 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.  Elements of Geometry - Σελίδα 76των Adrien Marie Legendre - 1819 - 208 σελίδεςΠλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | Edward Olney - 1872 - 562 σελίδες
...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).... | |
 | Benjamin Greenleaf - 1873 - 202 σελίδες
...their angles equal, and their homologous sides proportional; hence they are similar (172). 222. Cor. The perimeters of two regular polygons of the same...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 σελίδες
...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 - 1874 - 206 σελίδες
...their angles equal, and their homologous sides proportional; hence they are similar (176). 222. Cor. The perimeters of two regular polygons of the same...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 σελίδες
...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 σελίδες
...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 - 1877 - 458 σελίδες
...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.... | |
 | Robert Fowler Leighton - 1877 - 372 σελίδες
...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... | |
 | George Anthony Hill - 1881 - 332 σελίδες
...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... | |
 | Edward Olney - 1883 - 352 σελίδες
...are to each other as the corresponding diagonals (387), 416. COROLLARY 1.—The perimeters of regular polygons of the same number of sides are to each other as the apothems of the polygons 1382). 417. COROLLARY 2.—The circumferences of circles are to each other... | |
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