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" The surface of a sphere is equal to the product of its diameter by the circumference of a great circle. "
Elements of Geometry and Trigonometry: With Applications in Mensuration - Page 159
by Charles Davies - 1886 - 324 pages
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 574 pages
...at the same time the diameter of the circumscribed circle. THEOREM. 535. The surface of a sphere is equal to the product of its diameter by the circumference of a great circle. Demonstration. 1. We say that the diameter of a sphere multiplied by the circumference of a great circle...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 276 pages
...the same time the diameter of the circumscribed circle, • THEOREM. 535. The surface of a sphere is equal to the product of its diameter by the circumference of a great circle. Demonstration. 1. We say that the diameter of a sphere multiplied by the circumference of a great circle...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...at the same time the diameter of the circumscribed circle. THEOREM. 535. The surface of a sphere is equal to the product of its diameter by the circumference of a great circle. measure of^the surface of a greater sphere. For, if it be possiFig. 263. ble, let AB x circ. AC (Jig....
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The North American Review, Volume 27

Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - American fiction - 1828 - 598 pages
...parallel sides, or half the sum of the two circumferences. QED Theorem 535. ' The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.' This is incuded in the preceding corollary. ' The entire surface described by the revolution of a semipolygon...
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The North American Review, Volume 27

Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - American fiction - 1828 - 598 pages
...parallel sides, or half the sum of thetwo circumferences. QED Theorem 535. ' The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.' This is incuded in the preceding corollary. ' The entire surface described by the revolution of a semipolygon...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 pages
...the same time be the diameter of the circumscribed circle. THEOREM. 535. The surface of a sphere is equal to the product of its diameter by the circumference of a great circle. We shall first shew, that the diameter of a sphere multiplied by the circumference of its great circle...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 pages
...(HI + IP) xcirc. ON, or equal to HP x circ. ON. PROPOSITION X. THEOREM. The surface of a sphere is equal to the product of its diameter by the circumference-...perpendicular to one of the sides. Let the semicircle and the ' semi-polygon be revolved about the axis AE : the semicircumference ABCDE will describe the surface...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 376 pages
...(HI + IP) x circ. ON, or equal to IIP x circ. ON. PROPOSITION X. THEOREM. The surface of a sphere is equal to the product of its diameter by the circumference of a great circle. D E O A Let ABCDE be a semicircle. Inscribe in it any regular semi-polygon, and from the centre O draw...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...surface generated by the circular segment ABCD is a zone. Hence the area of the surface of a sphere is the product of its diameter by the circumference of a great circle. And, the area of a zone is the product of its altitude by the circumference of a great circle. 473....
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 372 pages
...(HI + IP) x circ. ON, or equal to HP x circ. ON. PROPOSITION X. THEOREM. The surface of a sphere is equal to the product of its diameter by the circumference...Inscribe in it any regular semi-polygon, and from the I centre O draw OF perpendicular to one of the sides. Let the semicircle and the semi-polygon be revolved...
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