 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...circumference of the inscribed circle. PROPOSITION X. THEOREM. The surface of a sphere is equal to its diameter by the circumference of a great circle. Let ABCDE be a semi-circumference, O its centre, and AE its diameter : then is the surface of the sphere generated... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...proposition may be formulated, PROPOSITION X.— THEOREM. 37. 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 Proposition IX., since the surface of the whole sphere may be regarded as... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...same from (773) and (753). QEU Proposition 1 O. Theorem. 789. The area of the surface of a sphere is equal to the product of its diameter by the circumference of a great circle. Hyp. Let the sphere be generated by the revolution of the semicircle ABDF about the diameter AF, let... | |
 | William Chauvenet - 1893 - 340 pages
...This proposition may be formulated, S = 2vRH. PROPOSITION X. The area of the surface of a sphere is equal to the product of its diameter by the circumference of a great circle. Corollary I. This may be formulated, S = 2irJR X 2.B = 4vrIP. Hence the surface of a sphere is equivalent... | |
 | Rutgers University. College of Agriculture - 1893 - 682 pages
...find its area on a sphere whose surface is 72 square inches. 9. The area of the surface of a sphere is equal to the product of its diameter by the circumference of a great circle. 10. Find the volume of the frustum of a right cone, the radii of whose bases are 4 and 2 feet and the... | |
 | George Clinton Shutts - Geometry - 1894 - 412 pages
...whose angles are 200°, 140° and ioo°? 347 PROPOSITION XXX. 699. Theorem. The area of a sphere is equal to the product of its diameter by the circumference of a great circle. „A О Let А С DB represent a semi-circle; AB its diameter and 0 the center of A B. Let А С DB... | |
 | Bothwell Graham - Arithmetic - 1895 - 240 pages
...circumference of its base by one-half its slant height. IV. That the area of a surface of a sphere is equal to the product of its diameter by the circumference of a great circle. V. That the area of the lateral surface of a pyramid is equal to the product of the perimeter of its... | |
 | 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
...the middle point of the line and terminated by the axis. 763. The area of the surface of a sphere is equal to the product of 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
...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 product of its diameter by the circumference of a great circle. University of the State of New York Examination Department I34TH EXAMINATION PLANE TRIGONOMETRY Thursday,... | |
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The surface of a sphere is equal to the product of its diameter by the circumference of a great circle. 
