 | George Albert Wentworth - Geometry - 1899 - 498 pages
...P:P' = OA: O'A' = OM : O'M'. § 445 §364 §431 § 436 Also, §357 § 351 § 361 Ax. 1 QED 448. COR. The areas of two regular polygons of the same number of sides are to each other as the squares of the radii of the circumscribed circles, and of the inscribed circles.... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...perimeters are in the same ratio as the apothems. The same holds true for the radii. 352. COROLLARY III. The areas of two regular polygons of the same number of sides are in the same ratio as the squares of their radii, or as the squares of their apothems. (Art. 315.) EXERCISES 1. Tangents to a... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...as the radii of the polygons, or as the apothems of the polygons. 351. COROLLARY II. The perimeters of two regular polygons of the same number of sides are in the same ratio as their radii, or as their apothems. Let Si and ,Sa be the lengths of the sides in two regular polygons... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...= OA: O'A' = OM : O'M'. § 445 §364 § 431 § 436 Also, . § 357 §351 § 361 Ax. 1 QED 448. COR. The areas of two regular polygons of the same number of sides are to each other as the squares of the radii of the circumscribed circles, and of the inscribed circles.... | |
 | Yale University. Sheffield Scientific School - 1905 - 1074 pages
...square and having the difference of its base and altitude equal to a given line. 4. The perimeters of two regular polygons' of the same number of sides are in the same ratio as the radii of the inscribed or circumseribed circles. 5. To construct a circle of a given radius tangent... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...number of sides are in the same ratio as their radii, or as their apothems. 434. The areas of regular polygons of the same number of sides are in the same ratio as the squares of their radii, or as the squares of their apothems. 435. The area of a regular polygon is... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...(§ 64, Axiom 5) (Why?) GH HI .'. the polygons are similar. 432. Corollary. The perimeters of regular polygons of the same number of sides are in the same ratio as any two corresponding sides. THEOREM IV 433. The perimeters of regular polygons of the same number... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 300 pages
...} '"' A'B' +B'C' + C'D' + -~ A1B' r'~a'' Draw the figure and give the proof in full. 348. THEOREM. The areas of two regular polygons of the same number of sides are in the same ratio as the squares of the corresponding radii or apothems. Outline of Proof : Divide the polygons into pairs of... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 304 pages
...A'B' +B'C' + C' D' + ••• A'B' r' a' Draw the figure and give the proof in full. 348. THEOREM. The areas of two regular polygons of the same number of sides are in the same ratio as the squares of the corresponding radii or apothems. Outline of Proof : Divide the polygons into pairs of... | |
 | George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...corresponding angles equal. Therefore the two polygons are similar, by § 282. QED 374. COROLLARY. The areas of two regular polygons of the same number of sides are to each other as the squares on any two corresponding sides. PROPOSITION IV. THEOREM 375. The perimeters... | |
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The areas of two regular polygons of the same number of sides are to each other as the squares of their radii, or as the squares of their apothems. 
