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" The perimeters of regular polygons of the same number of sides have the same ratio as their radii or as their apothems. ADB A' D' B' Hyp. P and P' are the perimeters of two regular polygons having the radii OA and O'A', and the apothems OD and O'D', respectively.... "
Metrical Geometry: An Elementary Treatise on Mensuration - Page 20
by George Bruce Halsted - 1881 - 232 pages
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...rectilinear figures, &c. PROP. LXXXV. THEOR. The circumferences of equilateral polygons, which have the same number of sides, have the same ratio as the radii of their circumscribing circles. Let ABCDEF, GHKILM be 2 equilat. polygons having an =no. sides inscrib. in...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...rectilinear figures, &c. PROP. LXXXV. THEOR. The circumferences of equilateral polygons, which have the same number of sides, have the same ratio as the radii of their circum-scribing circles. Let ABCDEF, GHKILM be 2 equilat. polygons having an =no. sides inscrib. in...
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Wentworth & Hill's Exercise Manuals: Geometry, Issue 3

George Albert Wentworth - 1884 - 264 pages
...Theorem. Two regular polygons of the same number of sides are similar. . 212. Them-em. 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 = } perimeter X apothem....
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The Elements of Geometry

George Bruce Halsted - Geometry - 1885 - 389 pages
...similar polygon similarly described on the second as the first sect is to the third. THEOREM XX. 548. The perimeters of any two regular polygons of the...ratio as the radii of their circumscribed circles. PROOF. The angles of two regular polygons of the same number of sides are all equal, and the ratio...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1886 - 394 pages
...limits are equal. THEOREM II. 800. Any two circles are to each other as their radii. PROOF. By 548, the perimeters of any two regular polygons of the...ratio as the radii of their circumscribed circles. The inscribed regular polygons remaining similar to each other when the number of sides is doubled,...
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Exercise Manuals, Issue 3

George Albert Wentworth - 1889 - 276 pages
...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 = i perimeter X apothem....
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Wentworth & Hills's Exercise Manuals: Geometry, Issue 3

George Albert Wentworth - 1889 - 264 pages
...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 = J perimeter X apothem....
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1891 - 424 pages
...sides are to each other as the squares of any two homologous* sides. (379) Proposition 4. Theorem. 417. The 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...
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Plane and Solid Geometry: Suggestive Method

Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 524 pages
...parts equal in area. SO2. PROPOSITION IV. THEOREM. tii' PROPOSITION V. THEOREM. 303. The perimeters of two regular polygons of the same number of sides have the same ratio at their radii, or their apothems. AM 13 Let ABCDEF and HK LPB Trepresent two regular polygons of the...
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Yale University Entrance Examinations in Mathematics: 1884 to 1898

Mathematics - 1898 - 228 pages
...circle is drawn, find the locus of the middle point of that chord. 4. (a) The perimeters of regular polygons of the same number of sides have the same ratio as any two homologous sides, (b) The areas of regular polygons of the same number of sides have the same...
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