...rule : The area of a circle is equal to its circumference multiplied by half its radius.* PROP. VII. THEOREM. The perimeters of two regular polygons of the same number of sides, are to each other as the radii of the circumscribed circles : and their areas are to each other,...

...polygon =nx AB X ^ FO ; but re x AB = the perimeter, .'. Area polygon = the perimeter x^ FO. i; n. u 72. THEOREM. The perimeters of two regular polygons of the same number of sides are to each other as the radii of the circumscribed circles ; and moreover their areas are to...

...the radius of the inscribed circle. Therefore, the 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 circles, and their surfaces are as the squares...

...the 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 any two circles are to each other in the same ratio as their radii. Proof: The perimeters of any two regular polygons of the same number of sides have the same ratio as the radii of their circumscribed circles. Ww. 374; (En. XII. 1, V. 12, Cv. V. 10). n. in*,. S"'n. G...

...polygon. 211. Theorem. Two regular polygons of the same number of sides are similar. . 212. Them-em. The perimeters of two regular polygons of the same...apothems. 213. Theorem. Area of a regular polygon = } perimeter X apothem. CIRCUMFERENCE AND AREA OF THE CIRCLE. The letter r is used to denote the radius...

...similarly described on the second as the first sect is to the third. THEOREM XX. 548. The perimeters of any two regular polygons of the same number of sides have the same ratio as the radii of their circumscribed circles. PROOF. The angles of two regular polygons of the same number...

...polygon. 208. Theorem. Each angle at the centre of a regular i * -A 360 ° polygon of n sides = fi, 209. Theorem. Each angle of a regular polygon is the...apothems. 213. Theorem. Area of a regular polygon = J perimeter X apothem. CIRCUMFERENCE AND AREA OF THE CIRCLE. The letter r is used to denote the radius...

...points of division form an inscribed regular polygon ; and the tangents drawn through these points torn a circumscribed regular polygon. 211. Theorem. Two...apothems. 213. Theorem. Area of a regular polygon = $ perimeter X apothem. CIRCUMFERENCE AND AREA OF THE CIRCLE. The letter r is used to denote the radius...

...THEOREM II. 800. Any two circles are to each other as their radii. PROOF. By 548, the perimeters of any two regular polygons of the same number of sides have the same ratio as the radii of their circumscribed circles. The inscribed regular polygons remaining similar to each...