## 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 |

### From inside the book

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**sine of the middle part is equal to the product of the cosines of the two opposite parts**. [ B. p . 436. ] Proof . To demonstrate the preceding rules , it is only necessary to compare all the equations which can be deduced from them ...### Other editions - View all

### Common terms and phrases

A₁ 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 corresponding cosec cosine cotan departure diff difference of latitude difference of longitude dist earth ecliptic equal Find the altitude formula given gives Greenwich Hence horizon horizontal parallax hour angle hypothenuse meridian altitude method middle latitude miles moon moon's motion N₁ Nautical Almanac Navigator obliquity observer at Boston obtuse opposite parallax perpendicular plane polar distance position prime vertical Problem Prop proportional logarithm radius right ascension right triangle sailing Scholium secant second member side sideral day solar Solution solve the triangle spherical right triangle spherical triangle star's sun's Table XXIII tang tangent Trig true latitude vernal equinox whence

### Popular passages

Page 105 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.

Page 31 - 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 28 - 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 156 - 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 231 - 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 150 - 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 67 - This method of calculating the difference of longitude may be rendered perfectly accurate by applying to the middle latitude a correction," which is given in the Navigator, and the method of computing which will be explained in the succeeding chapter.

Page 113 - II. The sine of the middle part is equal to the product of the cosines of the opposite parts.

Page 156 - ... 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 130 - XXIII, the following rule is obtained for finding the third side, when two sides and the included angle are given.