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. A Text-book of Geometry - Page 211by George Albert Wentworth - 1888 - 386 pagesFull view - About this book
| Adrien Marie Legendre - Geometry - 1819 - 574 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.... | |
| 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
...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, 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.... | |
| 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... | |
| 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 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
...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 - 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. The... | |
| 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... | |
| |