...Corollary. The volume of any prism is equal to the product of its base by its altitude. PROPOSITION XIII. If a pyramid is cut by a plane parallel to its base, 1st, the edges and the altitude are divided proportionally; 2d, the section is a polygon similar to...

...and the sides of the base are 24, 20, and 20 inches. SOLID GEOMETRY. Proposition 1 4. Theorem. 623. If a pyramid is cut by a plane parallel to its base : (1) The edges and the altitude are divided proportionally. (2) TJie section is a polygon similar...

...Corollary. The volume of any prism is equal to the product of its base by its altitude. PROPOSITION XIII. If a pyramid is cut by a plane parallel to its base, 1st, the edges and the altitude are divided proportionally ; 2d, the section is a polygon similar to...

...xx • A'B' A'B' A'B' That is, vol. ABCD AB' \o\.A'B'CD' A 'A" §274 §597 §709 §715 QED 728. COR. If a pyramid is cut by a plane parallel to its base,...the first, and the two pyramids are to each other as tlic cubes of any two homologous edges. Hint. — Prove first that the lateral edges are divided proportionally....

...one-half the sum of the perimeters of the bases multiplied by the slant height of the frustum. 598. If a pyramid is cut by a plane parallel to its base, I. The edges and altitude are divided proportionally : II. The section is a polygon similar to the...

...the perpendicular distance from the vertex to the plane of the base. PROPOSITION XVIII. THEOREM G95. If a pyramid is cut by a plane parallel to its base : I. The lateral edges and the altitude are divided proportionally. II. The section is a polygon similar...

...X A'D' AD A'B' That is, vol. A BCD y A'C A'D' 'A'B' A'B' AB vol. A'B'C'D' A'B' =;• QED 680. COR. If a pyramid is cut by a plane parallel to its base,...each other as the cubes of any two homologous edges. Hint.— Prove the lateral edges divided proportionally and hence the homologous faces of the two pyramids...

...AB . "A'B1' ~AB* A'C X A'B' A'D' • AB 'A'B' § 568 §673 ^ O7 1\ QED vo\. A'B'C'D' A'B' 680. COR. If a pyramid is cut by a plane parallel to its base,...similar to the first, and the two pyramids are to each othcr as the cubes of any two homologous edges. Hint. — Prove the lateral edges divided proportionally...

...the perpendicular distance from the vertex to the plane of the base. PROPOSITION XVIII. THEOREM 693. If a pyramid is cut by a plane parallel to its base : I. The lateral edges and the altitude are divided proportionally. II. The section is a polygon similar...

...straight lines at their point of intersection, it is perpendicular to the plane of those lines. 3. If a pyramid is cut by a plane parallel to its base, (a) the edges and altitude are divided proportionally ; (b) the section is a polygon similar to the...