 | Education - 1921 - 1190 pages
...Parallelograms or triangles of equal bases and 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... | |
 | Raleigh Schorling, William David Reeve - Mathematics - 1922 - 476 pages
...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 are to each other as their radii or as their apothems. Given the regular polygons AB • • • and A'ff • • • of... | |
 | Robert Remington Goff - 1922 - 136 pages
...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... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...A'O'. (303) But 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 pentagon... | |
 | National Committee on Mathematical Requirements - Mathematics - 1923 - 680 pages
...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... | |
 | David Eugene Smith - Geometry, Plane - 1923 - 314 pages
...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... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor, Eva Crane Farnum - Geometry, Modern - 1924 - 360 pages
...the areas of the triangles is the area of the polygon. ... A = 437. 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. § 387 (2) EXERCISES 1. If r is the radius... | |
 | Jacob William Albert Young - Mathematics - 1924 - 484 pages
...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
...tangents are drawn at the points of division, a regular circumscribed polygon is formed. 11. Perimeters of regular polygons of the same number of sides are to each other as their apothems or their radii. "K Series" of propositions, depending on one or more of A, B, C, D,... | |
 | John Charles Stone, James Franklin Millis - Geometry - 1916 - 296 pages
...^. Why? prh Write out the proof. 254. Corollary. — The areas of two regular polygons of the tame number of sides are to each other as the squares of the radii, or of the apothems. EXERCISES 1. Find the ratio of the perimeters and the ratio of the areas of two... | |
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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 areas are to each other as the squares of those sides (Prop. 
