| George Albert Wentworth - Geometry - 1899 - 496 pages
...§ 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... | |
| Webster Wells - Geometry - 1899 - 424 pages
...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,... | |
| Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
....-. = = .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... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...A'O'. (Why ?) But P:P' = AB:A'B' = AD:A'D'. (Why?) .'. P:P'=OD: O'D' = AO : A'O'. QED 407. COR. The **areas of regular polygons of the same number of sides are to each other as the squares** of their radii or apothems. Ex. 948. The lines joining the midpoints of the radii of a regular pentagon... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...AD: A'D'= OD: O'D' = AO: A'O'. But P:P' = AB:A'B' = AD:A'D'. (398) (Why?) (Why?) (Why?) 407. COR. The **areas of regular polygons of the same number of sides are to each other as the squares** of their radii or apothems. Ex. 948. The lines joining the midpoints of the radii of a regular pentagon... | |
| Arthur Schultze - 1901 - 260 pages
...Hence AD: A'D' = OD: O'D'= AO: A'O'. (W h y?) But P: P' = AB: A'B' = AD: A'D'. (Why ?) 407. COR. The **areas of regular polygons of the same number of sides are to each other as the squares** of their radii or apothems. Ex. 948. The lines joining the midpoints of the radii of a regular pentagon... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...Hence AD • A'D' = OD : O'D' = AO: A'O'. (Why ?) But P:P' = AB:A'B' = AD:A'D'. (Why?) 407. COR. The **areas of regular polygons of the same number of sides are to each other as the squares** of their radii or apothems. « Ex. 948. The lines joining the midpoints of the radii of a regular pentagon... | |
| John Alton Avery - Geometry, Modern - 1903 - 136 pages
...radius drawn to any vertex of a regular polygon bisects the angle at the vertex. 143. The perimeters **of regular polygons of the same number of sides are to each other as** any two homologous sides. 144. Find the area of a square inscribed in a circle whose radius is 6. 145.... | |
| George Albert Wentworth - Geometry - 1904 - 496 pages
...§ 351 OED 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. D' A! M Let... | |
| Fletcher Durell - Geometry - 1911 - 553 pages
...Art. 321. QED 268 BOOK V. PLANE GEOMETRY PROPOSITION VI. THEOREM 434. I. The perimeters of 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; II. Their areas are... | |
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