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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.
Elements of Geometry Upon the Inductive Method: To which is Added an ... - Page 65
by James Hayward - 1829 - 172 pages

## Plane and Solid Geometry

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...

## The Essentials of Geometry

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,...

## The Elements of Plane Geometry

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...

## Plane and Solid Geometry

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...

## Plane and Solid Geometry

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...

## Plane Geometry

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...

## Plane and Solid Geometry

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...

## Plane Geometry by the Suggestive Method

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....