| Charles Davies - Geometry - 1854 - 436 pages
...described by ED+DC, is equal to (HI+IP)xcirc. ON, or equal to HP x circ. ON. PROPOSITION X. THEOREM. **The surface of a sphere is equal to the product of...diameter by the circumference of a great circle. Let** ABCDE be a semicircle. Inscribe in it a regular semi•polygon, and from the centre O draw OF perpendicular... | |
| Charles Davies - Geometry - 1855 - 340 pages
...ED+DC, is equal to (HI+IP)x circumference ON, or equal to HPx circumference ON- 1 THEOREM 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... | |
| Jeremiah Day - Logarithms - 1855 - 344 pages
...surface of a hemisphere is equal to the product of its radius into the circumference of its base ; and **the surface of a sphere is equal to the product of its diameter** into its circumference. Cor. 1. From this demonstration it follows, that the surface of any segment... | |
| 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...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... | |
| 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...diameter by the circumference of a great circle. Let** ABCDEF be a semicircle in which is inscribed any regular semi-polygon ; from the centre, O, draw OI... | |
| 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...diameter by the circumference of a great circle. Let** ABCDEF be a semicircle in which is inscribed any regular semi-polygon ; from the center, 0, draw 0... | |
| 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 it.... | |
| Eli Todd Tappan - Geometry, Modern - 1864 - 288 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... | |
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