 | 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... | |
 | 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 - 394 pages
...denote the areas of the polygons AE and A'-E'. Then, 7 JF = §-?. Whence, ^-_^^rj. That is, £Ae 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 - Mathematics - 1896 - 68 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.... | |
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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 surfaces are to each other as the squares of those sides (Book IV. 
