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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 surfaces are to each other as the squares of those sides (Book IV. "
Elements of Geometry and Trigonometry Translated from the French of A.M ... - Page 105
by Charles Davies - 1849 - 359 pages
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Examinations Papers

1902
...from three given points and from a given straight line. When is it impossible to do so ? Q. Prove that the perimeters of two regular polygons of the same number of sides are to one another as the radii of their circumscribing circles. Prove that in a given circle the perimeter...
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Plane Geometry by the Suggestive Method

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

Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...homologous sides proportional. 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...
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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 - 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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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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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. 2s ( 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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