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. Elements of Geometry - Page 182by Adrien Marie Legendre - 1841 - 235 pagesFull view - About this book
| Adrien Marie Legendre - Geometry - 1819 - 574 pages
...and the solidity of the cylinder will be rR*xH, or »/?*//. MMMA. 520. The convex surface of a right prism is equal to the perimeter of its base multiplied by its altitude. Demonstration. This surface is equal to the sum of the rectangles AFGB, BGHC, CHID, &c. (j%. 25S),... | |
| Adrien Marie Legendre - Geometry - 1822 - 394 pages
...prism ; their bases AB, BC, CD, &c. taken together, make up the perimeter of the prism's base. Hence the sum of these rectangles, or the convex surface...perimeter of its base, multiplied by its altitude. Cor. If two right prisms have the same altitude, their convex surfaces will be to each other as the... | |
| Adrien Marie Legendre - 1825 - 570 pages
...prism is equal to the perimeter of its base multiplied by its altitude. Now the altitudes ^F, .BG, C7/, &c., of these rectangles are each equal to the altitude...The convex surface of a cylinder is greater than the conves surface of any inscribed prism, and less than the convex surface of any circumscribed prism.... | |
| Adrien Marie Legendre - Geometry - 1825 - 276 pages
...(fig. 252), which compose it. Fig. 2S2. Now the altitudes AF, BG, CH, &c., of these rectangles ate each equal to the altitude of the prism. Therefore...surfaces of these prisms will be to each other as th« perimeters of the bases. LEMMA. 522. The convex surface of a cylinder is greater than the convex... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...and the solidity of the cylinder will be n R' x H, or nR'H. LEMMA. 520. The convex surface of a right prism is equal to the perimeter of its base multiplied by its altitude. Now the altitudes AF, BG, CH, &c., of these rectangles are each equal to the altitude of the prism.... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...solidity of the cylinder will be n R2 x H, or nR*H. LEMMA. •* 520. The convex surface of a right prism is equal to the perimeter of its base multiplied by its altitude. Now the altitudes ^F, BG, CH, &c., of these rectangles arc each equal to the altitude of the prism.... | |
| Adrien Marie Legendre - Geometry - 1828 - 346 pages
...prism ; their bases AB, BC, CD, &c. taken together, make up the perimeter of the prism's base. Hence the sum of these rectangles, or the convex surface...perimeter of its base, multiplied by its altitude. 521. Cor. If two right prisms have the same altitude, their convex surfaces will be to each other as the... | |
| Adrien Marie Legendre - Geometry - 1836 - 394 pages
...Now, the altitudes AF, BG, CH, &c. of the rectangles, are equal to the altitude of the prism. Hence, the sum of these rectangles, or the convex surface of the prism, isequa!to BC AF ; that is, to the perimeter of the base of the prism multiplied by its altitude. Cor.... | |
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