 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...The area of a 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... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...The area of a circle is TrE2. PROOF. S = |EXC = ^EX 2 TrE = TrE2. 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' - TrE2 : TrE'2 = E2 : E'2 = D2 : D'2. 466 COROLLARY... | |
 | Webster Wells - Geometry - 1908 - 336 pages
...respectively. C' p2 D2 ThCn' f = S = f" A3 TT-fl. Jt and §- = te!Lt = VL (§337) That is, the areas of two 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 O, whose... | |
 | Webster Wells - Geometry, Plane - 1908 - 208 pages
...diameters D and 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... | |
 | Richard Ferris - Aeronautics - 1910 - 492 pages
...action on a proportionally larger area of air. The principle involved is simply the geometric rule that the areas of circles are to each other as the squares of their radii. Thus the surface of air acted on by two propellers, one of 6 feet diameter and the other of 8 feet... | |
 | Richard Ferris - 1910 - 488 pages
...action on a proportionally larger area of air. The principle involved is simply the geometric rule that the areas of circles are to each other as the squares of their radii. Thus the surface of air acted on by two propellers, one of 6 feet diameter and the other of 8 feet... | |
 | Shelby Saufley Roberts - Railroad tracks - 1910 - 682 pages
...line, a circle can be passed and but one. Circumferences of circles are to each other as their radii. Areas of circles are to each other as the squares of their radii. In the same or in equal circles, equal angles at the center subtend equal arcs; equal arcs subtend... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 328 pages
...(Proofs of these theorems will be found in the Appendix, §§ 585 and 590.) 563. Cor. n. The areas of two circles are to each other as the squares of their radii, or as the squares of their diameters. 564. Cor. m. The area of a sector whose angle is a° is - (See §651.)... | |
 | Geometry, Plane - 1911 - 192 pages
...The locus of a point. (e) A tangent to a circle. 2. Demonstrate: The areas of two similar segments of circles are to each other as the squares of their radii. 3. Compute the altitude H of a triangle in terms of its sides A, B and C. 4. Demonstrate: The square... | |
 | William Herschel Bruce, Claude Carr Cody - Geometry, Solid - 1912 - 134 pages
...equal to the area of four great circles. 792. COR. 3. The areas of the surfaces of two spheres are to each other as the squares of their radii or the squares of their diameters. 793. COR. 4. The area of a zone is equal to the product of its altitude by a great circle; Z=2 irRH.... | |
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The areas of circles are to each other as the squares of their radii. 
