 The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems.  Elements of Geometry - Page 170by Andrew Wheeler Phillips, Irving Fisher - 1897 - 354 pagesFull view - About this book
 | 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 - 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.... | |
 | 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.... | |
 | 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... | |
 | 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... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...Also, the polygons are similar (?). PR r 435. THEOREM. The areas of two regular polygons having the same number of sides are to each other as the squares of their radii and also as the squares of their apothems. Proof : If K and K' denote their areas, we have : But A'}... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...polygons are similar (?). A. Ij 1\ T AB QED 435. THEOREM. The areas of two regular polygons having the same number of sides are to each other as the squares of their radii and also as the squares of their apothems. Proof : If K and K' denote their areas, we have : But r2... | |
 | 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, 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... | |
 | 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... | |
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