| 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... | |
| 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 - 566 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 - 424 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 - 264 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... | |
| Elias Loomis - Geometry - 1877 - 458 pages
...of the inscribed circle. Therefore the a'rea of a regular polygon, etc. PROPOSITION VIII. THEOREM,. **The perimeters of two regular polygons of the same number of sides are to each other as** the radii of the inscribed or circumscribed circles, and their areas are as the squares of these radii.... | |
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