| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...to the base, or 661. Con. 2. Sections made by planes parallel to the bases of a circular cone are to **each other as the squares of their radii, or as the squares of their** distances from the vertex of the cone. PROPOSITION XXXI. THEOREM 662. The lateral area of a cone of... | |
| Edward Brooks - Geometry, Modern - 1901 - 278 pages
...it. We have S=jr.R2 Th. 10. Whence, S = n ( JD) 2 = kn D 2. COR. 2. — The arena of circles are to **each other as the squares of their radii or as the squares of their** diameters. Let S and R and .S" and R' denote respectively the areas and radii of two circles. Then,... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...to the base, or 661. COR. 2. Sections made by planes parallel to the bases of a circular cone are to **each other as the squares of their radii, or as the squares of their** distances from the vertex of the cone. PROPOSITION XXXI. THEOREM 662. The lateral area of a cone of... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...total areas, of two similar cones of revolution are to each other as the squares of their altitudes, **as the squares of their radii, or as the squares of their** slant heights ; and their volumes are to each other as the cubes of their altitudes, as the cubes of... | |
| Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...apothems. §351. (6) The areas of two regular polygons of the same number of sides are in the same ratio **as the squares of their radii, or as the squares of their** apothems. § 352. (7) The area of a regular polygon is equal to half the product of its perimeter and... | |
| Arthur Schultze - 1901 - 392 pages
...total areas, of two similar cones of revolution are to each other as the squares of their altitudes, **as the squares of their radii, or as the squares of their** slant heights ; and their volumes are to each other as the cubes of their altitudes, as the cubes of... | |
| George Albert Wentworth - Geometry, Solid - 1902 - 248 pages
...total areas, of two similar cones of revolution are to each other as the squares of their altitudes, **as the squares of their radii, or as the squares of their** slant heights ; and their volumes are to each other as the cubes of their altitudes, as the cubes of... | |
| Alan Sanders - Geometry - 1903 - 392 pages
...circumference of a great circle of the sphere. 1187. COROLLARY III. The surfaces of spheres are to **each other as the squares of their radii, or as the squares of their** diameters. QED SOLID GEOMETRY 1189. EXERCISE. Find the radius of a sphere if the area of its trirectangular... | |
| Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...Or K=nlP. Ax. 8. Again R=% 1> :. K= — —• Ax. 8. 4 452. COR. 2. The areas of two circles are to **each other as the squares of their radii, or as the squares of their** diameters. K _^__^_ £ _ ' "' ~'~~"~* als° '' = 453. The area of a sector is equal to one-half the... | |
| Fletcher Durell - Geometry - 1911 - 553 pages
...THEOREM 700* The lateral areas, or the total areas, of tic o similar cylinders of revolution are to **each other as the squares of their radii, or as the squares of their** altitudes; and their volumes are to each other as the cubes of their radii, or as the cubes of their... | |
| |