| 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 - 460 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... | |
| Geometry, Plane - 1911 - 192 pages
...drawn from the point of tangency, prove that they are divided proportionally by the smaller circle. 6. **The areas of two regular polygons of the same number of sides are** to each other as the squares of their radii or their apothems. 6. Prove that if one acute angle of... | |
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