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The area of a circle is equal to one-half the product of its circumference and radius.
Yale University Entrance Examinations in Mathematics: 1884 to 1898 - Page 171
1898 - 208 pages

Annual Report of the United States Civil Service Commission, Volume 1

...inscribed angle is measured by half the arc on which it stands. Give demonstration in full. Question 5. Prove that the area of a circle is equal to one-half the radius into the circumference. Give demonstration in full. (Third subject: Trigonometry.) Question...

Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 426 pages
...to the perimeter of the polygon. .'. the area of the polygon = £ RX P. PROPOSITION X. THEOREM. 380. The area of a circle is equal to one-half the product of its .radius by its circumference. Let R represent the radius, and С the circumference of a circle. We are to prove...

A Treatise on Special Or Elementary Geometry: Including an Elementary, and ...

Edward Olney - Geometry - 1879 - 502 pages
...especially worthy of note in the case of a triangle. See Fig. 60. PROPOSITION IX. 328. TJieorcm. — TJie area of a circle is equal to one-half the product of its radius into its circumference. DEM. — Let Oa be the radius of a circle. Circumscribe any regular polygoa....

Elements of Geometry

George Albert Wentworth - 1881 - 266 pages
...the perimeter of the polygon. .-. the area of the polygon = £ RX P. QED PROPOSITION X. THEOREM. 380. The area of a circle is equal to one-half the product of its radius by its circumference. Let R represent the radius, and С the circumference oí a circle. We are to...

A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1882 - 262 pages
...especially worthy of note in the case of a triangle. See Kg. 60. PROPOSITION IX. 328. Theorem. — The area of a circle is equal to one-half the product of its radius into its circumference. DKM. — Let Oa be the radius of a circle. Circumscribe any regular polygon....

Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - Geometry - 1883 - 352 pages
...circle as its limit, since the circle is the limit of such a polygon. PROPOSITION XI. 356. Theorem. — The area of a circle is equal to onehalf the product of its radius into its circumference. DEMONSTRATION. Let O<f (Fig. 179) be the radius of the circle. Fig. 179. We...

Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - Geometry - 1883 - 352 pages
...as its limit, since the circle is the limit of such a polygon. PROPOSITION XI. 356. Theorem.—The area of a circle is equal to onehalf the product of its radius into its circumference. We are to prove that the area of the circle is £Oa x the circumference. Circumscribe...

Annual Report of the United States Civil Service Commission

United States Civil Service Commission - Civil service - 1884 - 222 pages
...inscribed angle is measured by half the are on which it stands. « Owe demonstration in full. Question 5. Prove that the area of a circle is equal to one-half the radius into the circumference. Give demonstration in full. (Third subject: Trigonometry.) Question...