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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 Text-book of Geometry - Page 215
by George Albert Wentworth - 1888 - 386 pages
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...= 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...
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Examinations Papers

1902 - 762 pages
...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...other as the radii of their circumscribed circles, or as the radii of their inscribed circles; II. Their areas are to each other as the squares of these...
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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...other as the radii of their circumscribed circles, or as the radii of their inscribed circles; II. Their areas are to each other as the squares of these...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1904 - 496 pages
...O'A' = OM : O'M'. 445 364 431 436 Also, . 357 351 361 Ax. 1 QED 448. COR. The areas of two regular polygons of the same number of sides are to each other as the squares of the radii of the circumscribed circles, and of the inscribed circles. 413 PROPOSITION...
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Plane Geometry

Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...PLANE GEOMETRY PROPOSITION VI. THEOREM 484. I. The perimeters of two regular polygons of the stone 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 to each other as the squares of these...
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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...
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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,...
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