 | 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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The area of a regular polygon is equal to half the product of its perimeter and apothem. 
