Elements of geometry and trigonometry . the homologous angles and there will then be inscribed in the frustum of the cone, the frustum of a regular pyramid. The solidity of the frustum of the pyramid is equivalent to three pyramids having the common altitude of the frustum, and for bases, the lower base of the frustum, the upper base of the frustum, and a mean proportional between them (Book VII. Prop. XVIII.).Let now, the number of sides of the inscribed polygons be indefinitely increased: the bases of the frustum of the pyramid will then coincide w^ith the bases of the frustum of the cone, a
Elements of geometry and trigonometry . the homologous angles and there will then be inscribed in the frustum of the cone, the frustum of a regular pyramid. The solidity of the frustum of the pyramid is equivalent to three pyramids having the common altitude of the frustum, and for bases, the lower base of the frustum, the upper base of the frustum, and a mean proportional between them (Book VII. Prop. XVIII.).Let now, the number of sides of the inscribed polygons be indefinitely increased: the bases of the frustum of the pyramid will then coincide w^ith the bases of the frustum of the cone, and the two frustums will coincide and become the same solid. Since the area of a circle is equal to B?.n (Book V. Prop. XII. Cor. 2.), the expression for the solidities of the frustum will become for the first pyramid ^OP x OA^^.for the second iOP x PD^.tt for the third OPx AO x PD.^r ; since AO x is a mean proportional between ^ and PD^.tt Hence the solidity of the frustum of the cone is measured by JnOP X (OAHPDH AO X PD)..
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Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
