 | William Chauvenet - Geometry - 1884 - 384 pages
...Corollary II. Let S and S' be the surfaces of two spheres whose radii are R and R ' ; then, . S' R hence, the surfaces of two spheres are to each other as the squares of 'heir diameters, or as the squares of their radii, PROPOSITION XII.— LEMMA. 44. If a triangle... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...and D and D' the diameters of two spheres. Then by , 733, f - jg -£• Also S_*(2B)2_Iy '-~ That is, the surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters. 364 PROPOSITION XII. THEOREM. 735. The volume,... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...may be formulated, Hence the surface of a sphere is equivalent to four great circles. Corollary II. The surfaces of two spheres are to each other as the squares of their diameters, or as the squares of their radii. PROPOSITION XI. The volume of a sphere is equal to the area of its... | |
 | George Frederick Chambers - Astronomical instruments - 1889 - 758 pages
...therefore exceeds that of the Earth 1 1 ,900 times, whilst the volume is 1,306,000 times greater; since the surfaces of two spheres are to each other as the squares of their diameters, and the volumes as the cubes. The linear value of i" of arc at the mean distance of the Sun is about 450... | |
 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...Therefore, the area of the surface of a sphere is equal to the area of four great circles. 791. COR. 2. 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. 792. COR. 3. The area of a zone is equal to the... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...Therefore, the area of the surface of a sphere is equal to the area of four great circles. 791. COR. 2. TJie areas of the surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters. 792. COR. 3. The area of a zone is equal to the... | |
 | William Chauvenet - 1893 - 340 pages
...IvR X 25 = 4*5'. Hence the surface of a sphere is equivalent to four great circles. 39. COROLLARY II. The surfaces of two spheres are to each other as the squares of their diameters, or as the squares of their radii. 40. Scholium. The area of a spherical degree on a sphere 7^10 value,... | |
 | Arthur Latham Baker - Geometry, Solid - 1893 - 154 pages
...the squares of the radii of the spheres upon which they are situated. COmpare § 206. ^ 308. COR. 3. The surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters. V ^ 309. COR. 4. The area of a zone is equal... | |
 | William C. Bartol - Geometry, Solid - 1893 - 112 pages
...the semicircle as its limit and r will approach R as its limit; at the limit then, 183. COROLLARY 1. The surfaces of two spheres are to each other as the squares of the radii of the spheres. For, if we represent the surfaces of two spheres by S and S', and the... | |
 | Webster Wells - Geometry - 1894 - 400 pages
...and V their diameters. Then, — = 4 ^ = — , ft' d.*,Jf'* 7?'2 tJ ^t 7TJ.I' -Lit and — = That is, 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. 688. COR. III. Let O be the centre of the arc... | |
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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. 
