 | Edward Olney - Geometry - 1883 - 352 pages
...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 1382). 417. COROLLARY 2.—The circumferences of circles are to each other... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...the two polygons (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... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...III. Regular polygons of the same number of sides are similar. Corollary. 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 their areas are to each other as the squares of these... | |
 | George Albert Wentworth - Geometry - 1888 - 272 pages
...the two polygons are similar. § 319 QED REGULAR POLYGONS AND CIRCLES. PROPOSITION V. THEOREM. 413. 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. D BA M. B' Let P and... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...altitudes of similar A have the same ratio as their bases). .-.P:P'=OA:O'A'=OM:OM'. QED 414. COR. The areas of two regular polygons of the same number of sides are to each other as the squares of the radii of their circumscribed circles, and also as the squares of the radii of their... | |
 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...a regular pentedecagon in a given circle. Proposition X. A Theorem. Proposition XI. A Theorem. 276. The perimeters of two regular polygons of the same number of sides are to each other : I. As their sides. II. As the radii of circumscribed circles. III. As the radii of inscribed circles.... | |
 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...275. Two regular polygons of the same number of sides are similar. Proposition XI. A Theorem. 276. The perimeters of two regular polygons of the same number of sides are to each other : I. As their sides. II. As the radii of circumscribed circles. III. As the radii of inscribed circles.... | |
 | George Albert Wentworth - 1889 - 264 pages
...circumscribed regular polygon. 211. Theorem. Two regular polygons of the same number of sides are similar. 212. Theorem. The perimeters of two regular polygons of the same number of sides have the same ratio as their radii, or as their apothems. 213. Theorem. Area of a regular polygon... | |
 | George Albert Wentworth - 1889 - 276 pages
...circumscribed regular polygon. 211. Theorem. Two regular polygons of the same number of sides are similar. 212. Theorem. The perimeters of two regular polygons of the same number of sides have the same ratio as their radii, or as their apothems. 213. Theorem. Area of a regular polygon... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...number of sides are to each other as any two homologous* sides. (322) 416. COR. 2. The areas of regular polygons of the same number of sides are to each other as the squares of any two homologous* sides. (379) * Since the polygons are regular, any side of one may be... | |
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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. 
