Elements of plane and spherical trigonometry: with its applications to the principles of navigation and nautical astronomy; with logarithmic and trigonometrical tables

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E. H. Butler & co., 1848 - Geometry, Solid - 148 pages
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Page 5 - 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 20 - 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 67 - The latitude of a place is its distance from the equator, measured on the meridian of the place. Latitude, therefore, is north or south, according to the pole towards which it is measured, and cannot exceed 90.
Page 98 - Given two sides and the included angle, to find the third side and the remaining angles.
Page xiv - To Divide One Number by Another, Subtract the logarithm of the divisor from the logarithm of the dividend, and obtain the antilogarithm of the difference.
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 66 - The longitude of any place is the arc of the equator, intercepted between the meridian of that place and the first meridian ; the longitude, therefore, is the measure of the angle between the two meridians.
Page 81 - ... 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.
Page 77 - ... latitude, and when registered in a table, they form a table of meridional parts, given in all books on Navigation. The following may serve as a specimen of the manner in which such a table may be constructed, and, indeed, of actually formed by Mr. Wright, the proposer of this vain able method. Mer. pts. of 1' — nat. sec. 1'. Mer. pts. of 2' = nat. sec. 1' + nat. sec. 2'. Mer. pts. of 3' — nat. sec. 1' + nat. sec. 2
Page xxiii - Then, along the horizontal line, and under the given difference of latitude, is inserted the proper correction to be added to the middle latitude to obtain the latitude in which the meridian distance is accurately equal to the departure. Thus, if the middle latitude be 37, and the difference of latitude 18, the correction will be found on page 94, and is equal to 0 40'. EXAMPLES. 1. A ship, in latitude 51 18...

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