| 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... | |
| 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... | |
| Eli Todd Tappan - Geometry - 1868 - 444 pages
...this surface is that of a sphere, and the radius CI then becomes the radius of the sphere. Therefore, **the area of the surface "of a sphere is equal to the product of** the diameter by the circumference of a great circle. 787. Corollary. — The area of the surface of... | |
| Eli Todd Tappan - Geometry - 1868 - 432 pages
...circle is equal to the product of its circumference by one-fourth of the diameter. 788. Corollary — **The area of the surface of a sphere is equal to the** area of the curved surface of a circumscribing cylinder ; that is, a cylinder whose bases are tangent... | |
| 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... | |
| Isaac Todhunter - Measurement - 1869 - 312 pages
...is, the circumference of a great circle of the sphere. 348. It follows from Arts. 320 and 345, that **the area of the surface of a sphere is equal to the** area of the curved surface of a right circular cylinder which has itt height and the diameter of its... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...circle whose 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...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... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...circle •whose radius is the chord of the generating arc of the zone. PROPOSITION XI.— THEOREM. 41. **The area of the surface of a sphere is equal to the product of** itg diameter by the circumference of a great circle. This follows directly from the preceding proposition,... | |
| 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... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...circle whose radius is the chord of the generating arc of the zone. PROPOSITION XI.—THEOREM. 41. **The area of the surface of a sphere is equal to the...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... | |
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