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. Plane Geometry - Page 255by Fletcher Durell, Elmer Ellsworth Arnold - 1917 - 318 pagesFull view - About this book
| Adrien Marie Legendre - Geometry - 1819 - 574 pages
...circle is the same as the perpendicular let fall from the centre upon one of the sides. THEOREM. 282. The perimeters of regular polygons of the same number of sides are as the radii of the circumscribed circles, and also as the radii of Hie inscribed circles ; and their... | |
| 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 other as the squares of... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...circle is the same as the perpendicular let fall from the centre upon one of the sides. THEOREM. 282. The perimeters of regular polygons of the same number of sides are as the radii of the circumscribed circles, and also as the radii of the inscribed circles ; and their... | |
| Adrien Marie Legendre - Geometry - 1825 - 276 pages
...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
...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 - 138 pages
...given of a curved line (10) namely, that it is made up of infinitely small straight lines. 95. — The perimeters of regular polygons of the same number of sides are to each other as the radii of their circumscribed circles — . By the perimeter of a polygon we mean the sum of its sides. Then... | |
| Timothy Walker - Geometry - 1829 - 156 pages
...(10) namely, 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)... | |
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