| Robert Fowler Leighton - 1877 - 372 pages
...angle be if the chord passes through the centre of the circle ? 5. Prove that the perimeters of regular **polygons, of the same number of sides, are to each other as** the radii of the circumscribed circles. State, without proving, what the ratio of the areas of the... | |
| George Anthony Hill - Geometry - 1881 - 338 pages
...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... | |
| 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;... | |
| William Chauvenet - 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... | |
| George Albert Wentworth - Geometry - 1888 - 274 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.... | |
| George Albert Wentworth - Geometry - 1888 - 260 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.... | |
| Edward Albert Bowser - Geometry - 1890 - 414 pages
...the squares of any two homologous* sides. (379) Proposition 4. Theorem. 417. Tlie perimeters of any **two regular polygons of the same number of sides are to each other as** the radii of their circumscribed circles, or as the radii of their inscribed circles. Hyp. Let P and... | |
| |