 | Webster Wells - Geometry - 1898 - 264 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' Given P and P' the perimeters, R and R' the radii, and r and... | |
 | Webster Wells - Geometry - 1898 - 284 pages
...polygon AC, and K' of Aff. T7~ A Tt* (§ 322) ^ = ^=-^-. 777 73(2 «f2 -M Jl y-- That is, <fte areas q/~ 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. A '\ PROP. VI. THEOREM. *~~«^1 350. The... | |
 | 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.... | |
 | 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.... | |
 | 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... | |
 | 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... | |
 | 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 of sides are to each other as the squares of their radii, or as the squares of their apothems. PROP. VI. THEOREM. 350. The area of a... | |
 | 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... | |
 | 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'... | |
 | 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... | |
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The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop. 
