...circle is the same as the perpendicular let fall from the centre upon one of the sides. THEOREM. 282. The perimeters of regular polygons of the same number of sides are as the radii of the circumscribed circles, and also as the radii of Hie inscribed circles ; and their...

...circle is the same as the perpendicular let fall from the centre upon one of the sides. THEOREM. 282. The perimeters of regular polygons of the same number of sides are as the radii of the circumscribed circles, and also as the radii of the inscribed circles ; and their...

...Admitting our principle, this proposition is included in that of art. 282. It is there demonstrated, that ' the perimeters of regular polygons of the same number of sides, are as the radii of their inscribed circles ; and their surfaces are as the squares of these same radii.'...

...Admitting our principle, this proposition is included in that of art. 282. It is there demonstrated, that ' the perimeters of regular polygons of the same number of sides, are as the radii of their inscribed circles ; and their surfaces are as the squares of these same radii.'...

...given of a curved line (10) namely, that it is made up of infinitely small straight lines. 95. — The perimeters of regular polygons of the same number of sides are to each other as the radii of their circumscribed circles — . By the perimeter of a polygon we mean...

...the angle ABC= A'B'C. Hence, by art. 198, OP : OP' = AB : A'B' = OA : O'A'. 233. Corollary. Hence, the perimeters of regular polygons of the same number of sides are, by art. 207, The Ratio of a Circumference to its Diameter. to each other' as the radii of their inscribed...

...circle is the same as the perpendicular let fall from the centre upon one of the sides. THEOREM. 282. The perimeters of regular polygons of the same number of sides are as the radii of the circumscribed circles, and also as tlie radii of the inscribed circles ; and their...

...OA : O'A'. . ' ' ..'* <*»• The Ratio of a Circumference to its Diameter. 233. Corollary. Hence, the perimeters of regular polygons of the same number of sides are, by § 207, to each other as the radii of their inscribed circles, and also as the radii of their circumscribed...

...AD, AE, AF indefinitely, and in AB produced take Ab equal to G, and proceed as before. 91. PROP. VI. The perimeters of regular polygons of the same number of sides are proportional to the radii of their inscribed or circumscribing circles ; and their areas are proportional...

...or CD : C'D', 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 ;...