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" to prove that the area of a circle is equal to the product of its circumference by the half of its radius "
Reflexions on the Metaphysical Principles of the Infinitesimal Analysis - Page 85
by Lazare Carnot - 1832 - 132 pages
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Elements of Geometry and Trigonometry: With Notes

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...
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Elements of Geometry...: Translated from the French for the Use of the ...

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...
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Elements of Geometry: With Practical Applications, for the Use of Schools

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...
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Elements of geometry: with practical applications, for the use of schools

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...
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Elements of Geometry: With Practical Applications, for the Use of Schools

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...
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Elements of Geometry and Trigonometry

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....
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Elements of geometry and trigonometry

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....
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Elements of Geometry and Trigonometry

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....
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson, Sir David Brewster - 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...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 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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