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 11
... triangles . Right - angled triangles . As right - angled triangles are those whose several parts are the most easily determined we shall consider them first . Let ABC be any right - angled plane triangle , and with AB as a radius ...
... triangles . Right - angled triangles . As right - angled triangles are those whose several parts are the most easily determined we shall consider them first . Let ABC be any right - angled plane triangle , and with AB as a radius ...
Page 15
... triangle ABC to find the other parts . AC BC = 288 , ACB = 78 ° 12 ' . Let the perpendicular CD be drawn , then since it will bisect the angle C , we shall have A D given in the right - angled triangle For the method of determining the ...
... triangle ABC to find the other parts . AC BC = 288 , ACB = 78 ° 12 ' . Let the perpendicular CD be drawn , then since it will bisect the angle C , we shall have A D given in the right - angled triangle For the method of determining the ...
Page 16
... triangles in general . Oblique - Angled Triangles . Let ABC be any plane triangle , and let us denote the angles by the capital letters , A , B , C , at their vertices , and the sides opposite to them by the small letters a , b , c ...
... triangles in general . Oblique - Angled Triangles . Let ABC be any plane triangle , and let us denote the angles by the capital letters , A , B , C , at their vertices , and the sides opposite to them by the small letters a , b , c ...
Page 25
... triangle from its sine , whe- ther to take the acute angle given by the tables or the obtuse angle which is its ... ABC , AB'C ; where the angle B , opposite to the other given side in the one triangle , will be the supplement of the ...
... triangle from its sine , whe- ther to take the acute angle given by the tables or the obtuse angle which is its ... ABC , AB'C ; where the angle B , opposite to the other given side in the one triangle , will be the supplement of the ...
Page 26
... triangle ABC are given AC = 216 , CB = 117 , A = 22 ° 37 ′ , to find the rest . 1. To find the Angle B. As BC 117 : sin . A 22 ° 37 ' :: AC 216 arith . comp . 7 · 9318141 9.5849685 2.3344538 9.8512364 sin . B 45 ° 13 ′ 55 ′′ or 134 ° 46 ...
... triangle ABC are given AC = 216 , CB = 117 , A = 22 ° 37 ′ , to find the rest . 1. To find the Angle B. As BC 117 : sin . A 22 ° 37 ' :: AC 216 arith . comp . 7 · 9318141 9.5849685 2.3344538 9.8512364 sin . B 45 ° 13 ′ 55 ′′ or 134 ° 46 ...
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Common terms and phrases
a+b+c ABC are given arc BC arith Asin celestial centre circle circumference colatitude comp complement computation cos.² cos.c cosec cosine cotangent coversed sine declination deduced determine diameter diff difference of latitude distance equal equations EXAMPLES expression find the angle formula Geom Geometry given side hence horizon hypotenuse included angle logarithmic longitude measured meridian miles multiplying negative object observed opposite angle parallax parallel sailing perpendicular plane sailing plane triangle polar triangle pole PROBLEM quadrant quantities radius right ascension right-angled triangle rule sailing secant semidiameter ship side opposite sin.² sin.c sine and cosine solution sphere spherical angle spherical excess Spherical Geometry spherical triangle spherical trigonometry subtracted surface tabular line tangent theorem third side three angles three sides triangle ABC Trigono trigonometrical lines true altitude values
Popular passages
Page 6 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 140 - If the zenith distance and declination be of the same name, that is, both north or both south, their sum will be the latitude ; but, if of different names, their difference will be the latitude, of the same name as the greater.
Page 145 - PS' ; the coaltitudes zs, zs', and the hour angle SPS', which measures the interval between the observations ; and the quantity sought is the colatitude ZP. Now, 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...
Page 51 - The sum of 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. The arcs ABD, ACD, will be semicircumferenc.es, since (Prop.
Page 144 - It should also be observed here, that in the preceding examples the celestial object is supposed to be on the meridian above the pole ; that is, to be higher than the elevated pole. But, if a meridian altitude be taken below the pole, which may be done if the object is circumpolar, or so near to the elevated pole as to perform its apparent daily revolution about it without passing below the horizon, then the latitude of the place will be equal to the sum of the true altitude, and the codeclination...
Page 53 - ... that the two angles A and D lie on the same side of BC, the two B and E on the same side of AC, and the two C and F on the same side of AB.
Page 115 - ... the surface of the celestial sphere. The Zenith of an observer is that pole of his horizon which is exactly above his head. Vertical Circles are great circles passing through the zenith of an observer, and perpendicular to his horizon.