## 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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### Common terms and phrases

A₁ aberration acute Aldebaran altitude and azimuth apparent altitude ascension and declination azimuth azimuth error celestial equator celestial sphere change of declination circle of latitude computed Corollary corr correct central altitude correct meridian altitude correction of Table corresponds cosec cosine cotan departure diff difference of latitude difference of longitude dist earth ecliptic formula gives Greenwich Hence horizon horizontal parallax hour angle hypothenuse meridian altitude method middle latitude miles moon moon's motion Nautical Almanac Navigator obliquity observer at Boston obtuse opposite parallax perpendicular plane polar distance position prime vertical Problem Prop R₁ radius rhumb right ascension right triangle sailing Scholium secant second member semidiameter side sideral day solar Solution solve the triangle spherical triangle star's sun's Table XXIII tang tangent transit Trig true latitude vernal equinox whence

### Popular passages

Page 40 - 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 37 - 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 105 - 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 121 - II. The sine of the middle part is equal to the product of the cosines of the opposite parts.

Page 162 - ... are called hour circles. Small circles parallel to the celestial equator are called parallels of declination. The sensible horizon is that circle in the heavens whose plane touches the earth at the spectator; The rational horizon is a great circle in the heavens, passing through the earth's centre, parallel to the sensible horizon.

Page 142 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...

Page 68 - Call the differences of latitude corresponding to the 1st, 2d, 3d, and 4th tracks, the 1st, 2d, 3d, and 4th differences of latitude ; and call the corresponding departures the 1st, 2d, 3d, and 4th departures.

Page 121 - 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 95 - 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 155 - ... two sides of a spherical triangle, is to the sine of half their difference as the cotangent of half the...