| Adrien Marie Legendre - Geometry - 1819 - 208 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 - 367 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 other as the squares of those... | |
| Adrien Marie Legendre - 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, 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 - 158 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... | |
| 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)... | |
| James Hayward - Geometry - 1829 - 218 pages
...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 - 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 - 190 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... | |
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