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" The surface of a sphere is equal to the product of its diameter by the circumference of a great circle. "
A Treatise of Plane Trigonometry: To which is Prefixed a Summary View of the ... - Page 50
by Jeremiah Day - 1831 - 155 pages
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 574 pages
...circle. This axis FG will be 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...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 276 pages
...circle. This axis FG will be 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...
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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
...circle. This axis FG will be 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....
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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
...half the sum of all the 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...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 pages
...circle. This axis FG xvill at 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...
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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
...half the sum of all the 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...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 pages
...described by ED + DC, is equal to (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- of a great circle. Let ABCDE be -a semicircle. Inscribe in it any regular semi-polygon,...
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A Course of Mathematics: Containing the Principles of Plane ..., Volumes 1-3

Jeremiah Day - Geometry - 1839 - 434 pages
...which shall differ less than by any f.ven quantity from the circle in which it is inscribed; (Sup. uc. 4. 1.) and in which the perpendicular GC shall differ...radius into the circumference of its base ; and the stirface of a sphere is equal to the product of its diameter into its circumference. Cor. 1. From this...
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First Lessons in Geometry: With Practical Applications in Mensuration, and ...

Charles Davies - Geometrical drawing - 1840 - 262 pages
...circle. If it does not pass through the centre, the circle of section is called a small circle. 24. The surface of a sphere is equal to the product of its diameter by the circumference of a great circle. Thus, the surface of the sphere whose centre is C, is equal...
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Pantology: Or, A Systematic Survey of Human Knowledge; Proposing a ...

Roswell Park - Best books - 1841 - 722 pages
...multiplied by its slant height, or distance from the vertex to any point of the circumference just named: and the surface of a sphere, is equal to the product of its diameter by the circumference of a great circle, that is, of the sphere itself. The measure of the solidity...
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