 | Arthur A. Dodd, B. Thomas Chace - 1898 - 468 sider
...the diameter of the sphere? 692. Cor. IV. Show that 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. 693. Cor. V. Can you show that the area of a spher694. PROPOSITION XXX. Let the figure represent... | |
 | Webster Wells - 1898 - 284 sider
...S' irK* R'"' -, S T7r.D2 ZF~ /fi n,,-l\ 011t1 '== (§371) 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. TJie area of a sector is equal to one-half the product of its arc and radius.... | |
 | 1898 - 228 sider
...triangle is a, and the angle at the vertex is 30°; show that the length of the base equals \2 — i/3 7. The areas of two regular polygons of the same number of sides are in the same ratio as the squares of the radii of the inscribed or circumscribed circles. V JUNE, 1900.... | |
 | Yale University - 1898 - 212 sider
...triangle is a, and the angle at the vertex is 30°; show that the length of the base equals a\2 — -/3 7. The areas of two regular polygons of the same number of sides are in the same ratio as the squares of the radii of the inscribed or circumscribed circles. JUNE, 1900.... | |
 | James Howard Gore - 1898 - 232 sider
...A'B ' ' Perimeter of AB - F_ AB . Perimeter of A'B' - F' ~ A'B'' that is, The perimeters of regular polygons of the same number of sides are to each other as any two homologous sides or lines. PROPOSITION III. THEOREM. 292. The area of a regular polygon is... | |
 | Webster Wells - 1899 - 450 sider
...denote the area of polygon AC, and K' oiA'C'. (§322) ^B_^_r.wh JBT_^_r2. 3^~^"P! ^ ' ^~l5~^ That is, the areas of two regular polygons of the same number...their radii, or as the squares of their apothems. PROP. VI. THEOREM. 350. The area of a regular polygon is equal to one-half the product of its perimeter... | |
 | George Albert Wentworth - 1899 - 498 sider
...P:P' = OA: O'A' = OM : O'M'. § 445 §364 §431 § 436 Also, §357 § 351 § 361 Ax. 1 QED 448. COR. The areas of two regular polygons of the same number of sides are to each other as the squares of the radii of the circumscribed circles, and of the inscribed circles. § 413 PROPOSITION VI. THEOREM.... | |
 | George Albert Wentworth - 1899 - 496 sider
...homologous sides, § 412 216 REGULAR POLYGONS AND CIRCLES. PROPOSITION V. THEOREM. 447. The perimeters of two regular polygons of the same number of sides are to each other as the radii of their circumscribed circles, and also as the radii of their inscribed circles. A' it' B' Let... | |
 | George Albert Wentworth - 1899 - 278 sider
...homologous sides. § 412 REGULAR POLYGONS AND CIRCLES. PROPOSITION V. THEOREM. 447. The perimeters of two regular polygons of the same number of sides are to each other as the radii of their circumscribed circles, and also as the radii oftheir inscribed circles. D' MB A' M'... | |
 | Webster Wells - 1899 - 424 sider
...polygons fulfil the conditions of similarity given in § 252.) PROP. V. THEOREM. 348. The perimeters of two regular polygons of the same number of sides are to each other as their radii, or as their apothems. D D' FB F' B' Given P and P' the perimeters, R and R' the radii,... | |
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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. 
