| 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 - 264 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... | |
| Webster Wells - Geometry - 1894 - 398 pages
...A'B' B'C' C'D'' '" Therefore, AE and A'-E' are similar. = = CD PROPOSITION V. THEOREM. (§ 252.) 349. **The perimeters of two regular polygons of the same number of sides are to each other as their** radii, or as their apothems. D AFB D' Let P and P' denote their perimeters, R and R' their radii, and... | |
| George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...given parallelogram. State the 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,... | |
| Webster Wells - Geometry - 1894 - 400 pages
...Whence, AB* AW*' K' AB ^R_ A'B' ~ R' K ^ R2 _ Iff 7? '2 ~ .A. Ji (§ 320.) ,.'2 That is, 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 VI. THEOREM. 351. The... | |
| Webster Wells - Geometry - 1894 - 390 pages
...denote the areas of the polygons AE and A'-E'. Then, 7 JF = §-?. Whence, ^-_^^rj. That is, ŁAe areas **of two regular polygons of the same number of sides are to each other** ax the squares of their radii, or as the squares of their apothems. PROPOSITION VI. THEOREM. 351. The... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...are similar. AB OA Hence And 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... | |
| George Albert Wentworth - Geometry - 1896 - 50 pages
...polygons of the same number of 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.... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...are to each other 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... | |
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