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 178
AC : DF : : AB : DE, or AH* :aI :: CB : FE :: Ac :~DF Q. E. D. PROPOSITION IX.363, Hieoreni,—The areas of similar polygons are to eachother as the squares of the homologous sides of the polygons. * The only object in taking the largest angle is to make the perpendicular fall wUhin thetriangle. Any… … AREAS OF SIMILAR FIGURES. Dem.—Let ahcdef and ABCDEFbe two similar polygons. Desig-nate the former by p, and the lat-ter by P. Then p: P ::ab:: AB^*or as the squares of any other twohomologous sides. For, from the equal angles aand A drawing the diagonals, thecorresponding partial angles intowhich…
Geometry · Trigonometry
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