| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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 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... | |
| William Frothingham Bradbury - Geometry - 1872 - 262 pages
...great circle. A section made by a plane not passing through the centre is called a small circle. 61 i **The surface of a sphere is equal to the product of...diameter by the circumference of a great circle. Let** ABC DEF be the semicircle by whose revolution about the diameter AF, the sphere may be described; then... | |
| William Chauvenet - Mathematics - 1872 - 382 pages
...radius is the chord of the generating arc of the zone. B 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... | |
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