 | George Anthony Hill - Geometry - 1881 - 332 pages
...areas of two similar polygons with their perimeters (see § 177, Corollary 2). 2. Prove that the areas of regular polygons of the same number of sides are to each other, (»'.) as the squares of their sides; (»'.) as the squares of their perimeters. 3. If in two hexagonal parks a side... | |
 | Edward Olney - Geometry - 1882 - 262 pages
...homologous sides are to each other as the corresponding diagonals (350), p : P : : r : RQED 370. COR. 1. — The perimeters of regular polygons of the same number of sides are to each other as the apothems of the polygons. For the apothems are to each other as the sides of the polygons (351). 371.... | |
 | Edward Olney - Geometry - 1883 - 344 pages
...the homologous sides are to each other as the corresponding diagonals (387), 416. COROLLARY 1.—The perimeters of regular polygons of the same number of sides are to each other as the apothems of the polygons (382)417. COROLLARY 2.—The circumferences of circles are to each other as... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...(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; for... | |
 | Edward Olney - Geometry - 1886 - 348 pages
...the homologous sides are to each other as the corresponding diagonals (387), pr 416. COROLLARY 1. — The perimeters of regular polygons of the same number of sides are to each other as the apothems of the polygons (382)417. COROLLARY 2. — The circumferences of circles are to each other... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 336 pages
...circumscribed about any regular polygon, and a circle may also be inscribed in it. PROPOSITION III. Corollary. The perimeters of regular polygons of the same number...radii of the circumscribed circles, or as the radii of th^inscribed circles ; and their areas are to each other as the squares of these radii. Regular polygons... | |
 | George Albert Wentworth - Geometry - 1888 - 272 pages
...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... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...have their homologous* sides proportional. . • . the polygons are similar. (307) QED 415. COR. 1. The perimeters of regular polygons of the same number of sides are to each other as any two homologous* sides. (322) 416. COR. 2. The areas of regular polygons of the same number of sides... | |
 | Webster Wells - Geometry - 1894 - 400 pages
...A'-E' are similar. __ A'B' B'C' '' (§ 252.) PROPOSITION V. THEOREM. 349. The perimeters of two regular polygons of the same number of sides are to each other as their radii, or as their apothems. I" B' Let AE and A'-E' be two regular polygons of the same number... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...difference in the meaning of the word equal here and in question 2. 6. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. Define regular polygons, their radii, their apothems. CORNELL UNIVERSITY,... | |
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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. 
