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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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Elemento of Geometry, Theoretical and Practical: Containing a Full ...

George Clinton Whitlock - Mathematics - 1848 - 338 pages
...у = irx, ie, The circular sector is measured by half the product of (397) its radius and arc. Cor. The area of a circle is equal to the product of the (39S) radius multiplied into its semicircumference. Scholium. The celebrated Problem of the Quadrature...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 372 pages
...the squares of their radii; therefore sect. ACB : sect. DOE : : AC 2 : DO*. 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=iOAxcz'rc. OA. For, inscribe...
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Annual Report of the Controllers of the Public Schools of the ..., Volumes 31-34

Education - 1849 - 682 pages
...of a triangle, divides the base Ħalo two segments, which are proportional to the adjacent sides. 6. The area of a circle is equal to the product of its circumference by half the radius. 7. If two straight lines be cut by three parallel planes, they will be divided proportionally. 8. In...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...approximation to ten places of figures; Van Ceulen carried it to 36 places; Sharp comPROPOSITION XII. THEOREM. The area of a circle is equal to the product of its circumference by half the radius. Let ABE be a circle whose center is C and radius CA; the area of the circle is tqual to the product...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 218 pages
...Hence, the surface of the sphere is equal to A Ex circumference OE. Cor. Since the area of a great circle is equal to the product of its circumference by half the radius, or by one -fourth of the diameter (Bk. IV. Th. xxvii), it follows that the surface of a sphere is equal...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 238 pages
...Hence, the surface of the sphere is equal to AE x circumference OE. Cor. Since the area of a great circle is equal to the product of its circumference by half the radius, or by one-fourth of the diameter (Bk. IV. Th. xxvii), it follows that the surface of a sphere is equal...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1886 - 340 pages
...ABCDE Hence, the surface of the sphere is equal to AE X circum fercnce OECot Siace the area of a great circle is equal to the product of its circumference by half the radius, or by one-fourth of the diameter (Bk- IV- Th- xxvii), it follows that the surface of a sphere is equal...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...radius OE : hence, the surface of the sphere is equal to AExcirc. OE. Cor 1. Since the area of a great circle is equal to the product of its circumference by half the radius, or onefourth of the diameter (B. v., P. 15), it follows that the surface of a sphere is equal to four...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...radius OE: hence, the surface of the sphere is equal to AExcirc. OE. Cor 1. Since the area of a great circle is equal to the product of its circumference by half the radius, or one• fourth of the diameter (B. v., P. 15), it follows that the surface of a sphere is equal to...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1857 - 242 pages
...is equal to the product of its diameter by the constant number n. Cor. 3. According to Prop. XII., the area of a circle is equal to the product of its...that is, the area of a circle is equal to the product oftht square of its radius by the constant number n. Cor. 4. When R is equal to unity, we have A=TT...
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