 | William Hawney - Geometry - 1820 - 336 pages
...SA*xAB; ---- x -- = -- xAB, 3 5 )5 the sum of all the series of squares, ma", nc*, py2, Sfe. But as circles are to each other as the squares of their radii or diameters ; it evidently follows that -^ SA1 x.7854xAB will he the solidity of one-fourth of the spindle AbB,... | |
 | Timothy Walker - Geometry - 1829 - 156 pages
...demonstrated. 1. Two similar polygons are to each other as the squares of their homologous sides. 2. Two circles are to each other as the squares of their radii or diameters. 3. The surfaces of two spheres are to each, other as the squares of their radii. 4. The solidities... | |
 | Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...as their radii. 3. The area of a circle is IT multiplied by the square of the radius. Hence, any two circles are to each other as the squares of their radii, or as the squares of their diameters, or generally as the squares of any two homologous lines. 4. The... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...multiplied by the ratio of the circumference to the diameter. 9O1. Corollary. — The areas of two circles are to each other as the squares of their radii ; or, as the squares of their diameters. 502. Corollary — When the radius is unity, the area is expressed... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...multiplied by the ratio of the circumference to the diameter. 501. Corollary. — The areas of two circles are to each other as the squares of their radii ; or, as the squares of their diameters. 502. Corollary — When the radius is unity, the area is expressed... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...radius multiplied by the ratio of the circumference to the diameter. 501. Corollary — The areas of two circles are to each other as the squares of their radii ; or, as the squares of their diameters. 502. Corollary — When the radius is unity, the area is expressed... | |
 | George Anthony Hill - Geometry - 1880 - 348 pages
...We find that the areas are to each other as the numbers i, 4, 9, 16, etc. That is, — The areas of circles are to each other as the squares of their radii (or their diameters) . § 214. Problem. — To transform a given circle into a square. By computation.... | |
 | George Albert Wentworth - 1884 - 264 pages
...Theorem. Similar arcs are as their radii. 220. Them-&m. Arc of n° = -£- X 27rr. 360 222. Theorem. Two circles are to each other as the squares of their radii, or of their diameters. 223. Theorem. Similar sectors are to each other as the squares of their radii.... | |
 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...III. As the squares of the radii of inscribed circles. Proposition XIV. A Theorem. 279. The areas of circles are to each other as the squares of their radii or of their diameters. COROLLARY. The areas of similar sectors or segments are to each other as the squares... | |
 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...are to each other : I. As the squares of their sides. Proposition XIV. A Theorem. 279. The areas of circles are to each other as the squares of their radii or of their diameters. COROLLARY. The areas of similar sectors or segments are to each other as the squares... | |
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The areas of two circles are to each other as the squares of their radii ; or, as the squares of their diameters. 
