| 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... | |
| 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 - 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... | |
| 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... | |
| 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... | |
| 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 - 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'... | |
| 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... | |
| 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... | |
| 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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