 | Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...Theorem VIII. Two regular polygons of the same number of sides are similar. Corollary 1. The perimeters of regular polygons of the same number of sides are to each other as their apothems, as their radii, to their sides. Corollary 2. The areas of regular polygons are to each... | |
 | Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...Theorem VIII. Two regular polygons of the same number of sides are similar. Corollary 1. The perimeters of regular polygons of the same number of sides are to each other as their apothems, as their radii, to their sides. Corollary Z. The areas of regular polygons are to each... | |
 | 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 of sides... | |
 | William Betz - Geometry - 1916 - 536 pages
...circle into two arcs having the ratio 1:8 (1:5, 2:3, 3 : 7, 7 : 8). 454. The perimeters of two regular polygons of the same number of sides are to each other as their radii and also as their apothems. Given two regular polygons, each having n sides, and with the... | |
 | John Charles Stone, James Franklin Millis - Geometry - 1916 - 298 pages
...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,... | |
 | Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Plane - 1917 - 330 pages
...the circumscribed equilateral triangle is 1 to 4. 256 PROPOSITION VII. THEOREM 377. The perimeters of regular polygons of the same number of sides are to each other as the radii of the circumscribed circles, or as the radii of the inscribed circles. Given AC and A' C' two... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...AO : A'o'. (303) But P:P' = AB:A'B' = AD:A'D'. (Why?) ...P:P' = OD:O'D' = AO:A'0'. 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... | |
 | Claude Irwin Palmer - Geometry, Solid - 1918 - 192 pages
...equal to half the product of the perimeter by the apothem. § 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. . MEASUREMENT OF THE CIRCLE § 485. Theorems... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry - 1918 - 460 pages
...areas of the triangles is the area of the polygon, .-. A - %ap. 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 of a regular... | |
 | United States. Office of Education - 1921 - 1286 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 apothème. SOL[D GEOMETRY. In the following list the precise wording... | |
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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. 
