| Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...PROPOSITION X. THEOREM 724. The lateral areas, or the total areas, of two similar cones of revolution are to **each other as the squares of their radii, or as the squares of their** altitudes, or as the squares of their slant heights; and their volumes are to each other as the cubes... | |
| George Albert Wentworth - Geometry - 1904 - 496 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 D' the diameters, and S and S' the areas of the surfaces... | |
| Education - 1912 - 942 pages
...SYLLABUS 747 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.... | |
| Education - 1912 - 914 pages
...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.... | |
| Isaac Newton Failor - Geometry - 1906 - 431 pages
...AD x 2 TrE = 2 E x 2 TrE = 4 TrE2. 831 COROLLARY 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. 832 COROLLARY 3. The area of a zone is equal to the product of its altitude by the circumference... | |
| Isaac Newton Failor - Geometry - 1906 - 440 pages
...circle is irB2. PROOF. S = iRxC = £Rx2TrR = TrR2. 465 COROLLARY 2. The areas of two circles are to **each other as the squares of their radii, or as the squares of their** diameters. PROOF. S:S' = irR2:irRB = R1:R"=DI:D'2. 466 COROLLARY 3. The area of a sector is equal to... | |
| Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...cones of revolution : I. The lateral areas are to each other as the squares of their altitudes, or **as the squares of their radii, or as the squares of their** slant heights. II. The total areas are to each other as the squares of their altitudes, or as the squares... | |
| Webster Wells - Geometry - 1908 - 336 pages
...a sphere is equivalent to four great circles. 593. 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. (The proof is left to the pupil ; compare § 338.) Ex. 25. Find the area of the surface... | |
| Webster Wells - Geometry, Plane - 1908 - 208 pages
...D', respectively. Then, 8 ^ R2 and 2-t = t*"^ = ^- (§ 337) That is, the areas oftwo circles are to **each other as the squares of their radii, or as the squares of their** diameters. 339. Let s be the area, and c the arc, of a sector -of a 0, whose area is S, circumference... | |
| Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...of the zone generated by the arc CD = GO x 2irR. 711. Corollary 2. The areas of two spheres are to **each other as the squares of their radii, or as the squares of their** diameters. SUGGESTION. Let R and R' be the radii of two spheres, then 47rR2 and 4xR'J will be their... | |
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