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 134
... Declination . The right ascension is measured on the equinoctial from the first of Aries , in the order of the signs , and the declination is measured on the perpendicular to this , or cir- cle of declination passing through the object ...
... Declination . The right ascension is measured on the equinoctial from the first of Aries , in the order of the signs , and the declination is measured on the perpendicular to this , or cir- cle of declination passing through the object ...
Page 135
... declination and right ascension ; and parallels of latitude on the one correspond to parallels of declination on the other . Of these the two which are 23 ° 28 ′ from the equinoctial , one on each side , and which therefore touch the ...
... declination and right ascension ; and parallels of latitude on the one correspond to parallels of declination on the other . Of these the two which are 23 ° 28 ′ from the equinoctial , one on each side , and which therefore touch the ...
Page 136
... declination to determine his longitude and the obliquity of the ecliptic . E R Let n EsQ represent the celestial ... declination circle , passing through the sun S ; then ARS is a right - angle , and in the right - angled spherical ...
... declination to determine his longitude and the obliquity of the ecliptic . E R Let n EsQ represent the celestial ... declination circle , passing through the sun S ; then ARS is a right - angle , and in the right - angled spherical ...
Page 137
... declination is south and increasing , after which , or during the fourth quadrant , the declination , still south , decreases till the 21st of March . EXAMPLES . 1. Given the sun's right ascension on the 17th of May , 53 ° 38 ' , and ...
... declination is south and increasing , after which , or during the fourth quadrant , the declination , still south , decreases till the 21st of March . EXAMPLES . 1. Given the sun's right ascension on the 17th of May , 53 ° 38 ' , and ...
Page 138
... declination to find the time of his rising and setting at any place whose latitude is known . Let nEsQ represent the meridian of the place , Z being the zenith , and HO the horizon , and let s's " be the apparent path of the sun on the ...
... declination to find the time of his rising and setting at any place whose latitude is known . Let nEsQ represent the meridian of the place , Z being the zenith , and HO the horizon , and let s's " be the apparent path of the sun on the ...
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Common terms and phrases
ABC are given apparent altitude arc BC arith Asin called celestial sphere centre chord circle colatitude comp complement computation correction cosec cosine cotangent course and distance deduced departure determine diff difference of latitude difference of longitude direct course equal equations equinoctial expression find the angle formula given side Greenwich hence horizon hour angle hypotenuse included angle logarithmic measured meridian middle latitude miles Napier's Nautical Almanack negative oblique obtuse opposite angle parallax parallel parallel sailing perpendicular plane sailing plane triangle pole PROBLEM quadrant quantities radius right ascension right-angled triangle rule secant semidiameter ship sin.c sine sine and cosine solution sphere spherical angle spherical triangle spherical trigonometry subtracting supplement tabular line tangent third side three angles three sides triangle ABC trigono trigonometrical lines true altitude values vertical zenith
Popular passages
Page viii - 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.
Page 99 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
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 vi - 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 Summation of Infinite Series ; the Solution of Equations of the Higher Order, &c., for the use of Students.
Page 160 - 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 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 129 - To THE TANGENT OF THE COURSE ; So IS THE MERIDIONAL DIFFERENCE OF LATITUDE, To THE DIFFERENCE OF LONGITUDE. By this theorem, the difference of longitude may be calculated, without previously rinding the departure.
Page vi - MICHAEL O'SHANNESSY, AM 1 vol. 8vo. " The volume before us forms the third of an analytical course, which commences with the * Elements of Analytical Geometry.' More elegant t&xtbooks do not exist in the English language, and we trust they will speedily be adopted in our Mathematical Seminaries. The existence of such auxiliaries will, of itself, we hope, prove an inducement to the cultivation of Analytical Science ; for, to the want of such...
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 138 - PEP' (Fig. 22,) represent the meridian of the place, Z being the zenith, and HO the horizon ; and let LL' be the apparent path of the sun on the proposed day, cutting the horizon in S. Then the...