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 viii
... sides and the included angle are given ib . Examples • 25. When the three sides are given ib . Examples CHAP . III . Application of Plane Trigonometry to the Mensuration of Heights and Distances . 25. Various problems concerning heights ...
... sides and the included angle are given ib . Examples • 25. When the three sides are given ib . Examples CHAP . III . Application of Plane Trigonometry to the Mensuration of Heights and Distances . 25. Various problems concerning heights ...
Page ix
... side of a spherical triangle is less than the sum of the other two • PAGE . 65 66 67 68 ib . • ib . 69 39. The three sides are together less than a whole circumference 40. Characteristic property of the polar triangle ib . · 70 41 ...
... side of a spherical triangle is less than the sum of the other two • PAGE . 65 66 67 68 ib . • ib . 69 39. The three sides are together less than a whole circumference 40. Characteristic property of the polar triangle ib . · 70 41 ...
Page x
... three sides are given 57. When the three angles are given 58. When two sides and the included angle are given 59. When two angles and the interjacent side are given 60. When two sides and an opposite angle are given 61. When two angles ...
... three sides are given 57. When the three angles are given 58. When two sides and the included angle are given 59. When two angles and the interjacent side are given 60. When two sides and an opposite angle are given 61. When two angles ...
Page xi
... three sides and the three angles , and if any three of these six be given , provided only that a side be among them , the other three may always be determined either by geometrical construction , as shown in the Ele- ments of Geometry ...
... three sides and the three angles , and if any three of these six be given , provided only that a side be among them , the other three may always be determined either by geometrical construction , as shown in the Ele- ments of Geometry ...
Page 7
... three others , sometimes , although but seldom , employed ; these are the versed sine or sagitta , the coversed sine ... sides of similar triangles , that tan . w TRIGONOMETRICAL LINES . 7 Of the versed sine, coversed sine, and suversed sine.
... three others , sometimes , although but seldom , employed ; these are the versed sine or sagitta , the coversed sine ... sides of similar triangles , that tan . w TRIGONOMETRICAL LINES . 7 Of the versed sine, coversed sine, and suversed sine.
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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