# Elements of Plane and Spherical Trigonometry: With Its Applications to the Principles of Navigation and Nautical Astronomy. With the Logarithmic and Trigonometrical Tables

J. Souter, 1833 - Astronomy - 208 pages
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Page ii - In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page xvii - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 134 - If the zenith distance and declination be of the same name, that is, both north or both south, their sum will be the latitude ; but, if of different names, their difference will be the latitude, of the same name as the greater.
Page 139 - PS' ; the coaltitudes zs, zs', and the hour angle SPS', which measures the interval between the observations ; and the quantity sought is the colatitude ZP. Now, in the triangle PSS , we have given two sides and the included angle to find the third side ss', and one of the remaining angles, say the angle PSS'. In the triangle zss...
Page 45 - The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle ; produce the sides AB, AC, till they meet again in D. The arcs ABD, ACD, will be semicircumferenc.es, since (Prop.
Page 138 - It should also be observed here, that in the preceding examples the celestial object is supposed to be on the meridian above the pole ; that is, to be higher than the elevated pole. But, if a meridian altitude be taken below the pole, which may be done if the object is circumpolar, or so near to the elevated pole as to perform its apparent daily revolution about it without passing below the horizon, then the latitude of the place will be equal to the sum of the true altitude, and the codeclination...
Page 47 - ... that the two angles A and D lie on the same side of BC, the two B and E on the same side of AC, and the two C and F on the same side of AB.
Page 109 - ... the surface of the celestial sphere. The Zenith of an observer is that pole of his horizon which is exactly above his head. Vertical Circles are great circles passing through the zenith of an observer, and perpendicular to his horizon.