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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 - Page 82
by Adrien Marie Legendre - 1841 - 235 pages
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Plane and Solid Geometry

Fletcher Durell - Geometry - 1911 - 553 pages
...Hence .Kand Kf are similar. 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...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1904 - 496 pages
...the two polygons are similar. § 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...
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Catalogue ...

Yale University. Sheffield Scientific School - 1905 - 1074 pages
...equivalent to a given square and having the difference of its base and altitude equal to a given line. 4. The perimeters of two regular polygons' of the same number of sides are in the same ratio as the radii of the inscribed or circumseribed circles. 5. To construct a circle...
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 440 pages
...double the number of sides 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, OA and...
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 431 pages
...of double the number of sides 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 and O'A'...
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Pennsylvania School Journal, Volume 56

Education - 1907 - 652 pages
...according to its reading we would 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
...— •— st. 2£s (§ 193), 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 a regular...
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Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...= w~ st. 2£s (§ 193), n and are, therefore, equal. .-. ABCDEF ~ GHIKLM. § 363 0. ED 471. COR. 1. The perimeters of two regular polygons of the same number of sides are to each oiher as their radii or as their apothems. BOOK V. PLANE GEOMETRY. PROPOSITION VI. THEOREM. 473. The...
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Wentworth's Plane Geometry

George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...r:r' = a: a', by Ax. 8. §373 §291 §364 Ax. 8 §288 §282 §286 §282 OED 376. COROLLARY. The areas of two regular polygons of the same number of sides are to each other as the squares on the radii of the circumscribed circles, and also as the squares on the radii of the...
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Plane Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 332 pages
...inches and 72 inches, respectively ; what is the ratio of their areas ? PROPOSITION VIII. THEOREM 538. The perimeters of two regular polygons of the same number of sides are to each otlIer as their radii or as tlIeir apothems. E' Given regular polygons ABCDE and A'B'C'D'S' having...
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