| Adrien Marie Legendre - Geometry - 1819 - 574 pages
...their homologous sides proportional ; therefore they are similar (162). 264. Corollary. The perimeters **of two regular polygons of the same number of sides are to each other as** their homologous sides, and their surfaces are as the squares of these sides (221). 265. Scholium.... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...their homologous sides proportional ; therefore they are similar (162). 264. Corollary. The perimeters **of two regular polygons of the same number of sides are to each other as** their homologous sides, and their surfaces are as the squares of these sides (221). 265. Scholium.... | |
| Adrien Marie Legendre - Geometry - 1825 - 276 pages
...their homologous sides proportional ; therefore they are similar (162). 264. Corollary. The perimeters **of two regular polygons of the same number of sides are to each other as** their homologous sides, and their surfaces are as the squares of these sides (221). 265. Scholium.... | |
| Adrien Marie Legendre - Geometry - 1828 - 346 pages
...their homologous sides proportional ; consequently (102.) they -are similar. 264. Cor. The perimeters **of two regular polygons of the same number of sides, are to each other as** their homologous sides, and their surfaces, as the squares of those sides (221.) 265. Scholium. The... | |
| James Hayward - Geometry - 1829 - 228 pages
...circumscribed circles; and ON, on, are radii of the inscribed circles. We therefore say—The areas of regular **polygons of the same number of sides, are to each other as the** squares of the radii of the circumscribed circles, and also of the inscribed circles. (on)* 0 (boc)... | |
| Timothy Walker - Geometry - 1829 - 156 pages
...that it is made up of infinitely small straight lines. 95. THEOREM. — The pe.rime.le.rs of regular **polygons of the. same number of sides are to each other as the** radii of their circumscribed circles. By th^orimeter of a polygon we mean the sum of its sides;^Snen... | |
| Francis Joseph Grund - Geometry, Plane - 1834 - 202 pages
...the areas of the polygons and the areas of the circles themselves will be imperceptible ; and because **the areas of two regular polygons of the same number of sides are** in the same ratio as the areas of the squares upon the radii of the circles in which they are inscribed... | |
| Francis Joseph Grund - Geometry, Plane - 1834 - 212 pages
...are to each other in the proportion of the radii of the inscribed or circumscribed circles. 2. Tlie **areas of two regular polygons of the same number of sides, are** in the same ratio as the squares constructed upon the radii of the inscribed or circumscribed circles.... | |
| Adrien Marie Legendre - Geometry - 1836 - 394 pages
...sides proportional ; 'consequently they are einrilai (Book IV. Def. 1.). • . _' J Cor. The perimeters **of two regular polygons of the same number of sides, are to each other as** their homologous sides, and their surfaces are to each other as the squares of those sidei (Book IV.... | |
| Benjamin Peirce - Geometry - 1837 - 216 pages
...214, 215, 216, 217, 218, 219, 220, 221, and 228. , , 232. Theorem. 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. Demonstration.... | |
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