...pyramid may be found by dividing three times the solidity by the area of the bate. 6. If a pyramid be cut by a plane parallel to the base, the section will be similar to tbe base, and the section and the base will be to each other as the squares of their distances...

...SV, parallel to the base, the polygons NP, and SV, will each be equal to the base. 17. If a pyramid be cut by a plane parallel to the base, the section will be similar to the base. Thus, if the pyramid $ — ABCDE, be cut by the plane abode parallel to the base,...

...figure will it intersect the cylinder1 How does this rectangle compare with the revolving rectangle 1 3. If a cylinder be cut by a plane, parallel to the base, what will the section be ? 4. What is the convex surface of a cylinder equal to 1 Of the Round Bodies....

...measured. 30. Define similar rectilineal figures; and prove, that if a pyramid with a polygon for its base be cut by a plane parallel to the base, the section will be a polygon similar to the base. GEOMETRICAL EXERCISES ON BOOK XII. THEOREM I. // semicircles ADB, BEC...

...a cylinder, it will intersect it in a rectangle PG, which is double the revolving rectangle EB. 33. If a cylinder be cut by a plane parallel to the base, how is the section? If a cylinder be cut by a plane parallel to the base, the section will be a circle...

...the the prism or pyramid ; or again in the pyramid beyond the vertex, as PROP. V " cylinder or cone be cut by a plane parallel to the base, the section will be a circle ; and in the cylinder, this circle will be equal to the base. (1.) Let ABC be the circular base of...

...sphere the surface of which passes through the vertices of the four solid angles of the pyramid. 6. If a cylinder be cut by a plane parallel to the base, the section is a circle equal to the base. 7. If a cone be cut by a plane passing through its axis, perpendicular...

...solid which would be generated or formed would be a spheroid.^ 4. " If a cone be cut into two parts by a plane parallel to the base, the section will be a circle" (as C in Diagram}. EXERCISE. — 1. Each of the sections separately. 2. The whole of them in one figure....

...plane passing through the apex, the section will be a triangle; if the cone be cut through both sides by a plane parallel to the base, the section will be a circle; if the cone be cut slanting quit« through both sides, the section will be a parabola ; and if the...

...plane passing through the apex, the section will be a triangle. If the cone be cut through both sides by a plane parallel to the base, the section will be a circle. If the cone be cut slanting quite through both sides, the section will be an ellipse, fig. 6. If the...