...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...

...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...

...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....

...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...

...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....

...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...

...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...

...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...

...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...

...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...