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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Common terms and phrases
A₁ adjacent angle ascension and declination azimuth calculated celestial celestial equator celestial sphere circle column computed Corollary corr corresponding cosec cosine cotan denote departure diff difference of latitude difference of longitude dist earth earth's centre ecliptic equal to 90 equator find the sine formula given angle gives Greenwich Hence horizon horizontal parallax hour angle hypothenuse interval Let ABC fig logarithm mean meridian altitude method 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 R₁ radius right ascension Scholium secant second member semidiameter shadow sideral sideral day solar Solution solve a spherical solve the triangle spherical right triangle spherical triangle star star's sun's tang tangent Theorem transit triangle ABC Trig vernal equinox whence zenith
Popular passages
Page 138 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.
Page 38 - 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 117 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 41 - 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 160 - 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 31 - ... that is, the sine and cosecant of the supplement of an angle are the same as those of the angle itself; and the cosine, tangent, cotangent, and secant are the negatives of those of the angle.
Page 160 - ... 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 134 - XXIII, the following rule is obtained for finding the third side, when two sides and the included angle are given.
Page 154 - 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 88 - The area of a triangle is equal to half the product of its base by its altitude.