...The surfaces of segments and zones of the same sphere are to one another as their heights. COR. 4. The surface of a sphere is equal to four times the area of a great circle, and the convex surface of a hemisphere is double the area of its base. COR. 5. The...

...surface which is produced by a pressure of 4000 grains on the piston A, whose radius is one inch. NB — The surface of a sphere is equal to four times the area of one of its great circles. Am. Pressure = 1000 grains. This pressure is evidently distributed equally over the entire surface...

...The solidity of a sphere is equal to two thirds of the solidity of its circumscribing cylinder, 8. The surface of a sphere is equal to four times the area of a circle of the satne diameter as the sphere; or to the area of a circle whose madia tersis double...

...On these considerations the following calculations depend. It is well known and easily proved, that the surface of a sphere is equal to four times the area of any one of its great circles ; .-. Зтгг2 = area of the hemisphere BCLb'cQ. Let A° represent the...

...inches, then the circumference = 7x3-14 = 21-98, and the surface of the sphere = 21 -98 x 7 = 153-86. The surface of a sphere is equal to four times the area of a great circle ; ie, of the generating circle. Let d be the radius, then dx '7854 = area of circle,...

...generated by the polygon becomes a sphere ; and we get 47rß2 for the entire surface of the sphere. Hence, the surface of a sphere is equal to four times the area of one of its great circles. Again, it is easy to find the surface generated by any number of sides of the polygon. Thus, for example,...

...that is, to four times the base, for the height of the cylinder is equal to the diameter of the base. Hence the surface of a sphere is equal to four times the area of 'a circle of the same diameter. Its solid content is manifestly equal to that of a pyramid, whose base...

...generated by the polygon becomes a sphere; and we get 471- .R2 for the entire surface of the sphere. Hence, the surface of a sphere is equal to four times the area of one of its great circles. Again, it is easy to find the surface generated by any number of sides of the polygon. Thus, for example,...

...hence the surface of a sphere = 4»R2. Coit. 2. The area of a great circle = «R2 (IV., 12, Cor. 3) : hence the surface of a sphere is equal to four times the area of one of its great circles. BOOK VIII.] MEASUREMENT OF SOLIDS. COR. 3. The surfaces of two spheres are to each other as the squares...

...before Eudoxus) no one had discovered them. In like manner, none before Archimedes had discovered that the surface of a sphere is equal to four times the area of one of its great circles (prop. 35) ; the volume of a sphere to two thirds of the circumscribed cylinder having the same altitude,...