 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...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.... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...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.... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...inscribed circle. PROPOSITION IX. — THEOREM. 369. The perimeters of two regular polygons, havingthe same number of sides, are to each other as the radii of the circumscribed circles, and, also, as the radii of the inscribed circles ; and their areas are to... | |
 | Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...(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, for... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...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, Modern - 1864 - 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... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 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... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...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.... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...etc. 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... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...etc. 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... | |
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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. 
