| Adrien Marie Legendre - Geometry - 1822 - 367 pages
...base multiplied by the altitude cannot measure the surface of a greater cylinder. Hence, finally, the **convex surface of a cylinder is equal to the circumference of its base, multiplied by** the altitude. PROPOSITION V. THEOREM. The solidity of a cone is equal to the product of its base by... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...cylinder is less than that of any Fig. 253. circumscribed prism BCDKLH (fig. 253). THEOREM. 523. The **convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude,** Fig. 258. Demonstration. Let CA. (fig. 258) be the radius of the base of the given cylinder, H its... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...of the cylinder is less than that of any Fig. 253. circumscribed prism BCDKLH (fig. 253). / 523. The **convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude.** Fig. 258. Demonstration. Let CA (fig. 258) be the radius of the base of the given cylinder, H its altitude... | |
| Adrien Marie Legendre - Geometry - 1825 - 280 pages
...cylinder is less than that of any Pig. 253. circumscribed prism BCDKLH (fig. 253). THEOREM. 523. The **convex surface of a cylinder is equal to the circumference of its base** midliplied by its altitude. Fig. 258. Demonstration. Let CA (Jig. 258) be the radius of the base of... | |
| Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - American fiction - 1828
...Again, lemma 522 may be omitted, being only introduced for the sake of demonstrating theorem 523. The **convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude.** Now it has already been demonstrated, lemma 520, that ' the convex surface of a right prism, is equal... | |
| Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - American fiction - 1828
...Again, lemma 522 may be omitted, being only introduced for the sake of demonstrating theorem 523. The **convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude.** Now it has already been demonstrated, lemma 520, that ' the convex surface of a right prism, is equal... | |
| Adrien Marie Legendre - Geometry - 1828 - 346 pages
...fig. of Art. 512.) THEOREM. 523. The convex surface of a cylinder is equal to the circumference of Us **base multiplied by its altitude. Let CA be the radius of the given cylinder's base,** H its altitude ; the circumference whose radius is CA, being represented by circ. CA, we are to show... | |
| Timothy Walker - Geometry - 1829 - 129 pages
...that the convex surface=C x A, for (C x R) + (C x A) = ( A+R) x C. We are to demonstrate that — the **convex surface of a cylinder is equal to the circumference- of its base multiplied by its altitude** — . This will be evident if it be admitted that — the cylinder is a right prism of an infinite... | |
| Adrien Marie Legendre - Geometry - 1830 - 344 pages
...be less than that of any circumscribed prism BCDKLH. (See the fig. of Art. 512.) THEOREM. 533. The **con-vex surface of a cylinder is equal to the circumference...Let CA be the radius of the given cylinder's base,** H its altitude ; the circumference whose radius is CA, being represented by arc. CA, we are to show... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...perimeter of its base multiplied by H, whatever be the number of sides : hence, the convex surface of the **cylinder is equal to the circumference of its base multiplied by its altitude.** PROPOSITION II. THEOREM. The solidity of a cylinder is equal to the product of its base by its altitude.... | |
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