 | Benjamin Greenleaf - 1869 - 516 pages
...cylinder. The prism will be inscribed in the convex surface of the cylinder. The convex surface of this prism is equal to the perimeter of its base multiplied by its rititude, AG (Prop. I. Bk. VIII.). Conceive now the arcs subtending the sides of the polygon to be... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...together, from the perimeter of the base of the prism. Therefore, the sum of these parallelograms, or the convex surface of the prism, is equal to the...perimeter of its base, multiplied by its altitude. Cor. 1' two right prisms have the same altitude, theii convex surfaces will be to each other as the... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...and the area of each rectangle is equal to its base multiplied by its altitude (B. IV., PV) : hence, the sum of these rectangles, or the convex surface of the prism, is equal to, (AB + BC + CD + DE + EA) x AF ; that is, to the perimeter of the base multiplied by the altitude ;... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...perimeter of the prism. Therefore the sum of these rectangles, that is, the convex surface of the right prism, is equal to the perimeter of its base multiplied by its altitude. 1,>. Corollary. As a cylinder is a right prism (12), this demonstration includes the cylinder. If,... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...the rectangle whose revolution describes the cylinder ; as B C. I i. The convex surface of a right prism is equal to the perimeter of its base multiplied by its altitude. Let AH be a right prism; its convex surface Is equal to FG -\- GH -\- HI+IK+-KF multiplied by its altitude... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...cylinder. The prism will be inscribed in the convex surface of the cylinder. The convex surface of this prism is equal to the perimeter of its base multiplied by its altitude, AG (Theo. IX. Bk. V.). Conceive now the arcs subtending the sides of the polygon to be continually... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...and the area of each rectangle is equal to its base multiplied by its altitude (B. IV., PV) : hence, the sum of these rectangles, or the convex surface of the prism, is equal to, (AS + BG + CD + DE + EA) x AF ; that is, to the perimeter of the base multiplied by the altitude ;... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...cylinder. The prism will be inscribed in the convex surface of the cylinder. The convex surface of this prism is equal to the perimeter of its base multiplied by its altitude, AG (Theo. IX. Bk. V.). Conceive now the arcs subtending the sides of the polygon to be continually... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...the same altitude are equal to one another. Proposition 10. Theorem.—The lateral surface of a right prism is equal to the perimeter of its base multiplied by its altitude. Because the prism is a right prism (Def. 3) the angle ABC is a right angle. Hence the figur^ AC is... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...Therefore the convex surface = (B 0+ CD + DH + EF + IB) XAG H 21 • Cor. 1. The convex surface of a right prism is equal to the perimeter of its base multiplied by its altitude. 22. Cor. 2. As a cylinder is a prism (14), this demonstration includes the cylinder. In a circular... | |
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CD, &c., taken together, make up the perimeter of the prism's base : hence the sum of these rectangles, or the convex surface of the prism, is equal to the perimeter of its base multiplied by its altitude. 
