| 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... | |
| 1902 - 786 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... | |
| 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.... | |
| 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 are to each... | |
| 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 are to each... | |
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| Education - 1907 - 656 pages
...prove according to its reading we would find ourselves doing the impossible. As for example take the **theorem, " The perimeters of two regular polygons...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 " Of the... | |
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