Hart, C. A. (Clara Avis), b. 1863, Feldman, Daniel D., b. 1872 · New York, American Book Co · leaf 278
558. Def. The area of a circle is the common limit w^iichthe successive areas of inscribed and circumscribed regularpolygons approach as the number of sides is successively in-creased and ettch side approaches zero as a limit. BOOK V 267 Proposition XIV. Theorem 559. Th e area of a circle is equal… … Given circle 0, with radius R, circumference C, and area K. To prove K=\ CR, 1. 2.3. Argument Circumscribe about circle O a regularpolygon. Call its perimeter P andits area S. Then S = ^PR. As the number of sides of the regularcircumscribed polygon is repeatedlydoubled, P approaches C as a limit.…
Geometry, Plane · Geometry, Solid
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