 | Adrien Marie Legendre - 1819 - 574 σελίδες
...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.... | |
 | Adrien Marie Legendre - 1822 - 394 σελίδες
...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 other as the squares of those... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 280 σελίδες
...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.... | |
 | Adrien Marie Legendre - 1825 - 276 σελίδες
...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.... | |
 | Adrien Marie Legendre - 1828 - 346 σελίδες
...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... | |
 | 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 we say... | |
 | 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)... | |
 | James Hayward - 1829 - 218 σελίδες
...circles ; it follows (92) that — In regular polygons of the same number of sides, the perimeters are to each other as the radii of the circumscribed circles, and also as the radii of the inscribed circles. 140. Each angle of an equilateral triangle is an angle... | |
 | Francis Joseph Grund - 1830 - 274 σελίδες
...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 - 1834 - 204 σελίδες
...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. The... | |
| |
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. 
