 | Harvard University - Geometry - 1899 - 39 pages
...circumference of a circle is equal to the product of the radius and twice the constant number TT. THEOREM XI. The area of a circle is equal to half the product of its circumference and its radius. SOLID GEOMETRY. BOOKS VI TO IX. BOOK YL PLANES AND LINES IN SPACE. THEOREM... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...is equal to the perimeter of the polygon. Ax. 9 •'• S = \RX P. QED PROPOSITION XI. THEOREM. 461. The area of a circle is equal to half the product of its radius by its circumference. B" M Let R represent the radius, C the circumference, and S the area, of the circle whose centre is... | |
 | Michigan. Department of Public Instruction - Education - 1905 - 396 pages
...feet, and that of a regular octagon is the same. Find the difference in their areas. 7. Demonstrate: The area of a circle is equal to half the product of its circumference by radius. 8. Find the side of a regular inscribed decagon in terms of the radius of... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...is \ B, xb (§ 406). .-. S = (| K, xb)n = | E (bx n) = iExP. Ax. 13 QED PROPOSITION XII. THEOREM 463 The area of a circle is equal to half the product of its radius and circumference. HYPOTHESIS. R is the radius of a circle, C the circumference, and S the area. CONCLUSION.... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...^ R xb (§ 406). .-. S = (£ R xb)n = \ R (6 x n) = £RxP. Ax. 13 QED PROPOSITION XII. THEOREM 463 The area of a circle is equal to half the product of its radius and circumference. HYPOTHESIS. R is the radius of a circle, C the circumference, and S the area. CONCLUSION.... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...FORMULA. Let C = circumference and R = radius. Then, ; — = TT (443). .-. C = 2-nR (Ax. 3). 445. THEOREM. The area of a circle is equal to half the product of its circumference by its radius. Given : O whose circumference =C, area=S, radius = R. To Prove : s = £... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...FORMULA. Lot C = circumference and R = radius. Then, ^.=TT (443). ... C = 2irjj (Ax. 3). 445. THEOREM. The area of a circle is equal to half the product of its circumference by its radius. Given: O whose circumfer. ,,••,""""".. P ence = C, area=S, radius... | |
 | George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 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 8= 2 rcProof. Circumscribe... | |
 | Geometry, Plane - 1911 - 192 pages
...angle of a triangle divides the opposite side into segments proportioned to the adjacent sides. 4. The area of a circle is equal to half the product of its circumference and its radius. 6. ABC is a triangle inscribed in a circle with centre O. Take D the... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 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, But C = 466. The areas of two circles are to each other as the... | |
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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. 
