 | William James Milne - Geometry, Modern - 1899 - 258 pages
...with the ratio of any two homologous sides? With the ratio of their radii? Of their apothems? Theorem. The perimeters of regular polygons of the same number of sides are to each other as their radii and also as their apothems. D MG Data : Any two regular polygons of the... | |
 | John Alton Avery - Geometry, Modern - 1903 - 136 pages
...EXERCISES 142. The radius drawn to any vertex of a regular polygon bisects the angle at the vertex. 143. The perimeters of regular polygons of the same number of sides are to each other as any two homologous sides. 144. Find the area of a square inscribed in a circle whose... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...inscribed in, any regular polygon. 431. Regular polygons of the same number of sides are similai. 433. The perimeters of regular polygons of the same number of sides are in the same ratio as their radii, or as their apothems. 434. The areas of regular polygons of the same... | |
 | Eugene Randolph Smith - Geometry, Plane - 1909 - 424 pages
...area of a regular polygon equals one half the product of the perimeter by the apothem. 315. COR. 2. The perimeters of regular polygons of the same number of sides are proportional to their sides, apothems, or radii. 316. COR. 3. The areas of regular polygons of the... | |
 | Jacob William Albert Young, Lambert Lincoln Jackson - Geometry, Plane - 1916 - 328 pages
...is the number of sides. nAB OM nA'B' O'M' , or using r, r' for the radii, and P, P for 431. COR. 3. The perimeters of regular polygons of the same number of sides are proportional to their apothem.i. For, the radius of the inscribed circle of a regular polygon is the... | |
 | Edith Long, William Charles Brenke - Geometry, Plane - 1916 - 292 pages
...its apothem. 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 %. The areas of regular... | |
 | Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...its apothem. 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... | |
 | Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Plane - 1917 - 330 pages
...to the area of 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.... | |
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The perimeters of regular polygons of the same number of sides are to each other as the radii of the circumscribed circles... 
