 | William Guy Peck - Conic sections - 1876 - 376 pages
...polygons coincide with the circumference OA, their areas are equal to that of the circle OA. Cor. 2. The area of a circle is equal to half the product of its circumference and radius. PROPOSITION VI. THEOREM. The perimeters of two regular polygons having the... | |
 | 1876 - 646 pages
...a limit ? Give an example to illustrate the definition. (b) Apply the theory of limits to show that the area of a circle is equal to half the product of its circumference by its radius. 5. If from any point perpendiculars be dropped upon two intersecting planes,... | |
 | William Frothingham Bradbury - Arithmetic - 1879 - 392 pages
...circumference is 19 feet.? 30. What is the circumference of a circular pond whose diameter is 56 meters ? 483. The area of a circle is equal to half the product of its circumference and its radius. Or, it is equal to 0.7854 times the square of its diameter. Area = ^... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...circumference of the circle is the perimeter of the polygon, and its radius is the apothem; therefore the area of a circle is equal to half the product of its circumference and its radius. 50. Corollary. If C = the circumference, D = the diameter, R = the radius,... | |
 | Brookline (Mass.) - Brookline (Mass.) - 1881 - 674 pages
...construct a square equivalent to a given parallelogram, or to a given triangle. Proof of work. (i. The area of a circle is equal to half the product of its circumference by its radius. Give all the propositions on which the demonstration of the above proposition... | |
 | George Bruce Halsted - Measurement - 1881 - 266 pages
...47). Substituting this value of r in the expression for 2(7, we obtain 4A Cor. The area of a segment of a circle is equal to half the product of its radius and the excess of its arc over half the chord of double that arc. For sector AHB C = \lr, and £\ABG=\rxBL.... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...drawn between vertices similarly situated with regard to each other, are equal each to each. THEOREM The area of a circle is equal to half the product...circumference to be divided into equal arcs so small that we can not conceive of their length, the perimeter of the regular polygon formed by their chords (Theo.... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...similarly situated with regard to each other, are equal each to each. THEOREM XLI. The area of a circk is equal to half the product of its radius by its...circumference to be divided into equal arcs so small that we can not conceive of their length, the perimeter of the regular polygon formed by their chords (Theo.... | |
 | F. B. Stevens - Examinations - 1884 - 202 pages
...sides of a triangle and the angle opposite to one of them being given, to construct the triangle. 4. The area of a circle is equal to half the product of its circumference by its radius. 5. Calculate the area of a circle whose radius is 10 ft. II. — SOLID... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...measuring unit. By increasing the number of sides, we approximate still nearer. PROPOSITION XIV. THEOREM. The area of a circle is equal to half the product of its circumference and, radius. Let O be the centre of a circle, OC its radius, and ACDE its circumference... | |
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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. 
