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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 - Page 215
by Adrien Marie Legendre - 1852 - 432 pages
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 204 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. 474....
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A Treatise of Plane Trigonometry, and the Mensuration of Heights and ...

Jeremiah Day - Logarithms - 1848 - 354 pages
...surface of a hemisphere is equal to *the product of its radius into the circumference of its base; and the surface of a sphere is equal to the product of its diameter into its circumference. Cor. 1. From this demonstration it follows, that the surface of any segment...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 372 pages
...described by ED + DC, is equal to (HI +1P) x circ. ON, or equal to HP x circ., ON. PROPOSITION X. THEOREM. The surface of a sphere is equal to the product of...circle. Let ABCDE be a semicircle. Inscribe in it any regular semi-polygon, and from the centre O draw OF perpendicular to one of the sides. Let the...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...base of the frustum, its upper base, and a mean proportional between them. PROPOSITION VII. THEOREM. The surface of a sphere is equal to the product of its diameter b\j the circumference of a great circle. Let ABDF be the semicircle by the revolution of which the...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 238 pages
...by ED+DC, is equal to (HI+IP)x circumference ON, or equal to UP x circumference ON. THEOREM XXIII. The surface of a sphere is equal to the product of...circle. Let ABCDE be a semicircle. Inscribe in it any regular semi-polygon, and from the centre O draw OF perpendicular to one of the sides. Let the...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 218 pages
...by ED+DC, is equal to (HI+IP)x circumference OJV, or equal to HPx circumference ON. THEOREM XXIII. The surface of a sphere is equal to the product of...diameter by the circumference of a great circle. Let ABODE be a semicircle. Inscribe in it any regular semi-polygon, and from the centre 0 draw OF perpendicular...
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A Course of Mathematics: Containing the Principles of Plane Trigonometry ...

Jeremiah Day - Geometry - 1851 - 418 pages
...surface of a hemisphere is equal to the product of its radius into the circumference of its base ; and the surface of a sphere is equal to the product of its diameter into its circumference. Cor. 1. From this demonstration it follows, that the surface of any segment...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1886 - 340 pages
...(HI+IP)x circumference ON, or equal to HPx circumference ONTHEOREM XXIIIThe surface of a sphere 1s equal to the product of its diameter by the circumference of a great circleLet ABCDE be a semicircle- Inscribe in it any regular semi-polygon, and from the centre O draw...
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A Treatise on Surveying and Navigation: Uniting the Theoretical, Practical ...

Horatio Nelson Robinson - History - 1853 - 334 pages
...the application of the preceding rules. From theorem 16, book VII, Geometry, we learn that The convex surface of a sphere is equal to the product of its diameter into its circumference. The surface of a segment is equal to the circumference of the sphere, multiplied...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 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...in it a regular semi•polygon, and from the centre O draw OF perpendicular to one of the sides. Let the semicircle and the semi•polygon be revolved...
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