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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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Elements of Geometry and Trigonometry

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...
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First Principles of the Differential and Integral Calculus: Or The Doctrine ...

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...
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Elements of Geometry and Trigonometry

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....
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An Introduction to Natural Philosophy: Designed as a Text Book ..., Volume 1

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...
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Elements of Geometry

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...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which 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....
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An Introduction to Natural Philosophy: Designed as a Text Book, for the Use ...

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...
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A Practical System of Mensuration of Superficies and Solids ...

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...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

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...
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An Introduction to Geometry and the Science of Form: Prepared from the Most ...

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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