| United States Civil Service Commission - Civil service - 1424 pages
...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... | |
| 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... | |
| 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.... | |
| 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... | |
| 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.... | |
| 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... | |
| 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... | |
| 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... | |
| United States - 1885 - 296 pages
...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 dcvidii,ttration in full. (Third subject: Trigonometry.) Question... | |
| Webster Wells - Geometry - 1886 - 392 pages
...Two similar sectors are to each other as the squares of their radii. PROPOSITION XV. THEOREM. 396. **The area of a circle is equal to one-half the product of its** circumference and radius. (Compare §^322.) Let B and K denote the radii, C and^_the_circB Let R denote... | |
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