 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...(379) HOOK V.— REGULAR POLYGONS. 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 P'... | |
 | George Albert Wentworth - Geometry - 1888 - 466 pages
...proportional. Therefore the two polygons are similar. § 319 QED 412. COR. The areas of two regular polygons of the same number of sides are to each other as the squares of any two homologous sides. § 376 PROPOSITION V. THEOREM. 413. The perimeters of two regular polygons... | |
 | William Chauvenet - 1893 - 340 pages
...PROPOSITION 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 are... | |
 | 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,... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...sides are to each other as their radii or as their apothems. 483. COR. II. The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems. PROPOSITION V. THEOREM 484, The circumference of... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...as their radii or as their apothems. Hint.— Apply § 308. 483. COR. II. The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems. PROPOSITION V. THEOREM 484. The circumference of... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...sides are to each other as the squares of any two homologous sides. 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. 414. Cor. The... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...similar. § 285 AB OA AB OF And - = -- §2QO A'B' O'F' QED 482. COR. I. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. Hint.— Apply § 308. 483. COR. II. The areas of two regular polygons... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...A'B' AB O'A' OF §466 §150 §285 §274 §290 A'B' O'F' QED 482. COR. I. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. Hint.— Apply § 308. 483. COR. II. The areas of two regular polygons... | |
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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. 
