| William Frothingham Bradbury - Geometry - 1872 - 262 pages
...great circle. A section made by a plane not passing through the centre is called a small circle. 61 i **The surface of a sphere is equal to the product of...diameter by the circumference of a great circle. Let** ABC DEF be the semicircle by whose revolution about the diameter AF, the sphere may be described; then... | |
| William Frothingham Bradbury - Geometry - 1872 - 124 pages
...passes through the centre of the sphere, its radius will be the radius of the sphere. THEOREM XV. 61 . **The surface of a sphere is equal to the product of...diameter by the circumference of a great circle. Let** ABCDE F be the semicircle by whose revolution about the diameter AF, the sphere may be described ;... | |
| Eli Todd Tappan - Geometry - 1873 - 288 pages
...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** area of the curved surface of a circumscribing cylinder ; that is, a cylinder whose bases are tangent... | |
| Benjamin Greenleaf - Geometry - 1873 - 202 pages
...GH, HM, MN, NF, by the circ. OI, or to the product of the axis AF by the circ. O I. THEOREM IX. 361. **The surface of a sphere is equal to the product of...diameter by the circumference of a great circle. Let** ABCDEFbe& semicircle in which is inscribed any regular semi-polygon ; from the center, O, draw OI perpendicular... | |
| David Munn - 1873 - 160 pages
...a spherical zone is equal to the product of its altitude by the circumference of the sphere 68 IX. **The surface of a sphere is equal to the product of its diameter by the circumference of** the sphere 70 X. The ratio of the surface of the lune to the whole surface of the sphere is the same... | |
| Benjamin Greenleaf - Geometry - 1874 - 206 pages
...GH, HM, MN, NF, by the circ. O /, or to the product of the axis AF by the circ. O I. THEOREM IX. 361. **The surface of a sphere is equal to the product of...diameter by the circumference of a great circle. Let** ABCDEF\)e& semicircle in which is inscribed any regular semi-polygon ; from the center, O, draw OI... | |
| Edward Olney - Arithmetic - 1876 - 322 pages
...barrels does a cistern contain which is a circular cylinder 7 ft. in diameter and 8 ft. deep ? 25. **The area of the surface of a sphere is equal to the** area of 4 of its great circles.* What is the area of the surface of the earth, its radius being 3960... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...shall also touch the surface of a given sphere. GEOMETUY. BOOK VIII. PROPOSITION XXX. THEOREM. 761. **The area of the surface of a sphere is equal to the...diameter by the circumference of a great circle. Let** ABCDE be the circumference of a great circle, and AD the diameter, and OA the radius of a sphere. We... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...shall also touch the surface of a given sphere. GEOMETRY. BOOK VIH. PROPOSITION XXX. THEOREM. 761. **The area of the surface of a sphere is equal to the...its diameter by the circumference of a great circle.** AA Let ABC DE be the circumference of a great circle, and AD the diameter, and OA the radius of a sphere.... | |
| J. G - 1878 - 408 pages
...product of its altitude by the circumference of the sphere, ie, of a great circle, and thence that **the surface of a sphere is equal to the product of its diameter** into the circumference of the sphere ; for the surface of the sphere may be regarded as a zone whose... | |
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