 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...the triangles added together which compose it, is equal to the rectangle of the common altitude OD, and the halves of all the sides, or the half perimeter...circumference of the circle, and, consequently, the altitude OD will become equal to the radius, and the whole polygon equal to the circle. Consequently, the space... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...sides. The area of the polygon will be equal to its perimeter multiplied by half of CD (Prop. VII.). Conceive the number of sides of the polygon to be indefinitely increased, by continually bisecting the arcs subtended by the sides ; its perimeter will ultimately coincide with... | |
 | George Albert Wentworth - Geometry - 1899 - 496 pages
...polygon about the circle, and denote its perimeter by P, and its area by S'. Then S' = $RxP. §459 Conceive the number of sides of the polygon to be indefinitely increased. Then P approaches C as its limit, § 454 and S' approaches S as its limit. § 454 But S' = £ RXP, always.... | |
 | George Albert Wentworth - Geometry, Plane - 1899 - 278 pages
...polygon about the circle, and denote its perimeter by P, and its area by S'. Then S' = \ R x P. §459 Conceive the number of sides of the polygon to be indefinitely increased. Then P approaches C as its limit, § 454 %R x P approaches £ -BX C' as its limit, § 279 and S' approaches... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...polygon about the circle, and denote its perimeter by P, and its area by S'. Then S' = \RXP. §459 Conceive the number of sides of the polygon to be indefinitely increased. Then P approaches C as its limit, § 454 and S' approaches S as its limit. § 454 But S' = $RX P, always.... | |
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CD. conseconsequently the whole polygon, or all the triangles added together which compose it, is equal to the- rectangle of the common altitude CD, and the halves of all the sides, or the half perimeter of the polygon. Now, conceive the number of sides... 
