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. A Text-book of Geometry - Page 215by George Albert Wentworth - 1888 - 386 pagesFull view - About this book
| Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...corresponding side of 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... | |
| Benjamin Greenleaf - Geometry - 1868 - 340 pages
...angles equal, and their homologous sides proportional ; hence they are similar (Art. 210). 347. 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 (Prop. XXXI.... | |
| Eli Todd Tappan - Geometry - 1868 - 444 pages
...corresponding side of 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... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...Therefore the polygons fulfill the two conditions of similarity. 10. Corollary. 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 ; and their areas are to each other... | |
| Elias Loomis - Geometry - 1871 - 302 pages
...radius of the inscribed circle. Therefore *he area of a regular polygon, &c. PROPOSITION VIII. THEOREM. **The perimeters of two regular polygons of the same number of sides, are** as the radii of the inscribed or circumscribed cir cles, and their surfaces are as the squares of the... | |
| Eli Todd Tappan - Geometry - 1873 - 288 pages
...corresponding side of 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... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...Therefore the polygons fulfill the two conditions of similarity. 10. Corollary. 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; and their areas are to each other... | |
| Edward Olney - Geometry - 1872 - 472 pages
...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 - Geometry - 1872 - 562 pages
...the corresponding diagonals (35O), p : P : : r : R q. ED 370. COR. 1. — 77(6 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.... | |
| Harvard University - 1873 - 732 pages
...construct a polygon similar to a given polygon^ upon a given line. 6. The homologous sides of regular **polygons of the same number of sides are to each other...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... | |
| |