| Adrien Marie Legendre - Geometry - 1822 - 367 pages
...each other as their radii AC, DO; hence arc. AB : arc. DE : : AC : DO. PROPOSITION XII. THEOREM. The **area of a circle is equal to the product of its circumference by** half the radius Let us designate the surface of the circle whose radius is CA by surf. CA; we shall... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 224 pages
...^ntire circles ; but the entire circles are as the squares of their radii; therefore THEOREM. 289. The **area of a circle is equal to the product of its circumference by** half of the radius. Demonstration. Denoting by surf. CA the surface or area of a circle whose radius... | |
| Timothy Walker - Geometry - 1829 - 129 pages
...the polygon its perimeter multiplied by half the radius of the inscribed circle. 105. THEOREM.— The **area of a circle is equal to the product of its circumference by** half the radius. DEM.—This follows directly from the preceding. For the circumference of the circle... | |
| Timothy Walker - Geometry - 1829 - 104 pages
...area of the polygon its perimeter multiplied by half the radius of the inscribed . circle. 105. —The **area of a circle is equal to the product of its circumference by** half the radius—. This follows directly from the preceding. For the circumference of the circle is... | |
| Timothy Walker - Geometry - 1831 - 129 pages
...the polygon its perimeter multiplied by half the radius of the inscribed circle. 105. THEOREM.— The **area of a circle is equal to the product of its circumference by** half the radius. DEM.—This follows directly from the preceding. For the circun.ference of the circle... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...squares of their radii; therefore sect. ACB : sect. DOE : : AC 2 : DO 2 . PROPOSITION XII. THEOREM. The **area of a circle is equal to the product of its circumference by** half the radius.* Let ACDE be a circle whose centre is O and radius OA : then will area OA—^OAxcirc.... | |
| Adrien Marie Legendre - Geometry - 1839 - 359 pages
...squares of their radii; therefore sect. ACB : sect. DOE : : AC 2 : DO 2 . PROPOSITION XII. THEOREM. The **area of a circle is equal to the product of its circumference by** half the radius. Let ACDE be a circle whose centre is O and radius OA : then will area OA=|OAxc?rc.... | |
| Geometry - 1843 - 359 pages
...squares of their radii; therefore sect. ACB : sect. DOE : : AC 2 : DO 2 . PROPOSITION XII. THEOREM. The **area of a circle is equal to the product of its circumference by** half the radius. Let ACDE be a circle whose centre is O and radius OA : then will area OA=|OAxcirc.... | |
| James Bates Thomson - Geometry - 1844 - 237 pages
...squares of their radii; therefore, sect. ACB : sect. DOE : : AC 1 : DO". PROPOSITION XI. THEOREM. The **area of a circle is equal to the product of its circumference by** half the radius. Let the area of the circle whose radius is OT, be designated by area ON; then will... | |
| 1845
...reasoning as employed in (Prop. XXIV. and Cor. B. IV) will also apply to this. PROPOSITION XV. THEOREM. The **area of a circle is equal to the product of its circumference by** half the radius. For if about a circle whose radius is OH, we describe a regular polygon, ABCD, &c.,... | |
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