| Edward Albert Bowser - Geometry - 1890 - 414 pages
...have their homologous* sides proportional. . • . the polygons are similar. (307) QED 415. COR. 1. **The perimeters of regular polygons of the same number of sides are** to each other as any two homologous* sides. (322) 416. COR. 2. The areas of regular polygons of the... | |
| William Chauvenet - 1893 - 340 pages
...B'C', or CD : C'D', etc. Therefore the polygons fulfil the two conditions of similarity. 11. COROLLARY. **The perimeters of regular polygons of the same number of sides are** to each other as the radii of the circumscribed circles, or as the radii of the inscribed circles;... | |
| John Macnie - Geometry - 1895 - 390 pages
...similarly, all the sides about the equal A are proportional ; ... P is similar to p'. QED (284) 384 COR. **The perimeters of regular polygons of the same number of sides are as their** radii, or apothems; and their areas are as the squares of these lines. For the radii and apothems are... | |
| Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...m2 r2 s2 — =- — —='; -'. by substitution — = — ^ = -75 = —^ ' mrs P" a' m'2 r'2 s 2 2. **The perimeters of regular polygons of the same number of sides are** proportional to their apothems, their radii, or their sides. Proved with cor. 1. EXERCISES. 470. The... | |
| George Washington Hull - Geometry - 1897 - 408 pages
...§ 98 Hence /.A = Z G, ZJ3= Ztf, etc. Therefore ABCDEF and GHKLMN are similar. § 217 324. COR.— **The perimeters of regular polygons of the same number of sides are** to each other as the radii of the circumscribed circles, or as the radii of the inscribed circles;... | |
| James Howard Gore - Geometry - 1898 - 232 pages
...A'B' + B'C' + C'D' + etc. ~~ A'B ' ' Perimeter of AB - F_ AB . Perimeter of A'B' - F' ~ A'B'' that is, **The perimeters of regular polygons of the same number of sides are** to each other as any two homologous sides or lines. PROPOSITION III. THEOREM. 292. The area of a regular... | |
| William James Milne - Geometry, Modern - 1899 - 258 pages
...with the ratio of any two homologous sides? With the ratio of their radii? Of their apothems? Theorem. **The perimeters of regular polygons of the same number of sides are** to each other as their radii and also as their apothems. D MG Data : Any two regular polygons of the... | |
| William James Milne - Geometry - 1899 - 398 pages
...the ratio of any two homologous sides? With the ratio of their radii? Of their apothems ? Theorem. **The perimeters of regular polygons of the same number of sides are** to each other as their radii and also as their apothems. D M a Data : Any two regular polygons of the... | |
| Harvard University - Geometry - 1899 - 39 pages
...sides will be formed. THEOREM IV. Regular polygons of the same number of sides are similar. THEOREM V. **The perimeters of regular polygons of the same number of sides are** to each other as the radii of the circumscribed circles, or as the radii of the inscribed circles ;... | |
| Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...2 —,- -, = -, = —,; s'sby substitution — = -;-= = -.-, = -= s m' r' s' p' a m 2 r' 2 s' 2 2. **The perimeters of regular polygons of the same number of sides are** proportional to their apothems, their radii, or their sides. Proved with cor. 1. Exercises. 442. The... | |
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