 | Adrien Marie Legendre - 1819 - 574 σελίδες
...multiplied by its altitude cannot be the measure of the surface of a greater cylinder. We conclude then that the convex surface of a cylinder is equal to the circumference of the base multiplied by its altitude. THEOREM. 524. The solidity of a cone is equal to the product of... | |
 | Adrien Marie Legendre - 1822 - 394 σελίδες
...cylinder's 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 - 1825 - 294 σελίδες
...surface 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, John Farrar - 1825 - 280 σελίδες
...the 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 - 1825 - 276 σελίδες
...multiplied by its altitude cannot be the measure of the surface of a greater cylinder. We conclude then that the convex surface of a cylinder is equal to the circumference of the base multiplied by its altitude. 524. The solidity of a cone is equal to the product of its base... | |
 | Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - 1828 - 598 σελίδες
...QED 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 - 1828 - 598 σελίδες
...QED 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 - 1828 - 346 σελίδες
...shown to be less than that of any circumscribed prism BCDKLH. (See the 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... | |
 | Timothy Walker - 1829 - 138 σελίδες
...remains to prove 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...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... | |
 | Timothy Walker - 1829 - 156 σελίδες
...surface of a right prism is equal to the perimeter of the base multiplied by the altitude. Consequently the convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude ; but the altitude is the same as the axis. Therefore the convex surface= CxA. 2. — The entire surface... | |
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The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude. 
