| Charles Davies, William Guy Peck - Mathematics - 1855 - 630 pages
...other as the squares of their homologous sides ; hence, the convex surfaces of similar cones are to **each other as the squares of their altitudes, or as the squares of the radii of their bases.** If the cones arc conjugate, the areas of their generating triangles are equal ; and the convex surfaces... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...R) 2w(A + R r H+R h + r IT h* That is, the lateral areas, or the total areas, of similar cylinders **of revolution are to each other as the squares of...altitudes, or as the squares of the radii of their bases.** PROPOSITION III.— PROBLEM. 12. The volume of a cylinder is equal to the product of its base by i&... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...total areas, of similar cones of revolution are to each other as the squares of their slant heights, or **as the squares of their altitudes, or as the squares of the radii of their bases.** /"r\ -.vA-.y PROPOSITION VI.— THEOREM. >.. 26. The lateral area of a frustum of a cone of revolution... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...~ A2 : ^R H+R ~ rh + r R IP A' That is, the lateral areas, or the total areas, of similar cylinders **of revolution are to each other as the squares of...altitudes, or as the squares of the radii of their bases.** PROPOSITION III.— PROBLEM. 12. The volume of a cylinder is equal to the product of its base by itt... | |
| Edward Olney - Geometry - 1872 - 566 pages
...demonstrated. FIQ. 80Z. PROPOSITION XV. 498. Theorem. — The convex surfaces of similar cylinders **of revolution are to each other as the squares of their altitudes,** and as the squares of the radii of their bases. DEM. — Let H and h be the altitudes, and R and r... | |
| Edward Olney - Geometry - 1872 - 472 pages
...demonstrated. FIG. 382. PROPOSITION XT. 498. Theorem, — The convex surfaces of similar cylinders **of revolution are to each other as the squares of their altitudes,** and as the squares of the radii of their bases. DEM.— Let H and h be the altitudes, and R and r the... | |
| William Chauvenet - Geometry - 1875 - 390 pages
...' h ~~ h' ~~ r* ' -R) R H+RH* That is, the lateral areas, or the total areas, of similar cylinders **of revolution are to each other as the squares of their altitudes, or as the** square* of the radii of their bases. PROPOSITION III.— PROBLEM. 12. The volume of a cylinder is equal... | |
| William Chauvenet - Geometry - 1879 - 380 pages
...total areas, of similar cones of revolution are to each other as the squares of their slant heights, or **as the squares of their altitudes, or as the squares of the radii of** tfieir bases. PROPOSITION VI.— THEOREM. 26. The lateral area of a frustum of a cone of revolution... | |
| George Albert Wentworth - Geometry - 1882 - 434 pages
...R ' (JJ' + R') ~Tl' \Jj' + R' That is, the lateral areas, or the total areas, of similar cylinders **of revolution are to each other as the squares of...altitudes, or as the squares of the radii of their bases.** 334 GEOMETRY BOOK VII. PROPOSITION XXX. THEOREM. 623. The volume of a cylinder is equal to the product... | |
| Edward Olney - Geometry - 1883 - 354 pages
...QED r J °' bxh v m3 h3 PROPOSITION XVII. 605. Theorem. — The convex surfaces of similar cylinders **of revolution are to each other as the squares of their altitudes,** and as the squares of the radii of their bases. DEMONSTRATION. Let H and /« be the altitudes, and... | |
| |