| John Draper (of Whitehaven.) - 1772
...Globe or Sphere. Observations. The coat of this folid cannot be laid out in piano. But its area is juft **equal to four times the area of one of its great circles,** RULE. Multiply the fquare of its axis by 3.1416 (that is .7854X4) and the produft is the area of the... | |
| John Dougall - 1810 - 580 pages
...a sphere ,we multiply the circumference by the whole diameter, it follows that the superficial area **of -a sphere' is equal to four times the area of one of its great circles.** From the foregoing demonstrations it will also follow, that in order to obtain the superficial area... | |
| Thomas Keith - Navigation - 1810 - 420 pages
...surface of the sphere, 180°x wi=sx (A + B+C- 180°). SX(A + B4 c-180") S But the whole surface of the **sphere is equal to four times the area of one of its great** • cird es *, and the area of a great circle = •i- circumference x radius = 1 80° x radius, if... | |
| Edward Augustus Kendall - 1811
...about a diameter thereof, as an axis. All spheres are to one another as the cubes of their diameten. **The surface of a sphere is equal to four times the area of one of its great circles,** hence to find the superficies of any sphere, find the area of the great circle, and multiply it by... | |
| Samuel Vince - Calculus - 1812 - 256 pages
...ADFC to be a great circle of the sphere, its area = ^ /;a2, by Art. 49. Ex. 2. Cor. Hence, the whole **surface of a sphere is equal to four times the area of** a great circle of that sphere. Cor. As the surface *DAC=pax, it varies as x. Ex. 2. Let the solid AFH... | |
| Jeremiah Day - Measurement - 1815 - 96 pages
...surface of the segment produced by the revolution of BD about DN is equal to DN x circ CP. Cor. 2. **The surface of a sphere is equal to four times the area of** a circle of the same diameter; and therefore, the convex surface of a hemisphere is equal to twice... | |
| John Bonnycastle - Trigonometry - 1818 - 438 pages
...or arc, am : : surface of the sphere : the area of the lune AB c AQED COR. Since the surface of the **sphere is equal to four times the area of one of its great circles,** if d be put = diameter, c = circumference, and a — length of the arc B m, by the last mentioned proposition,... | |
| William Nicholson - Natural history - 1821
...pole. SPHERE, properties oftlte. \. AH spheres are to one another as the cubes of their diameters. 2. **The surface of a sphere is equal to four times the area of one of its great circles,** as is demonstrated by Archimedes in bis book of the Sphere and Cylinder, lib. i. prop. 37. Hence, to... | |
| William Nicholson - Natural history - 1821
...pole. SPRERE, properties of the. 1. All spheres are to one another as the cubes of their diameters. 2. **The surface of a sphere is equal to four times the area of one of its great circles,** as is demonstrated by Archimedes in his book of the Sphere and Cylinder, lib. i. prop. 37. Hence, to... | |
| Philosophy - 1843
...the thing can be otherwise. What ! is a strict demonstration necessary to enable us to assert, that **the surface of a sphere is equal to four times the area of** its great circle ; — and is not one required to warrant taking away the life of a citizen by a disgraceful... | |
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