...sides proportional ; therefore they are similar. THEOREM. 221. The paimeters of similar polygons are as their homologous sides, and their surfaces are as the squares of these sides. Demonstration. 1. By the nature of similar figures we have Fig. 129. AB '• FG : : BC : GH'• '•...

...sides proportional ; therefore they are similar. THEOREM. 221. The perimeters of similar polygons are as their homologous sides, and their surfaces are as the squares of these sides. ^ Demonstration. 1. By the nature of similar figures we have Fig. 129. AB : FG : : BC : GH : : CD :...

...sides proportional ; therefore they are similar. THEOREM. 221. The perimeters of similar polygons are as their homologous sides, and their surfaces are as the squares of these sides. Demonstration. 1. By the nature of similar figures we have Fig. 159. AB:FG::BC:GH::CD: HI, &c. (fig....

...proportional ; therefore they are similar. THEOREM. 221. Thf perimeters of similar polygons are as tfieir homologous sides, and their surfaces are as the squares of these sides. Demons I rat ion, 1. By the nature of similar figures we have Fig. 129. AB : FG : : BC : GH : : CD...

...angles equal, and their homologous sides proportional ; consequently (102.) they -are similar. 264. Cor. The perimeters of two regular polygons of the same...other as their homologous sides, and their surfaces, as the squares of those sides (221.) 265. Scholium. The angle of a regular polygon, like the angle...

...circumscribed circles; and ON, on, are radii of the inscribed circles. We therefore say—The areas of regular polygons of the same number of sides, are to each other as the squares of the radii of the circumscribed circles, and also of the inscribed circles. (on)* 0 (boc)...

...that it is made up of infinitely small straight lines. 95. THEOREM. — The pe.rime.le.rs of regular polygons of the. same number of sides are to each other as the radii of their circumscribed circles. By th^orimeter of a polygon we mean the sum of its sides;^Snen...

...perimeter of that figure. The above proportion may therefore be expressed in shorter terms; namely, the perimeters of two regular polygons of the same number of sides, are to each other in the proportion of the radii of the inscribed or circumscribed circles. 2. The areas of two regular...

...perimeter of that figure. The above proportion may therefore be expressed in shorter terms ; namely, the perimeters of two regular polygons of the same number of sides, are to each other in the proportion of the radii of the inscribed or circumscribed circles. 2. Tlie areas of two regular...

...each other in the same ratio, as the radii of the inscribed or circumscribed circles. 35. The areas of two regular polygons of the same number of sides, are to each other as the areas of the squares constructed upon the radii of the inscribed or circumscribed circles. 36....