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 9
... ( A + B ) = sin . A cos . B + sin . B cos . A ; in which the term on the left is of one dimension , and the terms on the right are each of two dimensions , will become homogeneous by intro- ducing the factor R into the left hand number ...
... ( A + B ) = sin . A cos . B + sin . B cos . A ; in which the term on the left is of one dimension , and the terms on the right are each of two dimensions , will become homogeneous by intro- ducing the factor R into the left hand number ...
Page 10
... cos . + sin . w cot . w This last line is the same as the first ; and any line will , obviously , re- main unaltered if we add to the corresponding arc a whole circumference or any number of circumferences . If we take a negatively , we ...
... cos . + sin . w cot . w This last line is the same as the first ; and any line will , obviously , re- main unaltered if we add to the corresponding arc a whole circumference or any number of circumferences . If we take a negatively , we ...
Page 11
... A. Also , by taking the hypotenuse for the radius , we have BC AC sin . A , AB AC cos . A. = These four equations , together with the geometrical property AC2AB + BC2 , enable us to solve every case of right - angled triangles . ( 13 ...
... A. Also , by taking the hypotenuse for the radius , we have BC AC sin . A , AB AC cos . A. = These four equations , together with the geometrical property AC2AB + BC2 , enable us to solve every case of right - angled triangles . ( 13 ...
Page 12
... a radius of 101o . Hence , in all formulas of trigonometry intended for logarithmic computation , the ra- dius R ... cos . A BC AC ; AB and all these equations may be comprehended in a single rule , expressed as below As the tabular ...
... a radius of 101o . Hence , in all formulas of trigonometry intended for logarithmic computation , the ra- dius R ... cos . A BC AC ; AB and all these equations may be comprehended in a single rule , expressed as below As the tabular ...
Page 14
... A 53 ° 8 ' 10.2218814 : AC 480-036 2.6812739 . : If we had made AC radius , the proportion would have been cos . A : AB rad . : AC . By way of showing the use of the arithme- tical complement , let us determine AC by this proportion cos . A ...
... A 53 ° 8 ' 10.2218814 : AC 480-036 2.6812739 . : If we had made AC radius , the proportion would have been cos . A : AB rad . : AC . By way of showing the use of the arithme- tical complement , let us determine AC by this proportion cos . A ...
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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