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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. "
A Treatise on Special Or Elementary Geometry - Page 152
by Edward Olney - 1877 - 239 pages
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Plane and Solid Geometry

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...
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Plane and Solid Geometry

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...
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Plane Geometry by the Suggestive Method

John Alton Avery - Geometry, Modern - 1903 - 136 pages
...142. The 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....
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Plane Geometry

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...
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Plane and Solid Geometry

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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Plane and Solid Geometry

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...
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 431 pages
...will be inscribed. PLANE GEOMETRY— BOOK V PROPOSITION V. THEOREM 448 The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. HYPOTHESIS. P and P' are the perimeters, O and O' the centers, OA...
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 440 pages
...will be inscribed. PLANE GEOMETRY — BOOK V PROPOSITION V. THEOREM 448 The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. B' HYPOTHESIS. P and P' are the perimeters, O and 0' the centers,...
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Pennsylvania School Journal, Volume 56

Education - 1907 - 656 pages
...find ourselves doing the impossible. As for example take the theorem, " 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." The phrase...
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Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...and are, therefore, equal. .-. ABCDEF ~ GHIKLM. §363 QED 471. COK. 1. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. BOOK V. PLANE GEOMETRY. PROPOSITION VI. THEOREM. 473. The area of...
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