| Adrien Marie Legendre - Geometry - 1819 - 576 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, 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... | |
| 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... | |
| Benjamin Peirce - Geometry - 1837 - 216 pages
...the angle ABC= A'B'C. Hence, by art. 198, OP : OP' = AB : A'B' = OA : O'A'. 233. Corollary. Hence, **the perimeters of regular polygons of the same number of sides are,** by art. 207, The Ratio of a Circumference to its Diameter. to each other' as the radii of their inscribed... | |
| Adrien Marie Legendre - Geometry - 1841 - 288 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 tlie radii of the inscribed circles ; and their... | |
| Benjamin Peirce - Geometry - 1847 - 204 pages
...OA : O'A'. . ' ' ..'* <*»• The Ratio of a Circumference to its Diameter. 233. Corollary. Hence, **the perimeters of regular polygons of the same number of sides are,** by § 207, to each other as the radii of their inscribed circles, and also as the radii of their circumscribed... | |
| Thomas Lund - Geometry - 1854 - 520 pages
...AD, AE, AF indefinitely, and in AB produced take Ab equal to G, and proceed as before. 91. PROP. VI. **The perimeters of regular polygons of the same number of sides are** proportional to the radii of their inscribed or circumscribing circles ; and their areas are proportional... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...or CD : C'D', etc. Therefore the polygons fulfill the two conditions of similarity. 10. Corollary. **The perimeters of regular polygons of the same number of sides are** to each other as the radii of the circumscribed circles, or as the radii of the inscribed circles ;... | |
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