| 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... | |
| William Frothingham Bradbury - Geometry - 1873 - 132 pages
...passes through the centre of the sphere, its radius will be the radius of the sphere. THEOREM XV. 611 **The surface of a sphere is equal to the product of...diameter by the circumference of a great circle. Let** ABCDEF\>Q the semicircle by whose revolution about the diameter AF, the sphere may be described; then... | |
| 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... | |
| Benjamin Greenleaf - Geometry - 1875 - 204 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...by the circumference of a great circle. Let ABCDE** Fbea semicircle in which is inscribed any regular semi-polygon; from the center, O, draw OI perpendicular... | |
| Aaron Schuyler - Geometry - 1876 - 384 pages
...and therefore fails; but formula (1) holds true. (?) 484. Proposition XXXI.— Theorem. The area of **the surface of a sphere is equal to the product of...diameter by the circumference of a great circle. Let** the semicircle ABD, and any regular inscribed semi-polygon, as ABCD, revolve together about the diameter... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...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 product of...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 are to... | |
| George Albert Wentworth - Geometry - 1877 - 426 pages
...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 product of...diameter by the circumference of a great circle. Let** ABСDE be the circumference of a great circle, and AD the diameter, and OA the radius of a sphere.... | |
| George Albert Wentworth - Geometry - 1877 - 436 pages
...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 product of...its diameter by the circumference of a great circle.** D Let ABСDE 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... | |
| |