| William Chauvenet - Geometry - 1871 - 380 pages
...Therefore the polygons fulfill the two conditions of similarity. 10. 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 ; and their areas... | |
| Eli Todd Tappan - Geometry - 1873 - 288 pages
...corresponding side of the second. Therefore, the polygons are similar (433). 450. Corollary. — The areas of two regular polygons of the same number of sides are to each other as the squares of their homologous lines (436). 451. Corollary — The ratio of the radius to the side... | |
| Edward Olney - Geometry - 1872 - 472 pages
...the corresponding diagonals (35O), p : P : : r : HQED , .g,370. COR. 1. — The perimeters of regular polygons of the same number of sides are to each other as the apothems of the polygons. For the apothems are to each other as the sides of the polygons (351).... | |
| Edward Olney - Geometry - 1872 - 562 pages
...the corresponding diagonals (35O), p : P : : r : R q. ED 370. COR. 1. — 77(6 perimeters of regular polygons of the same number of sides are to each other as the apothems of the polygons. For the apothems are to each other as the sides of the polygons (351).... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...Therefore the polygons fulfill the two conditions of similarity. 10. 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; and their areas are... | |
| Benjamin Greenleaf - Geometry - 1873 - 202 pages
...have their angles equal, and their homologous sides proportional; hence they are similar (172). 222. Cor. The perimeters of two regular polygons of the...to each other as their homologous sides, and their areas are to each other as the squares of those sides (Theo. XXI.). 223. Scholium. The angle of a regular... | |
| Harvard University - 1873 - 732 pages
...construct a polygon similar to a given polygon^ upon a given line. 6. The homologous sides of 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. Prove ;... | |
| Benjamin Greenleaf - Geometry - 1874 - 206 pages
...have their angles equal, and their homologous sides proportional; hence they are similar (176). 222. Cor. The perimeters of two regular polygons of the...to each other as their homologous sides, and their areas are to each other as the squares of those sides (Theo. XXI.). 223. Scholium. The angle of a regular... | |
| L J V. Gerard - 1874 - 428 pages
...perimeter of the other, as any one side of the first is to any one side of the second, WWTBD COROLLARY I. The perimeters of two regular polygons of the same number of sides, are to each other as their radii. THEOREM 61. A regular polygon is symmetric to each radius produced lieyond the centre. Let there... | |
| Richard Wormell - 1876 - 268 pages
...XCII. Two circumferences are to one another as their radii. This proposition follows from the fact that the perimeters of two regular polygons of the same number of sides are as the radii of the circumscribed or the radii of the inscribed circles. Let GH be a circumference... | |
| |