| Adrien Marie Legendre - Geometry - 1819 - 574 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 - 394 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 - 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, 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 - 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...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 - 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)... | |
| 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 - 394 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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