point of AB, draw IK perpendicular to CD;and through B, draw BO parallel to CD. We shall thenhave (b. iv.. p. 7, s.), AJI+BX=2IK, and AJiI-BX=AO, hence, {AM-{-BX)x{AJI-BX)=A~M^-BX=2IKxA0:… … But CPxAB is double the area of tlie triangle CAB\tlierefore, A0xCD^2CABi hence, the solid generated by the triangle CAB is measured by ^<i^xCABxIK=CABx^^XlK\ and since 2irxIK=circ. IK, we have, soYid= CAB Xlcirc. IK Cor. If the triangle isisosceles, the perpendicularCP will pass through I,the…
Geometry · Trigonometry
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