| Raleigh Schorling, William David Reeve - Mathematics - 1922 - 460 pages
...equal. 4. This is obvious from 3. 5. By definition of similar polygons. 420 535. Theorem. The perimeter of two regular polygons of the same number of sides are to each other as their radii or as their apothems. Given the regular polygons AB • • • and A'B • • • of the same... | |
| Raleigh Schorling, William David Reeve - Mathematics - 1922 - 476 pages
...equal. . 4. This is obvious from 3. 5. By definition of similar polygons. 534. Corollary. The areas of two regular polygons of the same number of sides are to each other as the squares of their sides. 535. Theorem. The perimeter of two regular polygons of the same number... | |
| Clarence Addison Willis - Geometry, Modern - 1922 - 320 pages
...of a regular hexagon whose apothem is 34.64? THE SECOND STEP IN CLASSIFICATION 336. Theorem I. — The perimeters of two regular polygons of the same number of sides are proportional to the radii of the polygons. Hypothesis. — Regular polygons 0 and 0', of the same number... | |
| Clarence Addison Willis - Geometry, Modern - 1922 - 318 pages
...a regular hexagon whose apothem is 34.64? THE SECOND STEP IN CLASSIFICATION 336. Theorem I.-—The perimeters of two regular polygons of the same number of sides are proportional to the radii of the polygons. Hypothesis.—Regular polygons 0 and 0', of the same number... | |
| National Committee on Mathematical Requirements - Mathematics - 1923 - 680 pages
...external segment. 21. Parallelograms or triangles of equal bases and equal altitudes are equal. 22. The perimeters of two regular polygons of the same number of sides are to each other as their radii and also as their apothems. Solid Geometry In the following list the precise wording and the... | |
| David Eugene Smith - Geometry, Plane - 1923 - 314 pages
...Post. 1 §§ 278, 224 § 271, Post. 9 §134,1 §213 §205 §210 §205 Ax. 5 281. Corollary. The areas of two regular polygons of the same number of sides are to each other as the squares on the radii of the circumscribed circles, and also as the squares on the radii of the... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 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... | |
| Jacob William Albert Young - Mathematics - 1924 - 484 pages
...external segment. 21. Parallelograms or triangles of equal bases and equal altitudes are equal. 22. The perimeters of two regular polygons of the same number of sides are to each other as their radii and also as their apot hems, Notes." I. The list I is typical, not exhaustive. 2. Concerning... | |
| Julius J. H. Hayn - Geometry, Plane - 1925 - 328 pages
...Group 91 283. Prop. V. Two regular polygons of the same number of sides are similar. 285. Prop. VII. The perimeters of two regular polygons of the same number of sides are to each other as their apothems or their radii. 284. Prop. VI. An equilateral polygon inscribed in a circle. 286. Prop. VIII.... | |
| Baltimore (Md.). Department of Education - Mathematics - 1924 - 182 pages
...the same number of sides are similar. 7. Two circles arc to each other as their radii. a. The areas of two regular polygons of the same number of sides are to each other as the squares of their sides, or as the squares of their radii. b. The areas of two circles arc to each... | |
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