| William Frothingham Bradbury - Arithmetic - 1895 - 398 pages
...a sphere is a line passing through the centre, and limited in both directions by the surface. 498. **The surface of a sphere is equal to the product of its** circumference and its diameter. Surface of a Sphere = Circumference x Diameter. 58. What is the surface... | |
| John Macnie - Geometry - 1895 - 386 pages
...from Prop. III. PROPOSITION VIII. THEOREM. 700. The area of the surface of a sphere is measured by **the product of its diameter by the circumference of a great circle.** Given : S, the surface of a sphere generated by the revolution of the semicircle ABODE about the diameter... | |
| George Albert Wentworth - Mathematics - 1896 - 68 pages
...radius is a perpendicular erected at the middle point of the line and terminated by the axis. 763. **The area of the surface of a sphere is equal to the...its diameter by the circumference of a great circle.** 764. Cor. 1. The surface of a sphere is equivalent to four great circles. 765. Cor. 2. The areas of... | |
| New York (State). Legislature. Senate - Government publications - 1897 - 1306 pages
...are equivalent. 13 Prove that every section of a sphere made by a plane is a circle. 14-15 Prove that **the area of the surface of a sphere is equal to the...its diameter by the circumference of a great circle.** University of the State of New York Examination Department I34TH EXAMINATION PLANE TRIGONOMETRY Thursday,... | |
| Oklahoma (Ter.). Dept. of Public Instruction - 1893 - 820 pages
...parallelepipeds having equal altitudes are to each other as their bases. Demonstrate. 9. Show that **the area of the surface of a sphere is equal to the** area of four great circles of that sphere. 10 A — BCDE is a cone. Write the theorem for following... | |
| James Howard Gore - Geometry - 1898 - 232 pages
...limit; hence S = AF x 2 TT x R. QED 533. COR. I. Since AF=2R, S = 2 B x 2 „•# = 4 ,rR 2 . Therefore, **the area of the surface of a sphere is equal to the** area of four great circles. 534. COR. 2. The areas of the surfaces of two spheres are to each other... | |
| Harvard University - Geometry - 1899 - 39 pages
...perpendicular erected at the middle of the line and terminated by the axis. THEOREM XXIII. 29 THEOREM XXIV. **The area of the surface of a sphere is equal to the...its diameter by the circumference of a great circle.** 8= 2-jrr X 2r=47rr2. Hence the surface of a sphere is equivalent to four great circles. Corollary.... | |
| George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...holds, but AE and CD coincide, and the truth follows from § 722. PROPOSITION XXVII. THEOREM. 823. **The area of the surface of a sphere is equal to the...its diameter by the circumference of a great circle.** AFOGE Let S denote the surface, R the radius, of a sphere generated by the semicircle ABCDE revolving... | |
| George Albert Wentworth - Geometry - 1899 - 500 pages
...holds, but AE and CD coincide, and the truth follows from § 722. PBOPOSITION XXVII. THEOREM. 823. **The area of the surface of a sphere is equal to the...its diameter by the circumference of a great circle.** c AF a E Let S denote the surface, R the radius, of a sphere generated by the semicircle ABODE revolving... | |
| William James Milne - Geometry - 1899 - 404 pages
...semipolygon, S' =0= rect. AD-2-TrOH. Hence, § 326, S =0= rect. AD • 2 irR. Therefore, etc. QED 725. Cor. I. **The area of the surface of a sphere is equal to the...its diameter by the circumference of a great circle.** 726. Cor. II. § 725, area = AD x 2 vR = 2 R x 2 vR = that is, the area of the surface of a sphere... | |
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