## 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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A₁ adjacent angle ascension and declination azimuth calculated celestial celestial equator celestial sphere circle column computed Corollary corr corresponding cosec cosine cotan course departure diff difference of latitude difference of longitude dist earth's centre ecliptic equal to 90 equator equinox find the sine formula gives Greenwich Hence horizon horizontal parallax hour angle hypothenuse included angle interval Let ABC fig logarithm mean meridian altitude method middle latitude miles moon moon's motion N₁ Napier's Rules Nautical Almanac Navigator obliquity observer at Boston obtuse parallel sailing perpendicular plane plane of reference pole Problem proportion radius right ascension Scholium secant second member semidiameter side sideral solar Solution solve a spherical solve the triangle spherical right triangle spherical triangle star star's sun's tang tangent Theorem transit Trig vernal equinox whence zenith

### Popular passages

Page 117 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.

Page 43 - 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 185 - ... any deviation in the plane of the instrument from the meridian, will evidently produce contrary effects upon the observed times of transit, exactly as in the upper and lower transits of the same star. The time, which elapses between the two observations, will differ from the time which should elapse by the sum of the effects of the deviation upon the two stars. In the use of this method, therefore, the time of the clock must be known, so that it can readily be reduced to sideral time. The deviations...

Page 168 - Secondaries to the celestial equator are called circles of declination; of these 24, which divide the equator into equal parts of 15° each, are called hour circles.

Page 40 - 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 320 - The apparent semi-diameter of the earth's shadow at the distance of the moon is the angle MEH.

Page 162 - 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 168 - ... equator and the ecliptic, and hence, also, the position of the equinoxes. In expressing the positions of stars, referred to the vernal equinox, at any given instant, the actual position of the equinox at the instant is understood, unless otherwise stated. The right ascension of a point of the sphere is the arc of the equator intercepted between its circle of declination and the vernal equinox, and is reckoned from the vernal equinox eastward from 0° to 360°, or, in time, from 0* to 24*.

Page 256 - ... meridian transit of the moon's bright limb and also the local mean time of the meridian transit of a fixed star near the moon and whose right ascension is known. A list of convenient stars called moon culminating stars is given in the Nautical Almanac. From the time interval between the culminations the right ascension of the moon's bright limb at the instant of observation may be found. In the Nautical Almanac the right ascension of the moon's bright limb is given for every hour for both lower...