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 158by Adrien Marie Legendre - 1825 - 224 pagesFull view - About this book
| Adrien Marie Legendre - Geometry - 1819 - 208 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 - 367 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 - 224 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 - 224 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 - Geometry - 1825 - 224 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 - 316 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 - 359 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.... | |
| Adrien Marie Legendre - Geometry - 1839 - 269 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, is equal to** (AB + BC + CD + DE + EA) x AF ; that is, to the perimeter of the base of the prism mult! plied by its... | |
| |