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 37
... ship at anchor , was observed to be 4 ° 52 ′ ; at the bottom of the castle the angle of depression OBS was 4 ° 2 ′ . Required the horizontal distance AS of the vessel , and the height of the hill above the level of the sea , the height ...
... ship at anchor , was observed to be 4 ° 52 ′ ; at the bottom of the castle the angle of depression OBS was 4 ° 2 ′ . Required the horizontal distance AS of the vessel , and the height of the hill above the level of the sea , the height ...
Page 109
... ship's 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 ...
... ship's 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
... 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 indicated by the ...
... 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 indicated by the ...
Page 112
... ship - board that the vertical plane , cutting the ship from stem to stern , may pass through the centre of the card , so that that point of the compass which is directed to the ship's head shows the compass - course , and the proper ...
... ship - board that the vertical plane , cutting the ship from stem to stern , may pass through the centre of the card , so that that point of the compass which is directed to the ship's head shows the compass - course , and the proper ...
Page 113
... ship in sailing on a single course from A to B. Conceive the path of the ship to be divided into portions Ab , bc , cd , & c . so small that each may differ insensibly from a straight line , and draw meridians through these several ...
... ship in sailing on a single course from A to B. Conceive the path of the ship to be divided into portions Ab , bc , cd , & c . so small that each may differ insensibly from a straight line , and draw meridians through these several ...
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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