This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1872 Excerpt: ...of any one of its lateral faces; as AC. 33 A Cone is a right pyramid whose base is a regular polygon of an infinite number of sides, that is, whose base is a circle. A cone can be described by the revolution of a right triangle about one of its sides which remains fixed. The other side describes the circular base, and ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1872 Excerpt: ...of any one of its lateral faces; as AC. 33 A Cone is a right pyramid whose base is a regular polygon of an infinite number of sides, that is, whose base is a circle. A cone can be described by the revolution of a right triangle about one of its sides which remains fixed. The other side describes the circular base, and the hypothcnusc the convex surface. Thus the right triangle ABC revolving about A B would describe the cone, B C the base, and the hypothenuse A C the convex surface. 34. The Axis of a cone is the lino from the vertex to tho centre of the base; or it is the fixed side of the right triangle v.'hose revolution describes tho cone; as A B. 33. Corollary. The axis of a cone is perpendicular to the base, and is therefore the altitude of the cone. 30. A Frustum of a pyramid is a part of the pyramid included between the base and a plane cutting the pyramid parallel to the a&DE. 37. The Altitude of a frustum is the perpendicular distance between the two parallel planes or bases; smFB. 38 The Slant Height of a frustum of a right pyramid is the perpendicular distance between the parallel edges of the bases; as G C. THEOREM VII. 39. If a pyramid is cut by a plane parallel to its base, 1st. The edges and altitude are divided proportionally; 2d. The section is a polygon similar to the base. Let A-BCDEFhe a pyramid whose al-A titude is A N, cut by a plane GI parallel to the base; then 1st. The edges and the altitude are divided proportionally. For suppose a plane passed through the vertex A parallel to the base; then the edges and altitude, being cut by three parallel planes, are divided proportionally (IV. 12), and we have AB: AG = AC: AH=AD: AI=AN 2d. The section GI is similar to the base BD. For the sides of GI are respectively parallel to the sides of B...
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