...is found by adding together the areas of all the triangles which form that surface. 5. If a pyramid be cut by a plane parallel to the base, the section will be a plane figure similar to the base; and these two figures will be in proportion to c&ch other as the...

...base of the triangle, is a chord, or diameter, of the circular base AB c » of the cone. 4. If a cone be cut by a plane parallel to the base, the section will be 11 circle. Thus, if the cone ABE, be cut by a plane parallel to AB, the section will be a circle, »f...

...cone, and any part of the base, the section will be a triangle. 3. If a cone be cut into two parts, by a plane parallel to the base, the section will be a circle. 4. If a cone be cut by a plane passing through its two slant sides, in an oblique direction, the section...

...two equal prisms by the plane CDEF. Therefore, if a solid &c. QED PROPOSITION IV. THEOREM. If a prism be cut by a plane parallel to the base the section will be equal and like to the base Let LB be a prism, of which the base is ABCDE, and a section parallel to...

...plane which also cuts the base, the section will be a triangle. 6. If a cone be cut into two parts, by a plane parallel to the base, the section will be a circle. 1. If a cone be cut by a plane which passes through its two slant sides in an oblique direction, the...

...plane perpendicular to the base, the section will be a triangle. 6. If a cone be cut into two parts by a plane parallel to the base, the section will be a circle. 7. If a cone be cut by a plane which passes through its two slant sides in an oblique direction 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. Fig. 3. Fig. 4. If the cone be cat slanting quite through both sides, the section will be an ellipse,...

...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, B a A b,fig....

...plane perpendicular to the base, the section will be a triangle. 6. If a cone be cut into two parts by a plane parallel to the base, the section will be a circle. 7. If a cone be cut by a plane which passes through its two slant sides in an 'oblique direction the...

...them, and the solids between each of them and the base, are cylinders. • COR. 3. — If a cone or cylinder be cut by a plane parallel to the base, the section is a circle. COR. 4. — Any plane touching the axis of a cone or cylinder, cuts every parallel section...