 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.  Wentworth's Plane Geometryτων George Albert Wentworth, David Eugene Smith - 1910 - 287 σελίδεςΠλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | Adrien Marie Legendre - 1819 - 574 σελίδες
...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 - 1825 - 280 σελίδες
...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 - 1825 - 276 σελίδες
...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 - 1828 - 346 σελίδες
...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 - 1829 - 228 σελίδες
...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) (bo) 2... | |
 | Timothy Walker - 1829 - 156 σελίδες
...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 - 1830 - 274 σελίδες
...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 - 1834 - 202 σελίδες
...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 - 1834 - 212 σελίδες
...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 - 1836 - 394 σελίδες
...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.... | |
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