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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: With Applications in Mensuration

Charles Davies - Geometry - 1864 - 358 pages
...THEOREM XXIII. The surface of a sphere is equal to ihr product of its diameter by the ctrcumference of a great 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. I,et the...

## Elements of Geometry and Trigonometry

C. Davies - 1867 - 342 pages
...by ED+DC, is equal to (HI+IP)x circumference ON, or equal to -/IP x circumference ONTHEOREM XXIIIThe surface of a sphere is 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...

## Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1868 - 340 pages
...the circ. 0I, or to the product of the axis AF by the circ. 0 I. PKO POSITION VIII. — THEOREM. 588. The surface of a sphere is equal to the product of...diameter by the circumference of a great circle. Let ABCDEP be a semicircle in which is inscribed any regular semi-polygon ; from the centre, 0, draw 01...

## Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1869 - 516 pages
...the circ. 0 1, or to the product of the axis AF by the circ. 0 1. PROPOSITION VIII. — THEOREM. 588. The surface of a sphere is equal to the product of...diameter by the circumference of a great circle. Let ABCDEF be a semicircle in which is inscribed any regular semi-polygon ; from the centre, 0, draw 0...

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

Charles Davies - Geometry - 1870 - 392 pages
...by ED+DC, is equal to (HI+IP)x circumference ON, or equal to HPx. 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 О draw OF perpendicular to one of the sides. Let the...

## A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...radius is the chord of the generating arc of the zone. ,i_ PROPOSITION XI.— THEOREM. 41. 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 the preceding proposition, since the surface of the whole sphere may be...

## Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 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 diaiiw ter by the circumference of a great circle. Let ABDF be the semicircle by the revolution of...

## An Elementary Geometry

William Frothingham Bradbury - Geometry - 1872 - 124 pages
...passes through the centre of the sphere, its radius will be the radius of the sphere. THEOREM XV. 61 . The surface of a sphere is equal to the product of...by the circumference of a great circle. Let ABCDE F be the semicircle by whose revolution about the diameter AF, the sphere may be described ; then the...