 | 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... | |
 | Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Plane - 1917 - 330 pages
...§317. 3. § 372, Ax. 1. 4. §188. 5. §311. 6. §§302,316. 7. Ax. 1. OED378. COR. The areas of regular polygons of the same number of sides are to each other as the squares of the radii of the inscribed, or circumscribed, circles. Ex. 1. If the sides of two regular... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry - 1918 - 460 pages
...sum of the 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... | |
 | Claude Irwin Palmer - Geometry, Solid - 1918 - 192 pages
...regular polygon is 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... | |
 | Herbert Ellsworth Slaught - 1918 - 344 pages
...the same number of sides is equal to the ratio of similitude of the two polygons. . 476. COROLLARY 2. The perimeters of two regular polygons of the same number of sides are in the same ratio as their radii or as their apothems. AREA OF A REGULAR POLYGON 478. THEOREM V. The... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1918 - 360 pages
...the same number of sides is equal to the ratio of similitude of the two polygons. 476. COROLLARY 2. The perimeters of two regular polygons of the same number of sides are in the same ratio as their radii or as their apothems. AREA OF A' REGULAR POLYGON 478. THEOREM V. The... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...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... | |
 | Education - 1921 - 1190 pages
...and its external segment. 21. 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 the... | |
 | United States. Office of Education - 1921 - 1286 pages
...and its external segment. 21. 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 and the... | |
 | 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 variable... | |
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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 surfaces are to each other as the squares of those sides (Book IV. 
