 | Francis Joseph Grund - Geometry, Plane - 1830 - 274 pages
...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 - 202 pages
...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. 86. The... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...; 'consequently they are einrilai (Book IV. Def. 1.). • . _' J Cor. The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their surfaces are to each other as the squares of those sidei (Book IV.... | |
 | 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... | |
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...its circumference multiplied by half its radius.* PROP. VII. THEOREM. The perimeters of two regular polygons of the same number of sides, are to each other as the radii of the circumscribed circles : and their areas are to each other, as the squares of those radii. Let ABCDEF, IKLPQR, be two regular... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...the apothem of the polygon. PROPOSITION VIII. THEOREM. The perimeters of two regular polygons, having 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 ; and their surfaces are to each other as the squares... | |
 | Nathan Scholfield - 1845 - 894 pages
...circle would be obtained. PROPOSITION XIII. THEOREM. The perimeters of two regular polygons, having the same number of sides, are to each other as the radii of the circumscribed circles, and also, as the inscribed circles ; and their areas are to each other as the squares of those radii.... | |
 | 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 Tate (mathematical master.) - 1848 - 284 pages
...perimeter, .'. Area polygon = the perimeter x^ FO. i; n. u 72. THEOREM. The perimeters of two regular polygons of the same number of sides are to each other as the radii of the circumscribed circles ; and moreover their areas are to each other as the squares of the radii. Let i and s be the centres... | |
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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. 
