 | Webster Wells - Geometry - 1899 - 424 pages
...and diameters D and D', respectively. S = irR2 = R2 ' S' irR'2 R'2' S , and That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters. 373. Cor. III. The area of a sector is equal to one-half the product... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...multiplied by it. We have S=jr.R2 Th. 10. Whence, S = n ( JD) 2 = kn D 2. COR. 2. — The arena of circles are to each other as the squares of their radii or as the squares of their diameters. Let S and R and .S" and R' denote respectively the areas and radii... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...by the method of Exhaustions. By the use of these he obtained such theorems as that the areas of two circles are to each other as the squares of their radii, or of their diameters. In the writings of Hero (Alexandria, 125 B. 0.) we first find the formula for the... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...by the method of Exhaustions. By the nse of these he obtained such theorems as that the areas of two circles are to each other as the squares of their radii, or of their diameters. In the writings of Hero (Alexandria, 125 BC) we first find the formula for the... | |
 | Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...by the method of Exhaustions. By the use of these he obtained such theorems as that the areas of two circles are to each other as the squares of their radii, or of their diameters. In the writings of Hero (Alexandria, 125 BC) we first find the formula for the... | |
 | 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... | |
 | 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.)... | |
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The areas of two circles are to each other as the squares of their radii ; or, as the squares of their diameters. 
