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" It follows, then, that the area of a circle is equal to half the product of its circumference and its radius. "
Primary Elements of Plane and Solid Geometry: For Schools and Academies - Page 47
by Evan Wilhelm Evans - 1862 - 98 pages
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Elements of Geometry: Including Plane, Solid, and Spherical Geometry

George Washington Hull - Geometry - 1807 - 398 pages
...obtained only approximately. For practical purposes 3.1410 is used. PROPOSITION XI. THEOREM. 343. Tfie area of a circle is equal to half the product of its circumference by its radius. Given — S the area, C the circumference, and R the radius of a circle....
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An Encyclopędia of Architecture: Historical, Theoretical, and Practical

Joseph Gwilt - Architects - 1842 - 1089 pages
...These three surfaces added together will give the whole surface of the figure ABCDFA. 933. PROP. LVI. The area of a circle is equal to half the product of its radius and circumference. A If the radius of the circle С (fig. 289.) be multiplied by Fig. 288. its circumference,...
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ELEMENTARY GEOMETRY, WITH APPLICATIONS IN MENSURATION.

CHARLES DAVIS, L.L. D. - 1850
...hence, the area of the polygon will be equal to half the product of CD by the perimeter. THEOREM XXVII. The area of a circle is equal to half the product of the radius by the circumference. Let C be the centre of a circle : then will its area be equal to half...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1886 - 324 pages
...hence, the area of the polygon will be equal to half the product of CD by the perimeter THEOREM XXV11. The area of a circle is equal to half the product of the radius by the c1rcumference. Let C be the centre of a circle : then will its area be equal to half...
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PLANE AND SOLID GEOMETRY

GEORGE R. PERKINS - 1856
...degree of approximation as may be desired. MEASURE OF THE CIRCLE AND OF ITS CIRCUMFERENCE. THEOREM XIII. The area of a circle is equal to half the product of the circumference into its radius. In effect, let us consider a series of regular circumscribed polygons,...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 443 pages
...of approximation as may be desired. MEASURE OF THE CIRCLE AND OF ITS CIRCUMFERENCE. k THEOREM XHI. The area of a circle is equal to half the product of the circumference into its radius. In effect, let us consider a series of regular circumscribed polygons,...
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ELEMENTS OF GEOMETRY AND TRIGONOMETRY

CHARLES DAVIES, LL.D. - 1863
...increasing the number of sides, a still closer approximation may be had. PROPOSITION XIV. THEOEEM. The area of a circle is equal to half the product of its circumference and radius. Let 0 be the centre of a circle, 00 its radius, and A CDE its circumference...
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A Collection of Elementary Test Questions in Pure and Mixed Mathematics with ...

James Robert Christie - Mathematics - 1866 - 404 pages
...the area of the triangle in which 6 = 124 feet, с = 16l-* feet, and A = 71° 12'. 8. Assuming that the area of a circle is equal to half the product of the radius and circumference, it is required to deduce the particular form, (1) in terms of the radius,...
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The Southern Review, Volume 1

Albert Taylor Bledsoe, Sophia M'Ilvaine Bledsoe Herrick - Reconstruction (U.S. history, 1865-1877) - 1867
...radii ; which was to be proved.'* In the same short and easy way, he demonstrates the theorem, that ' the area of a circle is equal to half the product of its circumference and * Davies' Legendre. Revised Ed., 1866. Book V. Prop. XIII. 4 290 The Teaching and...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 368 pages
...approximately. The letter ic, however, is used to symbolize its exact value. PROPOSITION XVI.— THEOREM. 42. The area of a circle is equal to half the product of its circumference by its radius. Let the area of any regular polygon circumscribed about the circle be...
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