| Benjamin Greenleaf - Geometry - 1873 - 202 pages
...(Theo. XXXII. Cor. 3, Bk. IV.), and the convex surface of the cylinder by THEOREM II. 341. The volume of a cylinder is equal to the product of its base by its altitude. Let ABCDEF—G be a cylinder whose base is the circle ABCDEF, and whose altitude is the line AG ; then... | |
| Benjamin Greenleaf - Geometry - 1874 - 206 pages
...(Theo. XXXII. Cor. 3, Bk. IV.), and the convex surface of the cylinder by THEOREM II. 341. The volume of a cylinder is equal to the product of its base by its altitude. Let ABCDEF-G be a cylinder whose base is the circle ABCDEF, and whose altitude is the line AG ; then its... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...Ю ~~Í'Ir*~~R'~í' ' (H' + A") ~R' \H' GEOMETRY BOOK VII. PROPOSITION XXX. THEOREM. 623. The volume of a cylinder is equal to the product of its base by its altitude. Let V denote the volume of the cylinder AG, B its base, and H its altitude. We are to prove V = BX II.... | |
| George Albert Wentworth - Geometry - 1877 - 426 pages
...— - 2 "• R ~ ' (H' + R') ~Я' W + Bf OKOMETHY HOOK VII. PROPOSITION XXX. THEOREM. 623. The volume of a cylinder is equal to the product of its base by its altitude. A Let V denote the volume of the cylinder AG, B its base, and H its altitude. We fire to... | |
| Elias Loomis - Conic sections - 1877 - 458 pages
...sides of the prism, its volume is equal to the product of its base by its altitude ; lience the volume of a cylinder is equal to the product of its base by its altitude. Cor. 1. If H represent the altitude of a cylinder, andR the radius of its base, the area... | |
| Simon Newcomb - Geometry - 1881 - 418 pages
...volume will approach the volume of the cone as its limit. Therefore . THEOREM XXIII. 886. The volume of a cylinder is equal to the product of its base by its altitude. Proof. Inscribe in the cylinder a prism of which the number of sides may be increased without... | |
| Alfred Hix Welsh - Geometry - 1883 - 326 pages
...whose base and altitude would be the circumference and altitude of the cylinder. THEOREM TI. The volume of a cylinder is equal to the product of its base by its altitude. Let AB be a cylinder ; then /B will its volume be equal to the product of its base by its altitude. For,... | |
| William Chauvenet - Geometry - 1887 - 336 pages
...the radii of their bases. Suggestion. - = s RH R> IP - RH PROPOSITION III.— THEOREM. 11. The volume of a cylinder is equal to the product of its base by its altitude. Let the volume of the cylinder be denoted by V, its base by B, and its altitude by H. Let the volume of... | |
| William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...squares of their altitudes, or as the squares of the radii of their bases. PROPOSITION III. The volume of a cylinder is equal to the product of its base by its altitude. Corollary I. For a cylinder of revolution this may be formulated, PROPOSITION IV. If a pyramid... | |
| William Chauvenet, William Elwood Byerly - Geometry - 1887 - 336 pages
...squares of their altitudes, or as the squares of the radii of their bases. PROPOSITION III. The volume of a cylinder is equal to the product of its base by its altitude. Corollary I. For a cylinder of revolution this may be formulated, PROPOSITION IV. If a pyramid... | |
| |