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apparent altitude arith azimuth bisect called celestial object celestial sphere centre chord circle colatitude comp computation correction cosec cosine course and distance deduced departure determine diff difference of latitude difference of longitude direct course ecliptic equal equations equinoctial example expression find the angle formula given Greenwich hence horizon hour angle hypotenuse included angle logarithmic measured meridian method middle latitude miles Nautical Almanack oblique observed altitude opposite angle parallax parallel parallel sailing perpendicular plane sailing plane triangle polar triangle pole problem quadrant quantities radius refraction right ascension right-angled triangle rule semidiameter ship sine sine and cosine solution sphere spherical angle spherical excess spherical triangle spherical trigonometry subtracting supplemental triangle surface tangent theorem third side three angles three sides triangle ABC trigono true altitude tude twilight values vertical
Page 22 - 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 165 - 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 69 - 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 164 - 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 71 - ... 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.