Elements of Plane and Spherical Trigonometry: With it Applications to the Principles of Navigation and Nautical Astronomy; with the Logarithmic and Trigonometrical TablesE.H. Butler & Company, 1848 - 200 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 98 - Given two sides and the included angle, to find the third side and the remaining angles.
Page 77 - To THE TANGENT OF THE COURSE ; So IS THE MERIDIONAL DIFFERENCE OF LATITUDE, To THE DIFFERENCE OF LONGITUDE. By this theorem, the difference of longitude may be calculated, without previously rinding the departure.
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 73 - It follows, therefore, that any problem in parallel sailing, may be solved by the traverse table, computed to degrees, as a simple case of plane sailing ; for by considering the latitude as the course, and the distance as the difference of latitude, the corresponding distance in the table will express the difference of longitude. EXAMPLES. 1. A ship from latitude 53° 56' N, longitude 10° 18' E., has sailed due west, 236 miles : required her present longitude.
Page 60 - Art. 87, the only part required happens to be the side opposite the given angle, the finding of the other two angles then becomes merely a subsidiary operation, and the determination of the required side, by Napier's analogies, seems somewhat lengthy. But a shorter method of solution is deducible from the fundamental formula, cos c = cos a cos b + sin a sin b cos c (1).
Page 48 - E the centre of the circle, and join EA, EB. Then because AF is equal to FB, and FE common to the two triangles AFE, BFE, there are two sides in the one equal to two sides in the other : but the base EA is equal to the base EB ; therefore the angle AFE is equal (8.
Page 46 - ... 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 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 valu able method. Mer. pts. of 1' — nat. sec. 1'. Mer. pts. of 2' = nat. sec. 1' + nat. sec. 2'. Mer. pts. of 8' = nat. sec. 1 + nat. sec. 2 + nat. sec. 3'.