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. Elements of Geometry - Page 82by Adrien Marie Legendre - 1841 - 235 pagesFull view - About this book
| Benjamin Greenleaf - Geometry - 1863 - 504 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...to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop. XXXI. Bk. IV.). 348. Scholium. The angle... | |
| Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...two polygons (Def. 3, Sec. VII, BI) Therefore, the perimeters, etc. BOOK II. 67 THEOREM XI. The areas of two regular polygons of the same number of sides are to each other as the squares of their sides. Let ABODE, abede, be two regular polygons of the same number of sides,... | |
| 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... | |
| 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...to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop. XXXI. Bk. IV.). 348. Scholium. The angle... | |
| Eli Todd Tappan - Geometry - 1868 - 438 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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).... | |
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