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 |
From inside the book
Results 1-5 of 21
Page 151
... Altitudes of Celestial Objects . ( 74. ) The true altitude of a celestial object is always understood to mean its angular distance from the rational horizon of the observer . This is not obtained directly by observation ; but is the ...
... Altitudes of Celestial Objects . ( 74. ) The true altitude of a celestial object is always understood to mean its angular distance from the rational horizon of the observer . This is not obtained directly by observation ; but is the ...
Page 152
... altitude . On this principle is formed the Table at the end , entitled Augmentation of the Moon's Semidiameter , and containing the proper correction to be added to the given horizontal semidiameter to obtain the true semidiameter . On ...
... altitude . On this principle is formed the Table at the end , entitled Augmentation of the Moon's Semidiameter , and containing the proper correction to be added to the given horizontal semidiameter to obtain the true semidiameter . On ...
Page 153
... altitudes , from the horizon to the zenith , and adapted to the mean state of the atmosphere ; but , as the actual state of the atmosphere generally differs from this , it becomes necessary , where the true altitude of the body is ...
... altitudes , from the horizon to the zenith , and adapted to the mean state of the atmosphere ; but , as the actual state of the atmosphere generally differs from this , it becomes necessary , where the true altitude of the body is ...
Page 154
... altitude , the result will be the true altitude of the centre above the visi- ble horizon , and it remains now to apply the correction necessary to reduce this to the true altitude of the centre above the rational horizon ; that is , to ...
... altitude , the result will be the true altitude of the centre above the visi- ble horizon , and it remains now to apply the correction necessary to reduce this to the true altitude of the centre above the rational horizon ; that is , to ...
Page 155
... true altitude above the sensible horizon , to obtain the true altitude above the rational horizon . The sun's parallax in altitude is given in a Table at the end ; and the moon's horizontal parallax is given for the noon and midnight at ...
... true altitude above the sensible horizon , to obtain the true altitude above the rational horizon . The sun's parallax in altitude is given in a Table at the end ; and the moon's horizontal parallax is given for the noon and midnight at ...
Contents
xi | |
2 | |
3 | |
5 | |
6 | |
7 | |
8 | |
9 | |
83 | |
86 | |
89 | |
93 | |
94 | |
96 | |
97 | |
100 | |
10 | |
11 | |
12 | |
13 | |
16 | |
18 | |
19 | |
20 | |
28 | |
34 | |
46 | |
59 | |
65 | |
71 | |
77 | |
78 | |
103 | |
106 | |
109 | |
110 | |
113 | |
114 | |
116 | |
117 | |
121 | |
122 | |
123 | |
126 | |
127 | |
129 | |
130 | |
131 | |
Other editions - View all
Common terms and phrases
ABC are given apparent altitude arc BC arith Asin called celestial sphere centre circle colatitude comp complement computation correction cos.² cos.a cos.c cosec cosine cotangent coversed sine deduced departure determine diff difference of latitude difference of longitude equal equations equinoctial expression find the angle formula given side Greenwich hence horizon hour angle hypotenuse included angle logarithmic longitude measured meridian miles Napier's Nautical Almanack negative obtuse opposite angle parallax parallel parallel sailing perpendicular plane sailing plane triangle pole positive PROBLEM quadrant quantities radius right ascension right-angled triangle rule sailing secant semidiameter ship sin.² sin.c sine and cosine solution sphere spherical angle spherical excess spherical triangle spherical trigonometry subtracted supplement tabular line tangent third side three angles three sides triangle ABC trigono trigonometrical lines true altitude vertical zenith
Popular passages
Page 22 - 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. By
Page viii - In a plane triangle the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles to the tangent of half their difference
Page vi - in cloth. 3. 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 Solution of Equations of the higher orders; the Summation of Infinite Series, &c. 8vo.
Page 69 - Any one side of a spherical triangle is less than the sum of the other two. Let ABC be any spherical triangle, and O the centre of the sphere;
Page 155 - 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' we have given the three sides to find the angle S'SZ; having then the angles PSS', S'SZ, the angle ZSP
Page 49 - Again, let the sum of the three arcs be 90°, or any multiple thereof, then the cosine of this sum will be 0, so that the second general equation above becomes cos. A cos. B cos. C = cos. A cos. B cos. C + sin. A cos. B
Page 177 - of the arithmetical complement of the log. cosine; subtract 10 from the index of the sum, and the remainder will be the logarithm of the number of seconds in the arc. 2. Let the log. tangent be given; then from the expression (3), last problem, we have
Page 69 - The sum of all 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,
Page 125 - That vertical which passes through the east and west points of the horizon is called the prime vertical; it necessarily intersects the meridian of the place (which passes through the north and south points) at
Page vi - 2. The ELEMENTS of the DIFFERENTIAL CALCULUS'. comprehending the General Theory of Curve Surfaces and of Curves of Double Curvature. 8s. in cloth. 3. An ELEMENTARY TREATISE on ALGEBRA, Theoretical and Practical; with