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 12
... angle ; but when we want to find an angle , then we must invert this proportion , beginning with a given side , which must be made the geometrical radius , as no other tabular line but the radius will be given , seeing that angles are ...
... angle ; but when we want to find an angle , then we must invert this proportion , beginning with a given side , which must be made the geometrical radius , as no other tabular line but the radius will be given , seeing that angles are ...
Page 14
... AB 288 2.4593925 :: Rad . : AC 480.036 10 2.6812739 . 2. Given the two perpendicular sides to find the hypotenuse and angles , viz . AB = 472 , BC = 765 , ( see last fig . ) 1. To find the Angle A. We must here , 14 PLANE TRIGONOMETRY .
... AB 288 2.4593925 :: Rad . : AC 480.036 10 2.6812739 . 2. Given the two perpendicular sides to find the hypotenuse and angles , viz . AB = 472 , BC = 765 , ( see last fig . ) 1. To find the Angle A. We must here , 14 PLANE TRIGONOMETRY .
Page 15
... angle A we may determine AC by the formula . AC AB2 + BC2 . 3. Given two sides and the included angle of an isosceles triangle ABC to find the other parts . AC BC = 288 , ACB = 78 ° 12 ' . = Let the perpendicular CD be drawn , then ...
... angle A we may determine AC by the formula . AC AB2 + BC2 . 3. Given two sides and the included angle of an isosceles triangle ABC to find the other parts . AC BC = 288 , ACB = 78 ° 12 ' . = Let the perpendicular CD be drawn , then ...
Page 16
... find AD , we have by making AC radius , Rad . · 10 : AC 288 2.4593925 :: cos . A 50 ° 54 ' 9.7998062 : AD 181.635 ... angle A = 37 ° 2 ′ 43 ′′ , and the hypotenuse AC = 173 · 2 to find the other parts ? C = 52 ° 57 ′ 17 ′′ , AB = 138.24 ...
... find AD , we have by making AC radius , Rad . · 10 : AC 288 2.4593925 :: cos . A 50 ° 54 ' 9.7998062 : AD 181.635 ... angle A = 37 ° 2 ′ 43 ′′ , and the hypotenuse AC = 173 · 2 to find the other parts ? C = 52 ° 57 ′ 17 ′′ , AB = 138.24 ...
Page 20
... angles , to find the sine and cosine of their sum and difference . Let AM = a , and AN = a ' , be any two arcs of the circle , the radius being unity , then drawing the chord of the arc NMaa ' , we shall have from the triangle NMG right ...
... angles , to find the sine and cosine of their sum and difference . Let AM = a , and AN = a ' , be any two arcs of the circle , the radius being unity , then drawing the chord of the arc NMaa ' , we shall have from the triangle NMG right ...
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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