 | Edward Olney - Geometry - 1872 - 472 pages
...other as the corresponding diagonals (35O), p : P : : r : HQED , .g,370. COR. 1. — The perimeters of regular polygons of the same number of sides are to each other as the apothems of the polygons. For the apothems are to each other as the sides of the polygons (351). 3TÍ... | |
 | Edward Olney - 1872 - 270 pages
...each other as the corresponding diagonals (35O), p : P :: r : S. QED 370. COR. 1.—The perimeters of regular polygons of the same number of sides are to each other as the apothems of the polygons. For the apothems are to each other as the sides of the polygons (351). 371,... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...squares of their homologous sides ; since they are similar figures (349). 366. COR. 3. — Regular polygons* of the same number of sides are to each other as the squares of their apothems. For their apothems are to each other as their sides. Hence the squares of... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...the second. Therefore, the polygons are similar (433). 450. Corollary. — The areas of two regular polygons of the same number of sides are to each other as the squares of their homologous lines (436). 451. Corollary — The ratio of the radius to the side of... | |
 | Harvard University - 1873 - 732 pages
...sides in a given circle. 5. To construct a polygon similar to a given polygon^ upon a given line. 6. The homologous sides of regular polygons of the same...and also as the radii of their inscribed circles. Prove ; and then by means of the corollary (which relates to the perimeters) apply to the case of two... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...homologous sides proportional; hence they are similar (172). 222. Cor. 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 (Theo. XXI.).... | |
 | Harvard University - 1874 - 668 pages
...a straight line, to draw a circle through the point! and touching the line. 11. Prove that regular polygons of the same number of sides are to each other as the squares of the radii of their circumscribed or of their inscribed circles. Extend the theorem to the... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...homologous sides proportional; hence they are similar (176). 222. Cor. 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 (Theo. XXI.).... | |
 | L J V. Gerard - 1874 - 428 pages
...polygons, is homologous to any sector triangle of the other. THEOREM 60. The perimeters of two regular polygons of the same number of sides, are to each other as their sides. Because two polygons of the same number of sides are similar to each other [59 ii], their... | |
 | Robert Fowler Leighton - 1877 - 372 pages
...will this angle be if the chord passes through the centre of the circle ? 5. Prove that the perimeters of regular polygons, of the same number of sides, are to each other as the radii of the circumscribed circles. State, without proving, what the ratio of the areas of the polygons is.... | |
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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. 
