 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...polygon is equal to half the product of its perimeter and its apothem (§ 456). It follows, then, that the area of a circle is equal to half the product of its circumference and its radius. C = 2 7TR. That is, But 466. The areas of two circles are to each other... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...arcs, sectors, and segments as correspond to equal angles at the center. PROPOSITION IX. THEOREM 388. The area of a circle is equal to half the product of its radius by its circumference. Given a circle with radius r, circumference c, and area s. To prove that s = ^ re. Proof. Circumscribe... | |
 | Jacob William Albert Young, Lambert Lincoln Jackson - Geometry, Plane - 1916 - 328 pages
...circle to its diameter is constant ; that is, ?*:_ Mmefor all circles. i PROPOSITION XI. THEOREM 479. The area of a circle is equal to half the product of its radius by its circumference. Given the circle with radius r, circumference c, and area A. To prove that A = \ re. Proof. 1. Circumscribe... | |
 | William Betz - Geometry - 1916 - 536 pages
...polygon is equal to half the product of its perimeter and its apothem (§ 456). It follows, then, that the area of a circle is equal to half the product of its circumference and its radius. That is, S = ±RC. But C = 2 irR. 466. The areas of two circles are to... | |
 | Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...and d — 2 r, c = 2 «r. Corollary 3. Two circumferences are proportional to their radii. Theorem X. The area of a circle is equal to half the product of circumference by radius. Corollary 1. The area of a circle = * r2. Corollary %. The areas of circles... | |
 | Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...and d = 2 r, c = 2 rr. Corollary 3. Two circumferences are proportional to their radii. Theorem X. The area of a circle is equal to half the product of circumference by radius. Corollary 1. The area of a circle = ir r2. Part II — Division of a Perigon.... | |
 | Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Plane - 1917 - 330 pages
...arcs subtend equal angles at the center. 262 MEASUREMENT OF THE CIRCLE PROPOSITION XI. THEOREM 390. The area of a circle is equal to half the product of its circumference and its radius. Given a O with circumference denoted by c, radius by r, and area by K.... | |
 | Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Solid - 1917 - 220 pages
...the symbol TT, — = TT ; hence, c = ird. d ' d Also, since d = 2 r, c— 7r(2 r) = 2 irr. 390. Tfie area of a circle is equal to half the product of its circumference and its radius. 391. Formulas for the area of a circle. — K= |(2 -nr^r, or K= Trr2.... | |
 | Matilda Auerbach, Charles Burton Walsh - Geometry, Plane - 1920 - 408 pages
...diameter is constant. Cor. 2. In any circle c =2iri. 63. The value of TT is approximately 3.14159. 64. The area of a circle is equal to half the product of its radius and its circumference. Cor. 1. The area of a circle is equal to ir times the square of its radius.... | |
 | Howard Whitley Eves - History - 1983 - 292 pages
...(f) The area of a regular polygon is equal to half the product of its perimeter and its apothem.* (g) The area of a circle is equal to half the product of its circumference and its radius. 3.5. Assuming (1) a central angle of a circle is measured by its intercepted... | |
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It follows, then, that the area of a circle is equal to half the product of its circumference and its radius. 
