## 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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ABC fig aberration adjacent angles angle given angle opposite ascension and declination calculated centre circle Corollary corr correction cosec cosine cotan departure diff difference of latitude difference of longitude dist earth eclipse of April equator equinox find the sine formula given angle Given two sides gives Greenwich Hence horizon horizontal parallax hour angle hypothenuse included angle interval logarithms mean meridian altitude middle latitude miles moon moon's motion Nautical Almanac Navigator obliquity observer obtuse parallax parallel sailing perpendicular plane Plane Sailing pole Problem proportion R₁ radius reduced right ascension Scholium secant second member semidiameter sideral sine and cosine Solar eclipse Solution solve the triangle spherical right triangle spherical triangle star star's sun's Table tang tangent Theorem transit triangle ABC triangle equal Trig TRIGONOMETRY vernal equinox whence zenith

### Popular passages

Page 172 - 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 135 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.

Page 39 - ... 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 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 193 - 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 40 - O will be equal to sixty degrees. Hence, if any two angles of a triangle be known, the third may be found by subtracting the sum of the two known angles from 180 degrees, the remainder will be the number of degrees in the third angle.

Page 145 - ... theorems, called, from their celebrated inventor, Napier's Rules. In these rules, the complements of the hypothenuse and the angles are used instead of the hypothenuse and the angles themselves, and the right angle is neglected. Of the five parts, then, the legs, the complement of the hypothennse, and the complements of the angles ; either part may be called the middle part.

Page 220 - ... 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 297 - 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 199 - ... 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*.