Elements of Plane and Spherical Trigonometry: With Its Applications to the Principles of Navigation and Nautical Astronomy. With the Logarithmic and Trigonometrical TablesJ. Souter, 1833 - 264 pages |
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Page vi
... Course . " More elegant Text- books do not exist in the English Language , and we trust they will speedily be adopted in our Mathematical Seminaries . The existence of such auxiliaries , will , of itself , we hope , prove an inducement ...
... Course . " More elegant Text- books do not exist in the English Language , and we trust they will speedily be adopted in our Mathematical Seminaries . The existence of such auxiliaries , will , of itself , we hope , prove an inducement ...
Page 32
... course , neither of these formulas will be used , as the unknown parts will be more readily found as in Ex- ample 3 , p . 15 . EXAMPLES . 1. The three sides of the triangle ABC are AB = 1637 , AC = 2065 , BC = 3387 · 974 ; required the ...
... course , neither of these formulas will be used , as the unknown parts will be more readily found as in Ex- ample 3 , p . 15 . EXAMPLES . 1. The three sides of the triangle ABC are AB = 1637 , AC = 2065 , BC = 3387 · 974 ; required the ...
Page 55
... course , all be deduced from the general expressions investigated in the beginning of this article , but , for simplicity sake , we shall go nearer to first principles , and deduce them from the expressions in art . ( 26 ) . Referring ...
... course , all be deduced from the general expressions investigated in the beginning of this article , but , for simplicity sake , we shall go nearer to first principles , and deduce them from the expressions in art . ( 26 ) . Referring ...
Page 109
... course and the distance sailed exactly ; so that after a long passage it would be unsafe to com- pute the place of the ship from the ship's reckoning . In such cases , therefore , the solution must be effected from other data ...
... course and the distance sailed exactly ; so that after a long passage it would be unsafe to com- pute the place of the ship from the ship's reckoning . In such cases , therefore , the solution must be effected from other data ...
Page 111
... course of a ship is the angle which her track makes with the meridians ; so long as this angle remains the same , the ship is said to sail on the same rhumb line , or loxodromic curve . The magnitude of the angle or the course is ...
... course of a ship is the angle which her track makes with the meridians ; so long as this angle remains the same , the ship is said to sail on the same rhumb line , or loxodromic curve . The magnitude of the angle or the course is ...
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Common terms and phrases
ABC are given apparent altitude arc BC arith Asin called celestial sphere centre chord circle colatitude comp complement computation correction cosec cosine cotangent course and distance deduced departure determine diff difference of latitude difference of longitude direct course equal equations equinoctial expression find the angle formula given side Greenwich hence horizon hour angle hypotenuse included angle logarithmic measured meridian middle latitude miles Napier's Nautical Almanack negative oblique obtuse opposite angle parallax parallel parallel sailing perpendicular plane sailing plane triangle pole PROBLEM quadrant quantities radius right ascension right-angled triangle rule secant semidiameter ship sin.c sine sine and cosine solution sphere spherical angle spherical triangle spherical trigonometry subtracting supplement tabular line tangent third side three angles three sides triangle ABC trigono trigonometrical lines true altitude values vertical zenith
Popular passages
Page viii - 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 99 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Page 22 - 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 vi - An Elementary Treatise on Algebra, Theoretical and Practical; with attempts to simplify some of the more difficult parts of the Science, particularly the Demonstration of the Binomial Theorem in its most general form ; the Summation of Infinite Series ; the Solution of Equations of the Higher Order, &c., for the use of Students.
Page 160 - 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 165 - 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 129 - 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 vi - MICHAEL O'SHANNESSY, AM 1 vol. 8vo. " The volume before us forms the third of an analytical course, which commences with the * Elements of Analytical Geometry.' More elegant t&xtbooks do not exist in the English language, and we trust they will speedily be adopted in our Mathematical Seminaries. The existence of such auxiliaries will, of itself, we hope, prove an inducement to the cultivation of Analytical Science ; for, to the want of such...
Page 69 - 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 - PEP' (Fig. 22,) represent the meridian of the place, Z being the zenith, and HO the horizon ; and let LL' be the apparent path of the sun on the proposed day, cutting the horizon in S. Then the...