| George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...334), and two regular polygons of the same number of sides are similar. PROPOSITION IV. THEOREM 375. **The perimeters of two regular polygons of the same number of sides are to each other as** their radii, and also as their apothems. D' AMU A' W B' Given the regular polygons with perimeters... | |
| George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...sides are to each other as the squares on any two corresponding sides. PROPOSITION IV. THEOREM 375. **The perimeters of two regular polygons of the same number of sides are to each other as** their radii, and also as their apothems. D' AMB A'~ M' B' Given the regular polygons with perimeters... | |
| George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 491 pages
...'sides are to each other as the squares on any two corresponding sides. PROPOSITION IV. THEOREM 375. **The perimeters of two regular polygons of the same number of sides are to each other as** their radii, and also as their apofhems. D r AMB A' M.' B' Given the regular polygons with perimeters... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...AO : A'O'. Hence, But .'. P: P' = OD : ' = AO:A'0'. (303) (Why?) QBD 417. COR. The areas of regular **polygons of the same number of sides are to each other as the** squares of their radii or apothems. Ex.- 1315. The lines joining the mid-points of the radii of a regular... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...P:P' = AB:A'B' = AD:A'D'. (Why?) .'. P: P'= OD : O'D'= AO:A'O'. QED 417. COR. The areas of regular **polygons of the same number of sides are to each other as the** squares of their radii or apothems. Ex. 1315. The lines joining the mid-points of the radii of a regular... | |
| Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry, Plane - 1915 - 320 pages
...polygon, and the sum of the areas of the triangles is the area of the polygon, 479. Theorem. The areas **of two regular polygons of the same number of sides are to each other as the** squares of their radii, and also as the squares of their apothems. EXERCISES 1. Prove that the area... | |
| John Charles Stone, James Franklin Millis - Geometry - 1916 - 298 pages
...number of sides are to each other as the squares of their sides. The proof is left to the student. 253. **Theorem. — The perimeters of two regular polygons of the same number of sides are to each other as** their radii, or as their apothems. Hypothesis. AB and CD are sides, and M and N the centers, respectively,... | |
| William Betz - Geometry - 1916 - 536 pages
...the sides of the polygons proportional ? 2. Are the polygons mutually equiangular ? 452. COROLLARY 1. **The perimeters of two regular polygons of the same number of sides are to each other as** any two homologous sides ; and the areas of two regular polygons of the same number of sides are to... | |
| John Charles Stone, James Franklin Millis - Geometry - 1916 - 306 pages
...-— . = -— -^ = etc. Ax. V MN NO 9. .-. ABCD MNOP -. Def. sim. poly. 252. Corollary. — The areas **of two regular polygons of the same number of sides are to each other as the** squares of their sides. 253. Theorem. — The perimeters of two regular polygons of the same number... | |
| Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...similar. Suggestion. The student can prove this by showing a close connection with Art. 226. Corollary 1. **The perimeters of two regular polygons of the same number of sides are** proportional to their sides, to their apothems, to their radii. Corollary 2. The areas of two regular... | |
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