| Adrien Marie Legendre - Geometry - 1819 - 208 pages
...of all. Therefore the convex surface AE is less thaii any which encloses it. •11 ' THEOREM. 516. **The solidity of a cylinder is equal to the product of its** but by its altitude. Fig. 258. Demonstration. Let CA {Jig. 258) he the radius of the basr of the given... | |
| Adrien Marie Legendre - Geometry - 1822 - 367 pages
...cylinder, multiplied by its altitude, cannot be the measure of 'a greater cylinder. Hence finally, **the solidity of a cylinder is equal to the product of its base by its** altitude. Cor. 1. Cylinders of the same altitude are to each other as their bases ; and cylinders of... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...of a cylin~ der by its altitude should be the measure of a greater cylinder. We conclude then, that **the solidity of a cylinder is equal to the product of its base by its** altitude. 517. Corollary i. Cylinders of the same altitude are to each other as their bases, and cylinders... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...base of a cylinder by its altitude should be the measure of a greater cylinder. We conclude then, that **the solidity of a cylinder is equal to the product of its base by its** altitude. 517. Corollary i. Cylinders of the same altitude are to each other as their bases, and cylinders... | |
| Adrien Marie Legendre - 1825 - 570 pages
...smallest of alL Therefore the convex surface AB is less than any which encloses it. THEOREM. 51 6. We' **solidity of a cylinder is equal to the product of its base by its** altitude. Fig. 258. Demonstration. Let CA (fig. 258) be the radius of the base of the given cylinder,... | |
| Adrien Marie Legendre - Geometry - 1828 - 346 pages
...THEOREM. 516. The solidity of ttcylinder is equal to the product of its base by its altitude. 31Let **CA be a radius of the given cylinder's base ; H the...to show that the solidity of the cylinder is surf.** CAxH. For, if surf. CAxH is no.t the measure of the given cylinder, it must be the measure of a greater... | |
| Adrien Marie Legendre - Geometry - 1830 - 344 pages
...all those which envelope it. THEOREM. 516. The solidity of a cylinder is equal to the product. of Us **base by its altitude. Let CA be a radius of the given...of the cylinder is surf. CA X H. • For, if surf.** CAxH is not the measure of the given cylinder, it must be the measure of a greater cylinder, or of... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...their convex surfaces perpendicular to the common base : hence the two solids will be equal ; therefore **the solidity of a cylinder is equal to the product of its base by its** altitude. Cor. 1. Cylinders of the same altitude are to each other as tKeir bases ; and cylinders of... | |
| Adrien Marie Legendre - Geometry - 1837 - 359 pages
...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** ill altitude. Let CA be the radius of the base of the cylinder, and II the altitude. Let the circ-le... | |
| Adrien Marie Legendre - Geometry - 1841 - 235 pages
...of a cylinder by its altitude should be the measure of a greater cylinder. We conclude, then, that **the solidity of a cylinder is equal to the product of its base by its** altitude. 517. Corollary i. Cylinders of the same altitude are to each other as their bases, and cylinders... | |
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