The Elements of Plane and Spherical Trigonometry: And Its Application to Astronomy, Dialling, and Trigonometrical Surveying. With Plates. Designed for Mathematical Students

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T. Ostell and Company, 1841 - Spherical astronomy - 191 pages
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Page 60 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 57 - From a window near the bottom of a house, which seemed to be on a level with the bottom of a steeple, I took the angle of elevation of the top of the steeple equal...
Page 31 - THEOREM I. The sides of a plane triangle are proportional to the sines of their opposite angles.
Page 68 - That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles.
Page 62 - A great circle may be drawn through any two points on the surface of a sphere, but not through more than two, taken at random.
Page 59 - Required the horizontal distance of the vessel, and the height of the promontory above the level of the sea, the light-house being 85 feet high. Ans. Distance 5296.4 feet, height 251.3 feet. Prob. 11. An observer, seeing a cloud in the west, measured its angle of elevation, and found it to be 64░. A second observer, situated half a mile due east from the first station, and on the same...
Page 56 - What is the perpendicular height of a hill ; its angle of elevation, taken at the bottom of it, being 46░, and 200 yards farther off, on a level with the bottom, the angle was 31░?
Page 59 - ... it is required from these measures to determine the magnitude of the whole earth, and the utmost distance that can be seen on its surface from the top of the mountain, supposing the form of the earth to be perfectly...
Page x - CB : CA : : sin A : sin B. For, with A as a centre, and AD equal to the less side...
Page 59 - Required the distance from A to B. Ans. 345.5 yards. Prob. 10. From the top of a light-house, the angle of depression of a ship at anchor was 3░ 38', and at the bottom of the light-house the angle of depression was 2░ 43'.

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