 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 - Page 82by Adrien Marie Legendre - 1841 - 235 pagesFull view - About this book
 | Elias Loomis - Conic sections - 1849 - 252 pages
...radius of the inscribed circle. Therefore, the area of a regular polygon, &c. PROPOSITION VIII. THEOREM. The perimeters of two regular polygons of the same number of sides, are as the radii of the inscribed or circumscribed circles, and their surfaces are as the squares of the... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...consequently they are similar, (B. IV, Def. 3.) Cor. The perimeters of two regular polygons having 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, (B. IV, Prop.-xvi.) (92.) It has been shown,... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...sides taken in the same order proportional ; consequently, they are similar (B. IV., D. 1). Cor. 1. The perimeters of two regular polygons of the same...as their homologous sides, and their surfaces are to each other as the squares of those sides (B. iv., P. 27). Cor. 2, The angle of a regular polygon,... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...sides taken in the same order proportional ; consequently, they are similar (B. IV., D. 1). Cor. 1. The perimeters of two regular polygons of the same...as their homologous sides, and their surfaces are to each other as the squares of those sides (B. 1v., P. 27). 136 GEOMETRY. Cor. 2. The angle of a regular... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...triangle OGA, OG = >/OA2-AG2; that is, r = ^W^^tf. We also have p=na; consequently, na THEOREM vI. The perimeters of two regular polygons of the same number of sides are proportional to the radii of their inscribed circles, or of their circumscribed circles ; and their... | |
 | Elias Loomis - Conic sections - 1857 - 242 pages
...IV.). Therefore, regular polygons, &c. Cor. The perimeters of two regular polygons of the same ..lumber of sides, are to each other as their homologous sides. and their areas are us the squares of those sides (Prop. XXVI., B. IV.). Scholium. The angles of a regular polygon... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...IV.). Therefore, regular polygons, &c. Cor. The perimeters of two regular polygons of the same Climber of sides, are to each other as their homologous sides. and their areas are us the squares of those sides ^Prop. XXVI., B. IV.). Scholium. The angles of a regular polygon... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...right-angled triangle OGA, OG = VOA'-AG2; that is, r = We also have j> = na; consequently, "" - a THEOREM VI. The perimeters of two regular polygons of the same number of sides are proportional to the radii of their inscribed circles, or of their circumscribed circles ; and their... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...angles equal, and their homologous sides proportional ; hence they are similar (Art. 210). 347. 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 (Prop. XXXI. Bk. IV.). 348. Scholium. The angle... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...angles equal, and their homologous sides proportional ; hence they are similar (Art. 210). 347. 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 (Prop. XXXI. Bk. IV.). 348. Scholium. The angle... | |
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