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. A Text-book of Geometry - Page 211by George Albert Wentworth - 1888 - 386 pagesFull view - About this book
| Robert Remington Goff - 1922 - 136 pages
...*2Q0. The perimeters of two similar polygons are to each other as any two corresponding sides. *2g1. **The perimeters of two regular polygons of the same number of sides are to each other as** their radii and as their apothems. 292. What is a Constant, a Variable, a Limit? What is the usual... | |
| 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 of sides... | |
| 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... | |
| 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... | |
| David Eugene Smith - Geometry, Plane - 1923 - 314 pages
...corresponding sides. FUNDAMENTAL THEOREMS BOOK V Proposition 5. Perimeters of Regular Polygons 280. Theorem. **The perimeters of two regular polygons of the same number of sides are to each other as** their radii, and also as their apothems. A' M' B Given two regular polygons of n sides, with centers... | |
| 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... | |
| 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 a regular... | |
| 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.... | |
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