 | Timothy Walker - Geometry - 1829 - 138 pages
...the same, they are as their bases. If the bases are the same, they are as their altitudes. 164. — The surfaces of two spheres are to each other as the squares of their radii, and the solidities are as the cubes of thtir radii — . 1. Let S be the surface of... | |
 | Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...the following formulas for the are again subdivided into varieties, &c. For ' surface, , - 4;rr3 = The surfaces of two spheres are to each other as the squares of their radii, or as the squares as spherical angle, spherical triangle, spherical polygon, &c. SPHERICAL... | |
 | Robert Linton - Planets - 1858 - 54 pages
...Define then the laws of the sphere, and their application to distance. Definition 1st. The surfaces of spheres are to each other as the squares of their diameters, and therefore their diameters are to each other as the square root of their surfaces. Definition 2nd. The... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...the same ratios as in other similar solids. These principles may be demonstrated as follows : 806. Theorem The areas of the surfaces of two spheres are...For the superficial area of any sphere is equal to i: times the diameter multiplied by the diameter (786) ; that is ~D2. But TT is a certain or constant... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...Corollary II. Let S and S' be the surfaces of two spheres whose radii are R and R ' ; then, R2 hence, the surfaces of two spheres are to each other as the squares of their diameters, or as the squares of their radii. ./v PROPOSITION XII.— LEMMA. 44. If a triangle revolves about an... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...the same ratios as in other similar solids. These principles may be demonstrated as follows : SO6. Theorem The areas of the surfaces of two spheres are to each of her as the squares of their diameters ; and their volumes arc as the cubes of their diameters, or... | |
 | William Chauvenet - Geometry - 1875 - 390 pages
...surfaces of two spheres whose radii are R and R ' ; then, S ^ 4xR' _ (2.R)2 _IP_t ~ ~ ~ R"' hence, the surfaces of two spheres are to each other as the squares of their diameters, or as the squares of their radii. PROPOSITION XII— LEMMA. 44. If a triangle revolves about an axis... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...equal to four times the area of one of its great circles. BOOK VIII.] MEASUREMENT OF SOLIDS. COR. 3. The surfaces of two spheres are to each other as the squares of their radii. COR. 4. If a right cylinder be circumscribed about a sphere whose radius is R, then... | |
 | Charles Scott Venable - 1881 - 380 pages
...the sphere is equal to^ the area of the circle whose radius is the diameter of the sphere. COR. 3. The surfaces of two spheres are to each other as the squares of their radii or the squares of their diameters, or as the squares of the circumferences of their... | |
 | Joseph Anthony Gillet - Astronomy - 1882 - 496 pages
...distance through its centre. The radius of a sphere is the distance from the surface to the centre. The surfaces of two spheres are to each other as the squares of their radii or diameters ; and the volumes of two spheres are to each other as the cubes of their... | |
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The areas of the surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters. 
