 | Charles Davies, William Guy Peck - 1855 - 628 σελίδες
...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 - 1871 - 380 σελίδες
...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 - 1871 - 380 σελίδες
...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 - 1872 - 382 σελίδες
...~ 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 - 1872 - 562 σελίδες
...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 - 1872 - 472 σελίδες
...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 - 1875 - 390 σελίδες
...' 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 - 1879 - 380 σελίδες
...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 - 1882 - 442 σελίδες
...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 - 1883 - 352 σελίδες
...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... | |
| |
The lateral areas, or the total -areas, of two similar cones of revolution are to each other as the squares of their altitudes... 
