 | Elias Loomis - Conic sections - 1858 - 256 pages
...regard the circle as . regular polygon of an infinite number of sides. i • PROPOSITION XII. THEOREM. The area of a circle is equal to the product of its circumference by half the radius. Let ABE be a circle whose center is C and radius CA ; the area of the circle is *qual to the product... | |
 | Elias Loomis - Conic sections - 1860 - 246 pages
...is equal to the product of its diameter by the constant number n. Cor. 3. According to Prop. XII., the area of a circle is equal to the product of its...If we put A to represent the area of a circle, then Cor. 4. When R is equal to unity, we have A=TT; that is, TT is equal to the area of a circle whose... | |
 | Elias Loomis - Conic sections - 1861 - 254 pages
...therefore regard the circle as f. regular polygon of an infinite number of sides. PROPOSITION XII. THEOREM. The area of a circle is equal to the product of its circum~ ference by half the radius. Let ABE be a circle whose center is C and radius CA ; the area... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...(Prop. XIII.) ; therefore Sector ACB : Sector D 0 E : : R3 : r*. PROPOSITION XV. — THEOREM. 380. The area of a circle is equal to the product of the circumference by half the radius. Let C denote the circumference of the circle, whose centre is 0,... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...(Prop. XIII.) ; therefore Sector ACB : Sector D 0 E : : R2 : r*. PROPOSITION XV. — THEOREM. 380. The area of a circle is equal to the product of the circumference by half the radius. Let C denote the circumference of the circle, whose centre is 0,... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...circle. 589. Cor. 1. The surface of a sphere is equal to the area of four of its great circles. For the area of a circle is equal to the product of the circumference by half the radius, or one fourth of the diameter (Prop. XV. Bk. VI.). 590. Cor. 2. The... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...787. Corollary — The area of the surface of a sphere is four times the area of a great circle. For the area of a circle is equal to the product of its circumference by one-fourth of the diameter. 788. Corollary — The area of the surface of a sphere is equal to the... | |
 | Benjamin Greenleaf - Geometry - 1866 - 328 pages
...DX'r=2RXT. Multiplying both numbers of this equation by | R, we have CX i R = R2 X JT, or A = R2 X n • that is, the area of a circle is equal to the product...of the square of its radius by the constant number n. 383. Cor. 3. The circumference of every circle is equal to the product of its diameter, or twice... | |
 | Education - 1867 - 774 pages
...vertical and adjacent angles; between a corollary and a scholium. NOTE.—Omit all corollaries. 8 & 9. The area of a circle is equal to the product of its circumference by half the radius. SECOND CLASS. HIGH SCHOOL. 1872. Latin. 1. Translate: Fuere ea tempestate, qui dicerent, Catilinam,... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...787. Corollary. — The area of the surface of a sphere is four times the area of a great circle. For the area of a circle is equal to the product of its circumference by one-fourth of the diameter. 788. Corollary — The area of the surface of a sphere is equal to the... | |
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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. 
