...radii; therefore sect. ACB : sect. DOE : ACa : DO2. 96 PROPOSITION XII. THEOREM. The area of a circle is equal to the product of its circumference by half the radius Let us designate the surface of the circle whose radius is CA by surf. CA ; we shall have surf. CA=JCA...

...their radii, and the same theorem is sufficient for both cases. QED Theorem 289. The area of a circle is equal to the product of its circumference by half the radius. It was demonstrated, 280, that ' the area of a regular polygon is equal to the product of its perimeter...

...their radii, and the same theorem is sufficient for both cases. QED Theorem 289. The area of a circle is equal to the product of its circumference by half the radius. It was demonstrated, 280, that ' the area of a regular polygon is equal to the product of its perimeter...

...perimeter multiplied by half the radius of the inscribed circle. 105. THEOREM. — The area of a circle is equal to the product of its circumference by half the radius. DEM. — This follows directlv from the preceding. For the circumference of the circle is the perimeter...

...absolutely exact, as is thus shown. The similar triangles QPM, MPT, give qP : MP : : MP : PT; whence PT= - = -—, as above. QP a — x' The above result...given, it is seen that great advantage, is obtained by employing quantities which are very small compared with the principal quantities in question. The same...

...similar triangles QPM, MPT, give qP : MP : : MP : PT; whence „„, MP y3 r 1 = ——- = —Z — as above. QP a — x' The above result is thus obtained...given, it is seen that great advantage is obtained by employing quantities which are very small compared with the principal quantities in question. The same...

...radii ; therefore sect. ACB : sect. DOE : : AC2 : DO2. 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— ^OAxcirc. OA, For, inscribe...

...this theory of indeterminates to some examples. Let it be proposed to prove that the area of a circle is equal to the product of its circumference by half the radius; that is, that calling this radius R, the ratio of the circumference to radius, n, and consequently...

...radii ; therefore, sect. ACB : sect. DOE : : AC' : DO'. PROPOSITION XI. THEOREM. The area of a circle is equal to the product of its circumference by half the radius. Let the area of the circle whose radius is OT, be designated by area ON ; then will area ON=iOTxaVc....

...(Prop. XXIV. and Cor. B. IV) will also apply to this. PROPOSITION XV. THEOREM. The area of a circle is equal to the product of its circumference by half the radius. For if about a circle whose radius is OH, we describe a regular polygon, ABCD, &c., the area of the...