Elements of Plane and Spherical Trigonometry: With Numerous Practical Problems

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Ivison, Blakeman, Taylor, 1880 - Trigonometry - 208 pages
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Page 322 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 259 - In every triangle the sum of the three angles is equal to two right angles.
Page 256 - If a perpendicular be let fall from any angle of a triangle to its opposite side or base, this base is to the sum of the other two sides, as the difference of the sides is to the difference of the segments of the base.
Page 363 - Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex ; construct the triangle.
Page 307 - A point of land was observed, by a ship at sea, to bear east-by-south ; and after sailing north-east 12 miles, it was found to bear south-east-by-east. It is required to determine the place of that headland, and the ship's distance from it at the last observation ? Ans.
Page 332 - Two triangles, having an angle in the one equal to an angle in the other, are to each other as the rectangles of the sides which contain the equal angles.
Page 311 - Axis of any circle of a sphere is that diameter of the sphere which is perpendicular to the plane of the circle.
Page 326 - The area of a lune is to the surface of the sphere, as the angle of the lune is to four right angles.
Page 336 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 293 - D = 31░ 17' 19". We are required to find AE, the angle DAE, and the angle E. Observe that the angle E must be less than the angle DAE, because it is opposite a less &.de. From 180░ Take D, 31░ 17' 19", Sum of the other two angles, = 148░ 42

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