 | 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 ; and then by... | |
 | 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.... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...their angles equal, and their homologous sides proportional; hence they are similar (176). 222. Cor. The perimeters of two regular polygons of the same number of sides are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Theo. XXI.).... | |
 | Harvard University - 1874 - 668 pages
...a straight line, to draw a circle through the point! and touching the line. 11. Prove that regular polygons of the same number of sides are to each other as the squares of the radii of their circumscribed or of their inscribed circles. Extend the theorem to the... | |
 | 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... | |
 | Robert Fowler Leighton - 1877 - 372 pages
...angle be if the chord passes through the centre of the circle ? 5. Prove that the perimeters of regular polygons, of the same number of sides, are to each other as the radii of the circumscribed circles. State, without proving, what the ratio of the areas of the polygons is. 6. Find the area of the circle... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...proportional ; they are consequently similar (B. IV., Def. 4). Therefore, regular polygons, etc. Cor. The perimeters of two regular polygons of the same number of sides are to each other as their homologous sides, and their areas are as the squares of those sides (B. IV., Pr. 27). Scholium.... | |
 | Charles Scott Venable - 1881 - 380 pages
...called the apothem of the polygon. PROPOSITION X. THEOREM. The perimeters of regular polygons having the same number of sides are to each other as the radii of the circumscribed circles, and, also, as the radii of the inscribed circles ; their surfaces are to each other as the squares of these... | |
 | George Anthony Hill - Geometry - 1881 - 332 pages
...similar polygons with their perimeters (see § 177, Corollary 2). 2. Prove that the areas of regular polygons of the same number of sides are to each other, (»'.) as the squares of their sides; (»'.) as the squares of their perimeters. 3. If in two hexagonal parks a side... | |
 | Harvard University - 1882 - 336 pages
...have the same value in whatever direction the secant be drawn. 4. Prove that 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 hence show that the ratio of the circumference to the... | |
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The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop. 
