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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.
A Text-book of Geometry - Page 215
by George Albert Wentworth - 1888 - 386 pages

An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Part 1

Francis Joseph Grund - Geometry, Plane - 1834 - 202 pages
...Two regular polygons of the same number of sides are similar figures. 34. The sums of all the sides of two regular polygons of the same number of sides, are to each other in the same ratio, as the radii of the inscribed or circumscribed circles. 35. The areas of two regular...

Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 pages
...homologous sides proportional ; '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....

An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...214, 215, 216, 217, 218, 219, 220, 221, and 228. , , 232. Theorem. The homologous sides of regular polygons of the same number of sides are to each other...-and also as the radii of their inscribed circles. Demonstration. Let ABCD, &c., A'B'C'D', &c. (fig. 126) be regular polygons of the same number of sides,...

Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 288 pages
...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....

Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...area of a circle is equal to 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,...

Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

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...

Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

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...

An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 204 pages
...circumscribed about a circle by means of §§ 212-221, and 228. 232. Theorem. The homologous sides of regular polygons of the same number of sides are to each other...and also as the radii of their inscribed circles. Proof. Let ABCD, &c., A'B'C'D', &c. (fig. 126) be regular polygons of the same number of sides, and...