An Elementary Treatise on Plane & Spherical Trigonometry: With Their Applications to Navigation, Surveying, Heights, and Distances, and Spherical Astronomy, and Particularly Adapted to Explaining the Construction of Bowditch's Navigator, and the Nautical Almanac |
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Page 2
... VI . • Precession and Nutation VII . Time . VIII . Longitude IX . Aberration X. Refraction XI . Parallax XII . Eclipses 288 306 322 353 • 369 380 400 PLANE TRIGONOMETRY . CHAPTER I. GENERAL PRINCIPLES OF PLANE TRIGONOMETRY iv CONTENTS .
... VI . • Precession and Nutation VII . Time . VIII . Longitude IX . Aberration X. Refraction XI . Parallax XII . Eclipses 288 306 322 353 • 369 380 400 PLANE TRIGONOMETRY . CHAPTER I. GENERAL PRINCIPLES OF PLANE TRIGONOMETRY iv CONTENTS .
Page 352
... R. A. = 9h 33m 24.57 , Dec. = 14 ° 31 ′ 28 ′′ .2 N. D's R. A. = 13 8 27.62 , Dec. = 10 25 54 .5 S. Ans . 58 ° 50 ′ 38 ′′ Annual and diurnal aberration . CHAPTER IX . ABERRATION . 352 [ CH . VIII . SPHERICAL ASTRONOMY .
... R. A. = 9h 33m 24.57 , Dec. = 14 ° 31 ′ 28 ′′ .2 N. D's R. A. = 13 8 27.62 , Dec. = 10 25 54 .5 S. Ans . 58 ° 50 ′ 38 ′′ Annual and diurnal aberration . CHAPTER IX . ABERRATION . 352 [ CH . VIII . SPHERICAL ASTRONOMY .
Page 353
... aberration . CHAPTER IX . ABERRATION . 104. The apparent position of the stars is affected by two sources of optical deception , so that they are not in the direction in which they appear to be . The first ... ABERRATION . 104 Aberration •
... aberration . CHAPTER IX . ABERRATION . 104. The apparent position of the stars is affected by two sources of optical deception , so that they are not in the direction in which they appear to be . The first ... ABERRATION . 104 Aberration •
Page 354
... Aberration in latitude and longitude . If , then , we put V = the velocity of light , v = the earth's velocity , I = TOP = RTO , $ I = — ROT the aberration from the true place , = v m = V sin . 1 " ' ( 647 ) we have , V : : v = OR : TR ...
... Aberration in latitude and longitude . If , then , we put V = the velocity of light , v = the earth's velocity , I = TOP = RTO , $ I = — ROT the aberration from the true place , = v m = V sin . 1 " ' ( 647 ) we have , V : : v = OR : TR ...
Page 355
... Aberration in latitude and longitude . and , by ( 346 and 347 ) , sin . 84 - sin . ( 2 41 — 8 4 ) 1 sin . & I sin ... aberration in distance and direction from the vernal equinox . Aberration from vernal equinox . Solution . Let A ...
... Aberration in latitude and longitude . and , by ( 346 and 347 ) , sin . 84 - sin . ( 2 41 — 8 4 ) 1 sin . & I sin ... aberration in distance and direction from the vernal equinox . Aberration from vernal equinox . Solution . Let A ...
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Common terms and phrases
A₁ aberration altitude and azimuth angle given ascension and declination azimuth celestial equator celestial sphere centre circle computed Corollary corr correct central altitude corresponding cosec cosine cotan diff difference of latitude difference of longitude dist earth eclipse of April equal to 90 formula gives Greenwich Hence horizon horizontal parallax hour angle hypothenuse included angle interval latitude and longitude lunar distance mean meridian altitude method middle latitude moon's motion N₁ Napier's Rules Nautical Almanac Navigator Nutation obliquity obtuse perpendicular plane polar triangle prime vertical Problem R₁ radius reduced right ascension sailing Scholium second member semidiameter sideral sideral day solar eclipse Solution solve the triangle spherical right triangle spherical triangle star's sun's Table XXIII tang tangent Theorem transit triangle ABC Trig true latitude tude vernal equinox whence
Popular passages
Page 156 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 145 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 48 - As the sine of the angle opposite the given side is to the sine of the angle opposite the required side, so is the given side to the required side. Thus, if a (fig.
Page 50 - The third side is found by the proportion. As the sine of the given angle is to the sine of the angle opposite the required side, so is the side opposite the given angle to the required side.
Page 41 - Since, when an angle is acute its supplement is obtuse, it follows from the preceding proposition, that the sine and cosecant of an obtuse angle are positive, while its cosine, tangent, cotangent, and secant, are negative.
Page 53 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Page 182 - But a' = 180° - A, b' = 180° - ß, c' = 180° - C. and A' = 180° - a. Therefore, — cos A = (— cos B)(— cos C) + sin B sin C(— cos a...