 | George Albert Wentworth - Geometry, Plane - 1899 - 278 pages
...proportional. Therefore the two polygons are similar. § 351 QBD 446. COR. The areas of two regular polygon* of the same number of sides are to each other as the squares of any two homologous sides. § 412 REGULAR POLYGONS AND CIRCLES. PROPOSITION V. THEOREM. 447.... | |
 | 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 - 394 pages
...Hence AD: A'D' = OD: O'D' = AO: A'O'. (Why?) But P:P' = AB:A'B' = AD: A'D'. (WRy?) 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... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...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... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...(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... | |
 | Arthur Schultze - 1901 - 260 pages
...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... | |
 | 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.... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...Hence K and K' are similar. Art. 321. QED PROPOSITION VI. THEOKEM 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 to each other as the squares of these... | |
 | 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 to each other as the squares of these... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...PLANE GEOMETRY PROPOSITION VI. THEOREM 484. I. The perimeters of two regular polygons of the stone 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 to each other as the squares of these... | |
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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. 
