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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. "
Elements of Geometry - Page 180
by Adrien Marie Legendre - 1825 - 224 pages
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Elements of Geometry and Trigonometry: With Notes

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...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 280 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...
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Elements of Geometry

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....
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Elements of Geometry...: Translated from the French for the Use of the ...

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....
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Elements of Geometry and Trigonometry: With Notes

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...
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The North American Review, Volume 27

Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - American fiction - 1828
...its altitude. Now it has already been demonstrated, lemma 520, that ' the convex surface of a right prism, is equal to the perimeter of its base multiplied by its altitude.' Admitting, then, our principle, the convex surface of a cylinder will consist of an infinite number...
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The North American Review, Volume 27

Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - American fiction - 1828
...its altitude. Now it has already been demonstrated, lemma 520, that ' the convex surface of a right prism, is equal to the perimeter of its base multiplied by its altitude.' Admitting, then, our principle, the convex surface of a cylinder will consist of an infinite number...
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Elements of Geometry and Trigonometry

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....
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1839 - 372 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...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 235 pages
...the solidity of the cylinder will be * W x If, or * IPH. LEMMA. 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. (fig. 252),...
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