 | 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... | |
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The surface of a sphere is equal to the product of its diameter by the circumference of a great circle. 
