An Elementary Treatise on Plane and 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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... Meridian IV . Latitude · V. The Ecliptic VI . Precession and Nutation VII . Time • VIII . Longitude IX . Aberration X. Refraction XI . Parallax XII . Eclipses · PAGE 167 171 182 192 218 229 243 · 255 279 292 301 317 NOTE ON MIDDLE ...
... Meridian IV . Latitude · V. The Ecliptic VI . Precession and Nutation VII . Time • VIII . Longitude IX . Aberration X. Refraction XI . Parallax XII . Eclipses · PAGE 167 171 182 192 218 229 243 · 255 279 292 301 317 NOTE ON MIDDLE ...
Page 65
... meridian is one arbitrarily assumed , to which all others are referred . In most countries , that has been taken as the first meridian which passes through the capital of the country . 4. The latitude of a place is its angular distance ...
... meridian is one arbitrarily assumed , to which all others are referred . In most countries , that has been taken as the first meridian which passes through the capital of the country . 4. The latitude of a place is its angular distance ...
Page 66
... meridian passing through the place . [ B. , p . 48. ] If D ( fig . 18 ) is the centre of the earth , C one of the poles , A'B ' a portion of the equator , and BC a portion of a meridian , the latitude of the place B is the angle B'DB or ...
... meridian passing through the place . [ B. , p . 48. ] If D ( fig . 18 ) is the centre of the earth , C one of the poles , A'B ' a portion of the equator , and BC a portion of a meridian , the latitude of the place B is the angle B'DB or ...
Page 67
... meridian , and to the sum of their longitudes , if they are on opposite sides of the first meridian , unless their sum be greater than 180 ° , in which case the sum must be subtracted from 360 ° to give the difference of longitude . [ B ...
... meridian , and to the sum of their longitudes , if they are on opposite sides of the first meridian , unless their sum be greater than 180 ° , in which case the sum must be subtracted from 360 ° to give the difference of longitude . [ B ...
Page 68
... meridian of the other . But if the distance is great , let it be divided into very small portions , and the departure of the places is the sum of the departures corresponding to all these portions ; and , since the portions may be made ...
... meridian of the other . But if the distance is great , let it be divided into very small portions , and the departure of the places is the sum of the departures corresponding to all these portions ; and , since the portions may be made ...
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Common terms and phrases
A₁ aberration acute adjacent Aldebaran ascension and declination azimuth celestial equator celestial sphere circle computed Corollary corr correct central altitude correction of Table corresponding cosec cosine cotan denote departure diff difference of latitude difference of longitude dist earth ecliptic equal to 90 formulas given angle gives Greenwich Hence horizon horizontal parallax hour angle hypothenuse included angle interval mean meridian altitude method middle latitude miles moon moon's motion N₁ Nautical Almanac Navigator obliquity observer at Boston obtuse opposite parallax perpendicular plane pole position prime vertical Problem Prop R₁ radius rhumb right ascension sailing Scholium secant second member sideral sideral day solar Solution solve the triangle spherical right triangle spherical triangle star star's sun's tang tangent Theorem transit Trig true latitude vernal equinox vertical whence zenith
Popular passages
Page 44 - 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 125 - II. The sine of the middle part is equal to the product of the cosines of the opposite parts.
Page 109 - PROBLEM III. To find the height of an INACCESSIBLE OBJECT above a HORIZONTAL PLANE. 11. TAKE TWO STATIONS IN A VERTICAL PLANE PASSING THROUGH THE TOP OF THE OBJECT, MEASURE THE DISTANCE FROM ONE STATION TO THE OTHER, AND THE ANGLE OF ELEVATION AT EACH. If the base AB (Fig.
Page 41 - To find a side, work the following proportion: — 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.
Page 243 - Solar Day is the interval of time between two successive transits of the sun over the same meridian ; and the hour angle of the sun is called Solar Time. This is the most natural and direct measure of time. But the intervals between the successive returns of the sun to the meridian are not exactly equal, but depend upon the variable> motion of the sun in right ascension. - The want of uniformity in the sun's motion in right ascension arises from two different causes ; one, that the sun does not move...
Page 117 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 125 - NAPIER'S CIRCULAR PARTS. Thus, in the spherical triangle A. BC, right-angled at C, the circular parts are p, b, and the complements of h, A, and B. 167. When any one of the five parts is taken for the middle part, the two adjacent to it, one on either side, are called the adjacent parts, and the other two parts are called the opposite parts. Then, whatever be the middle part, we have as THE EULES OF NAPIER.
Page 163 - The cosine of half the sum of two sides of a spherical triangle is to the cosine of half their difference as the cotangent of half the included angle is to the tangent of half the sum of the other two angles. The sine of half the sum of two sides of a spherical...
Page 99 - Now the sum of the areas of the triangles is the area of the polygon, and the sum of the angles of the triangles is the sum of the angles of the polygon.
Page 299 - Twilight begins and ends when the sun is about 18° below the horizon.