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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

## Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...circumference of the inscribed circle. PROPOSITION X. THEOREM. The surface of a sphere is equal to its diameter by the circumference of a great circle. Let ABCDE be a semi-circumference, O its centre, and AE its diameter : then is the surface of the sphere generated...

## Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1886 - 352 pages
...(HI+IP)x circumference ON, or equal to HPxci1cum. ference ON. THEOREM XXIII. The surface of a sphere 1s equal to the product of its diameter by the circumference...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...

## Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...circumference of a great circle. Corollary. This proposition may be formulated, PROPOSITION X. The area of the surface of a sphere is equal to the product of...its diameter by the circumference of a great circle. Corollary I. This may be formulated, Hence the surface of a sphere is equivalent to four great circles....

## The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...surface, the result is the same from (773) and (753). QEU Proposition 1 O. Theorem. 789. The area of the surface of a sphere is equal to the product of...its diameter by the circumference of a great circle. Hyp. Let the sphere be generated by the revolution of the semicircle ABDF about the diameter AF, let...

## A Text-book of Geometry

George Albert Wentworth - Geometry - 1892 - 468 pages
...in the first equation, we obtain area AB = CD X ZirMR. PROPOSITION XXVII. THEOREM. 763. The area of the surface of a sphere is equal to the product of...its diameter by the circumference of a great circle. C ^^ B. G- E Let the sphere be generated by the semicircle ABCDE revolving about the diameter AE, and...

## Elementary Geometry

William Chauvenet - 1893 - 340 pages
...circle. 36. COROLLARY. The proposition may be formulated, S = PROPOSITION X.—THEOREM. 37. The area of the surface of a sphere is equal to the product of...its diameter by the circumference of a great circle. This follows directly from Proposition IX., since the surface of the whole sphere may be regarded as...

## Report

Rutgers University. College of Agriculture - 1893 - 682 pages
...angle of a lune is 50°, find its area on a sphere whose surface is 72 square inches. 9. The area of the surface of a sphere is equal to the product of...its diameter by the circumference of a great circle. 10. Find the volume of the frustum of a right cone, the radii of whose bases are 4 and 2 feet and the...

## Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1894 - 412 pages
...spherical triangle whose angles are 200°, 140° and ioo°? 347 PROPOSITION XXX. 699. Theorem. The area of a sphere is equal to the product of its diameter by the circumference of a great circle. „A О Let А С DB represent a semi-circle; AB its diameter and 0 the center of A B. Let А С DB...