Elements of Plane and Spherical Trigonometry: With Its Applications to the Principles of Navigation and Nautical Astronomy. With the Logarithmic and Trigonometrical Tables |
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Page viii
... opposite angles to the tan- gent of half their difference 21 ib . Examples 20. Formulas for determining an angle in terms of the sides 21. Remarks on these formulas 22. Solution of plane triangles in general 23. Examples of the solution ...
... opposite angles to the tan- gent of half their difference 21 ib . Examples 20. Formulas for determining an angle in terms of the sides 21. Remarks on these formulas 22. Solution of plane triangles in general 23. Examples of the solution ...
Page ix
... opposite angles 76 47. Formulas for the angles in terms of the sides 48. Formulas involving only a , b , A , C 49. Formulas for the sides in terms of the angles similarly involving angles and sides 50. To convert any formula involving ...
... opposite angles 76 47. Formulas for the angles in terms of the sides 48. Formulas involving only a , b , A , C 49. Formulas for the sides in terms of the angles similarly involving angles and sides 50. To convert any formula involving ...
Page x
... opposite angle are given 61. When two angles and an opposite side are given PAGE . 83 86 89 93 94 • 96 97 100 • 103 106 PART III . APPLICATION OF TRIGONOMETRY TO NAVIGATION AND NAUTICAL ASTRONOMY . 62. Introductory remarks CHAP . I. On ...
... opposite angle are given 61. When two angles and an opposite side are given PAGE . 83 86 89 93 94 • 96 97 100 • 103 106 PART III . APPLICATION OF TRIGONOMETRY TO NAVIGATION AND NAUTICAL ASTRONOMY . 62. Introductory remarks CHAP . I. On ...
Page 3
... opposite direction as negative ; thus the complement CD of the arc BC commences at C where BC terminates , and may be considered as generated by the motion of C , the extremity of the radius AC , in the direction CD ; but the complement ...
... opposite direction as negative ; thus the complement CD of the arc BC commences at C where BC terminates , and may be considered as generated by the motion of C , the extremity of the radius AC , in the direction CD ; but the complement ...
Page 5
... opposite directions take opposite signs , those above the fixed line B , B being regarded as positive , and those below as negative , so that the sines in the first and second quad- rants are positive , those in the third and fourth ...
... opposite directions take opposite signs , those above the fixed line B , B being regarded as positive , and those below as negative , so that the sines in the first and second quad- rants are positive , those in the third and fourth ...
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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...