A treatise on special or elementary geometry (1877)
Olney, Edward, 1827-1887, Olney, Edward, 1827-1887. Elements of trigonometry, plane and spherical · New York : Sheldon · leaf 218
thelatter h. Since FP and AF are cut by-parallel planes, we have AF : a/ :: H : A; and AB : aJ :: H : h,since by definition AF : af :: AB : ab^ etc.Call the base of H-ABCDE B, and of Now, as the bases are similar polygons, B : 6 :: Ab : :^ : : H^ : h\ H : /i : : AB : a6 : : H : ^. B X H : 6 X 7i ::… … Fig. .302. h-abcde b. ButHence, PROPOSITION XV. 408, Theorem,—The convex surfaces of similar cylinders ofrevolution are to each other as the squares of their altitudes, and as{lie squares of the radii of their bases. Dem.—Let H and h be the altitudes, and R and r the radii of the base^ oftwo…
Geometry · Trigonometry
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