 | George Albert Wentworth - Geometry - 1877 - 426 pages
...V. PROPOSITION V. THEOREM. 373. The homologous sides of similar regular polygons have the same ratio as the radii of their circumscribed circles, and, also as the radii of their inscribed circles. 1) Let 0 and 0' be the centres of the two similar regular polygons ABС, etc., and A' B'С', etc. From... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...consequently similar (B. IV., Def. 4). Therefore, regular polygons, etc. Cor. The perimeters of two regular polygons of the same number of sides are to each other as their homologous sides, and their areas are as the squares of those sides (B. IV., Pr. 27). Scholium.... | |
 | George Anthony Hill - Geometry - 1880 - 348 pages
...areas of two similar polygons with their perimeters (see § 177, Corollary 2). 2. Prove that the areas of regular polygons of the same number of sides are to each other, (t.) as the squares of their sides ; («.) as the squares of their perimeters. 3. If in two hexagonal... | |
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...PROPOSITION V. THEOREM. .373. The homologous sides of similar regular polygons have the same ratio as the radii of their circumscribed circles, and, also as the radii of their inscribed circles. E Let 0 and 0' be the centres of the two similar regular polygons ABC, etc., and A'B'C', etc. From... | |
 | George Anthony Hill - Geometry - 1881 - 332 pages
...areas of two similar polygons with their perimeters (see § 177, Corollary 2). 2. Prove that the areas of regular polygons of the same number of sides are to each other, (»'.) as the squares of their sides; (»'.) as the squares of their perimeters. 3. If in two hexagonal parks a side... | |
 | Charles Scott Venable - 1881 - 380 pages
...called the apothem of the polygon. PROPOSITION X. THEOREM. The perimeters of regular polygons having the same number of sides are to each other as the radii of the circumscribed circles, and, also, as the radii of the inscribed circles ; their surfaces are to... | |
 | Harvard University - 1882 - 336 pages
...segment will have the same value in whatever direction the secant be drawn. 4. Prove that the perimeters of regular polygons of the same number of sides are to each other as the radii of the circumscribed circles, or as the radii of the inscribed circles, and hence show that the ratio... | |
 | Edward Olney - Geometry - 1883 - 344 pages
...homologous sides are to each other as the corresponding diagonals (387), 416. COROLLARY 1.—The perimeters of regular polygons of the same number of sides are to each other as the apothems of the polygons (382)417. COROLLARY 2.—The circumferences of circles are to each other as... | |
 | George Albert Wentworth - Geometry - 1884 - 422 pages
...PROPOSITION V. THEOREM. 373. Tlie homologous sides of similar regular polygons have the same ratio as ihe radii of their circumscribed circles, and, also as the radii of their inscribed circles. Let 0 and 0' be the centres of the two similar regular polygons ABC, etc., and A'B'C', etc. From 0... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...(Def. 3, Sec. VII, Book I). Therefore, the perimeters, etc. THEOREM XVII. The areas of two regular polygons of the same number of sides are to each other as the squares of their sides. Let ABCDE, abcde, be two regular polygons of the same number of sides; for... | |
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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. 
