Elements of geometry and trigonometry . - ]) equal to AD x ( ^ ).. For, inscribe in the bases of thefrustums two regular polygons of thesame number of sides, and havingtheir homologous sides parallel, eachto each. The lines joining the ver-tices of the homologous angles maybe regarded as the edges of the frus-tum of a regular pyramid inscribedin the frustum of the cone. The con-vex surface of the frustum of thepyramid is equal to half the sum of the perimeters of its basesmultiplied by the slant height fh (Book YII. Prop. IV. Cor.). Let now the number of sides of the inscribed polygons b
Elements of geometry and trigonometry . - ]) equal to AD x ( ^ ).. For, inscribe in the bases of thefrustums two regular polygons of thesame number of sides, and havingtheir homologous sides parallel, eachto each. The lines joining the ver-tices of the homologous angles maybe regarded as the edges of the frus-tum of a regular pyramid inscribedin the frustum of the cone. The con-vex surface of the frustum of thepyramid is equal to half the sum of the perimeters of its basesmultiplied by the slant height fh (Book YII. Prop. IV. Cor.). Let now the number of sides of the inscribed polygons beindefinitely increased : the perimeters of the polygons will be-come equal to the circumferences BIA, EGD ; the slant height?fh will become equal to the side AD or BE, and the surfacesof the two frustums will coincide and become the same surface. But the convex surface of the frustum of the pyramid willstill be equal to half the sum of the perimeters of the upperand lower bases multipliod by the slant height ; hence the sur-face of the frustum of a cone is equal to
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Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
