 | Adrien Marie Legendre - Geometry - 1819 - 576 pages
...angles equal and 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. The angle... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 pages
...angles equal and 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. The angle... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...angles equal and 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. The angle... | |
 | Adrien Marie Legendre - Geometry - 1828 - 346 pages
...angles equal, and 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 angle... | |
 | 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... | |
 | 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
...perimeter of that figure. The above proportion may therefore be expressed in shorter terms; namely, the perimeters of two regular polygons of the same number of sides, are to each other in the proportion of the radii of the inscribed or circumscribed circles. 2. The areas of two regular... | |
 | Francis Joseph Grund - Geometry, Plane - 1834 - 212 pages
...perimeter of that figure. The above proportion may therefore be expressed in shorter terms ; namely, the perimeters of two regular polygons of the same number of sides, are to each other in the proportion of the radii of the inscribed or circumscribed circles. 2. Tlie areas of two regular... | |
 | Francis Joseph Grund - Geometry, Plane - 1834 - 204 pages
...each other in 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.... | |
 | Francis Joseph Grund - Geometry, Plane - 1834 - 202 pages
...Two regular polygons of the same number of sides are similar figures. 34. The sums of all the sides of two regular polygons of the same number of sides, are to each other in the same ratio, as the radii of the inscribed or circumscribed circles. 35. The areas of two regular... | |
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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. 
