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" 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. "
Elements of Geometry, Conic Sections, and Plane Trigonometry - Page 124
by Elias Loomis - 1877 - 443 pages
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New Elements of Mathematics: Or Euclid Corrected. Containing Plane Gometry ...

John Muller - Mathematics - 1773 - 204 pages
...to r ; then unity is to r as the radius PM (y) is to ry its femi-circumference, by Art. 40 ; and as the area of a circle is equal to the product of the radius by half its circumference, by Art. 41 ; ihall have yXry or ryy, for the circle defcribed, defcribed...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 208 pages
...entire circles are as the squares of the.' therefore sect. ACB : 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 whosc radius is...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 367 pages
...the squares of their radii; therefore sect. ACB : sect. DOE : ACa : DO2. 96 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 have surf. CA=JCA...
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First Principles of the Differential and Integral Calculus, Or, the ...

Etienne Bézout - Calculus - 1824 - 195 pages
...made. Let us apply this theory of indeterminates to some examples. Let it be proposed to prove that the area of a circle is equal to the product of its circumference by half the radius; that is, that calling this radius R, the ratio of the circumference to radius sr, and consequently...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 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 is...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
..."ntire circles ; but the entire circles are as the squares of their radii ; therefore I 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...
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The North American Review, Volume 27

Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - American fiction - 1828
...circles, the words their radii, and the same theorem is sufficient for both cases. QED Theorem 289. The area of a circle is equal to the product of its circumference by half the radius. It was demonstrated, 280, that ' the area of a regular polygon is equal to the product of its perimeter...
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The North American Review, Volume 27

Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - American fiction - 1828
...circles, the words their radii, and the same theorem is sufficient for both cases. QED Theorem 289. The area of a circle is equal to the product of its circumference by half the radius. It was demonstrated, 280, that ' the area of a regular polygon is equal to the product of its perimeter...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 316 pages
...again are as the squares of their radii ; therefore sect. ACB : sect. DOE : AC2 DOJ THEOREM. ' 289. The area of a circle is equal to the product of its circumference by half the radiusl Let us designate the surface of the circle whose radius is CA by surf. CA ; we shall have surf....
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 129 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 the perimeter...
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