| Adrien Marie Legendre - Geometry - 1819 - 208 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 - 1822 - 367 pages
...of the inscribed circle. PROPOSITION VIII. THEOREM. The perimeters of two regular polygons, Juming **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... | |
| Adrien Marie Legendre - 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, 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 - 1828 - 316 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 - 158 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...other as the radii of their circumscribed circles.** By th^orimeter of a polygon we mean the sum of its sides;^Snen we say that the perimeter ABCDEF (fig.... | |
| James Hayward - Geometry - 1829 - 172 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)... | |
| 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 - 190 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 - 359 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.... | |
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