| Thomas Franklin Holgate - Geometry - 1901 - 440 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, Frank Louis Sevenoak - Geometry - 1901 - 370 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 - 218 pages
...the area of the surface of a sphere. § 823 825. COR. 2. The areas of the surfaces of two spheres are **as the squares of their radii, or as the squares of their diameters.** Let R and R' denote the radii, D and I)' the diameters, and S and »S" the areas of the surfaces of... | |
| George Albert Wentworth - Geometry, Solid - 1902 - 218 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 - 384 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 triangle... | |
| Fletcher Durell - Geometry, Plane - 1904 - 372 pages
...quantities by the method of Exhaustions. By the use of these he obtained such theorems as that the areas of **two circles are to each other as the squares of their radii, or** of their diameters. In the writings of Hero (Alexandria, 125 B. 0.) we first find the formula for the... | |
| Fletcher Durell - Geometry, Solid - 1904 - 206 pages
...quantities by the method of Exhaustions. By the use of these he obtained such theorems as that the areas of **two circles are to each other as the squares of their radii, or** of their diameters. In the writings of Hero (Alexandria, 125 BC) we first find the formula for the... | |
| FLETCHER DURELL. PH.D. - 1911
...quantities by the method of Exhaustions. By the nse of these he obtained such theorems as that the areas of **two circles are to each other as the squares of their radii, or** of their diameters. In the writings of Hero (Alexandria, 125 BC) we first find the formula for the... | |
| George Albert Wentworth - Geometry - 1904 - 473 pages
...COR. 2. The area of a circle is equal to TT times the square of its radius. 464. COR. 3. The areas of **two circles are to each other as the squares of their radii.** For, if S and S' denote the areas, and R and R' the radii, 465. COR. 4. Similar arcs are to each other... | |
| Science - 1912
...revolution. Proposition 15. The lateral areas, or total areas, of similar cylinders of revolution are to **each other as the squares of their radii, or as the squares of their** altitudes. Definition. Pyramidal surface. Pyramidal space. Edges. Faces. Vertex. Transverse section.... | |
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