 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 215by Andrew Wheeler Phillips, Irving Fisher - 1896Full view - About this book
 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...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... | |
 | Yale University - 1898 - 212 pages
...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.... | |
 | Mathematics - 1898 - 228 pages
...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.... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...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 - Geometry - 1899 - 450 pages
...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 - Geometry - 1899 - 498 pages
...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 - Geometry, Plane - 1899 - 278 pages
...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'... | |
 | George Albert Wentworth - Geometry - 1899 - 496 pages
...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... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...AB BC CD ,,, .-. = = .etc. (?) FG GH HK .: .Pand Q are similar polygons. QED COB. I. The perimeters of two regular polygons of the same number of sides are to each other as any two homologous sides. 206 Proposition 199. Theorem. 236. The perimeters of two regular polygons... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...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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