 | Adrien Marie Legendre - Geometry - 1819 - 576 pages
...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
...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
...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
...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... | |
 | Timothy Walker - Geometry - 1829 - 156 pages
...(10) namely, 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 - 1830 - 274 pages
...the same ratio, as the radii of the inscribed or circumscribed circles. 35. The areas of two regular polygons of the same number of sides, are to each other as the areas of the squares, constructed upon the radii of the inscribed or circumscribed circles. 36. The... | |
 | Francis Joseph Grund - Geometry, Plane - 1834 - 202 pages
...the same ratio, as the radii of the inscribed or circumscribed circles. 35. The areas of two regular polygons of the same number of sides, are to each other as the areas of the squares constructed upon the radii of the inscribed or circumscribed circles. 86. The... | |
 | Adrien Marie Legendre - Geometry - 1836 - 382 pages
...; '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
...arts. 212, 213, 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.... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...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.... | |
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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. 
