 | Nathan Scholfield - 1845 - 894 pages
...•2. El. Geom.) ; and the solidity of the cylinder will be -rR'XH, or TR'.H. PROPOSITION III. THEOREM. The solidity of a cylinder is equal to the product of its convex surface multiplied by half the radius of its base. Let ABDEF-G be the surface of the cylinder,... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...number of sides of the prism, its solidity is equal to the product of its base by its altitude; hence the solidity of a cylinder is equal to the product of its base by its altitude. Cor. 1. If A represent the altitude of a cylinder, and R the radius of its base, the area... | |
 | Charles Davies - Trigonometry - 1849 - 372 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 their bases ; and cylinders of... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...a 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... | |
 | Elias Loomis - Calculus - 1851 - 300 pages
...altitude AB. Then =nb'x+C. AB Taking the integral between the limits x=0 and a;=AB=A, we have that is, the solidity of a cylinder is equal to the product of its base by its altitude. Ex. 2. It is required to determine the solidity of a cone. Let A represent the altitude of... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...the cylinder is equal to tlie circumference of its base multiplied by its altitude. PROPOSITION II. THEOEEM. The solidity of a cylinder is equal to the product of its base by its altitude. 207 For; inscribe in the base of the cylinder any regular polygon BDEFGA, and construct on... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...circumference of its base multiplied by its altitude. PROPOSITION II. THEOREM. The solidity of a cyl1nder is equal to the product of its base by its altitude. Let CA be the radius of the base of the cylinder, and H the altitude. Let the circle whose radius is CA be denoted... | |
 | Elias Loomis - Conic sections - 1857 - 242 pages
...XIII., Cor. 2, B. VI.) ; and the convex surface of the cylinder by 2TrHA. PROPOSITION II. THEOREM. The solidity of a cylinder is equal to the product of its bast by its altitude. Let ACE-G be a cylinder whose base is the circle ACE and altitude AG ; its solidity... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...XIII., Cor. 2, B. VI.) ; and the convex surface of the cylinder by 2TrRA. PROPOSITION II. THEOREM. The solidity of a cylinder is equal to the product of its bast by its altitude. Let ACE-G be a cylinder whose base is the circle ACE and altitude AG ; its solidity... | |
 | Elias Loomis - Calculus - 1859 - 320 pages
...the altitude AB. Then AB Taking the integral between the limits z=0 and x=AB— h, we have that is, the solidity of a cylinder is equal to the product of its base by its altitude. Ex. 2. It is required to determine the solidity of a cone. Let h represent the altitude of... | |
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We conclude then, that the solidity of a cylinder is equal to the product of its base by its altitude. 
