| Adrien Marie Legendre - Geometry - 1836 - 394 pages
...the squares of their radii ; therefore sect. ACB : sect. DOE : : AC2 : DO2. 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. OA, For, inscribe... | |
| Etienne Bézout - Calculus - 1836 - 216 pages
...centre upon one of the sides. Therefore the circle, considered as a polygon of a great number of sides, is equal to the product of its circumference by half the radius ; a proposition which is no less exact than the result found above. In the examples just given, it... | |
| Adrien Marie Legendre - Geometry - 1837 - 376 pages
...the squares of their radii ; therefore sect. ACB : sect. DOE : : AC2 : DO2. PROPOSITION XII. THEOREM. The area of a circle is equal to the product of its circumference by > 1 half the radius. Let ACDE be a circle whose centre is O and radius OA : then will area OA=:£OAxc/rc.... | |
| Denison Olmsted - Physics - 1838 - 376 pages
...the line CD, the circumference described by it will be half the length of the circumference ADB ; and the area of a circle is equal to the product of the radius into half the circumference. B Again, the small circle, having its center coincident with the... | |
| Adrien Marie Legendre - Geometry - 1841 - 288 pages
...circles are as the squares of their radii ; therefore sect. A CB : sect. DOE:: AC: DO. 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 is... | |
| James Bates Thomson - Geometry - 1844 - 268 pages
...the squares of their radii ; therefore, sect. ACB : sect. DOE : : AC' : 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 area ON=iOTxaVc.... | |
| Denison Olmsted - Physics - 1844 - 618 pages
...the line CD, the circumference described by it will be half the length of the circumference ADB ; and the area of a circle is equal to the product of the radius into half the circumference. 2. Jf a surface having any figure whatsoever, revolves about an... | |
| J. M. Scribner - Measurement - 1844 - 130 pages
...diameter into the circumference, and divide the product by 4; in either case the product will be the area. The area of a circle is equal to the product of the diameter i'.to the circumference. Now, we have just seen, (Art. 18,) that if the diameter be 1, the... | |
| Nathan Scholfield - 1845 - 894 pages
...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., the area of the... | |
| Anna Cabot Lowell - Geometry - 1846 - 216 pages
...diameter of a sphere is a line passing through the centre and terminating both ways in the surface. The area of a circle is equal to the product of its circumference by half its radius, or one fourth of its diameter, (183 ;) consequently the surface of a sphere is equal to... | |
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