 | Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...the two polygons (Def. 3, Sec. VII, Book I). Therefore, the perimeters, etc. THEOREM XVII. The areas of two regular polygons of the same number of sides are to each other as the squares of their sides. Let ABCDE, abcde, be two regular polygons of the same number of sides;... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...III. Regular polygons of the same number of sides are similar. 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 ; and their areas... | |
 | George Albert Wentworth - Geometry - 1888 - 272 pages
...the two polygons are similar. § 319 QED REGULAR POLYGONS AND CIRCLES. PROPOSITION V. THEOREM. 413. The perimeters of two regular polygons of the same number of sides are to each other as the radii of their circumscribed circles, and also as the radii of their inscribed circles. D BA M.... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...altitudes of similar A have the same ratio as their bases). .-.P:P'=OA:O'A'=OM:OM'. QED 414. COR. The areas of two regular polygons of the same number of sides are to each other as the squares of the radii of their circumscribed circles, and also as the squares of the radii of their... | |
 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...a regular pentedecagon in a given circle. Proposition X. A Theorem. Proposition XI. A Theorem. 276. The perimeters of two regular polygons of the same number of sides are to each other : I. As their sides. II. As the radii of circumscribed circles. III. As the radii of inscribed circles.... | |
 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...275. Two regular polygons of the same number of sides are similar. Proposition XI. A Theorem. 276. The perimeters of two regular polygons of the same number of sides are to each other : I. As their sides. II. As the radii of circumscribed circles. III. As the radii of inscribed circles.... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...the squares of any two homologous* sides. (379) Proposition 4. Theorem. 417. Tlie perimeters of any two regular polygons of the same number of sides are to each other as the radii of their circumscribed circles, or as the radii of their inscribed circles. Hyp. Let P and... | |
 | George Irving Hopkins - Geometry, Plane - 1891 - 208 pages
...sides are in the same ratio as the radii of their circumscribed circles. Sug. Consult 359 and 492. 495. The perimeters of two regular polygons of the same number of sides are in the same ratio as their apothegms. 496. The areas of two regular polygons of the same number of... | |
 | George Albert Wentworth - Geometry, Plane - 1892 - 266 pages
...sides proportional. Therefore the two polygons are similar. § 3^9 Q.LO. PROPOSITION V. THEOREM. 413. The perimeters of two regular polygons of the same number of sides are to each oilier as the radii of their circumscribed circles, and also as the radii of their inscribed circles.... | |
 | William Chauvenet - 1893 - 340 pages
...III. Regular polygons of the same number of sides are similar. 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 ; and their areas... | |
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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. 
