 | Elias Loomis - Conic sections - 1857 - 242 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 diarrw ter by the circumference of a great circle. Let ABDF be the semicircle by the revolution of... | |
 | Elias Loomis - Conic sections - 1858 - 256 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 diame ter by the circumference of a great circle. Let ABDF be the semicircle by the revolution of which... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 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 its diameter by the circumference of a great circle. Let ABCDEF be a semicircle in which is inscribed any regular... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...the circ. OI, or to the product of the axis AF by the circ. O I. PROPOSITION VIII. — THEOREM. 588. The surface of a sphere is equal to the product of its diameter by the circumference of a great circle. Let ABCDEF be a semicircle in which is inscribed any regular... | |
 | Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...inscribed polygon, it is evident that KE will be its apothegm (Cor. 2, Theo. XXVIII, B. I). THEOREM XIV. The surface of a sphere is equal to the product of its diameter by its circumference. Let ABCDEF be a semicircle, having the half of a regular polygon inscribed in... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...the circ. 0 I, or to the product of the axis AF by the circ. 0 I. PROPOSITION VIII. — THEOREM. 588. The surface of a sphere is equal to the product of its diameter by the circumference of a great circle. Let ABCDEF be a semicircle in which is inscribed any regular... | |
 | 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 its diameter by the circumference of a great circle. Let ABCDEP be a semicircle in which is inscribed any regular... | |
 | 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 its diameter by the circumference of a great circle. Let ABCDEF be a semicircle in which is inscribed any regular... | |
 | 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... | |
 | 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... | |
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The surface of a sphere is equal to the product of its diameter by the circumference of a great circle. 
