 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.  Elements of Geometry - Page 82by Adrien Marie Legendre - 1841 - 235 pagesFull view - About this book
 | 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 - 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... | |
 | 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.... | |
 | 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... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 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... | |
 | Webster Wells - Geometry - 1898 - 250 pages
...polygon AC, and K' of A'C ' . But -Br. whence K_K>_r> *' A'B' ~R'~r" ' K' -R»-^ 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. PROP. VI. THEOREM. 350. The area of... | |
 | Webster Wells - Geometry - 1898 - 284 pages
...polygon AC, and K' of Aff. T7~ A Tt* (§ 322) ^ = ^=-^-. 777 73(2 «f2 -M Jl y-- That is, <fte areas q/~ 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. A '\ PROP. VI. THEOREM. *~~«^1 350.... | |
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