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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Page 4
... column of a table all the possible values of the angle A , from 0 ° to 90 ° , and then calculate and arrange in other columns the corresponding values of the six ratios and and of the angle B , we shall have a series of right triangles ...
... column of a table all the possible values of the angle A , from 0 ° to 90 ° , and then calculate and arrange in other columns the corresponding values of the six ratios and and of the angle B , we shall have a series of right triangles ...
Page 16
... columns in Table XXVII , with which at present we have nothing to do , and the insertion of angles . greater than 90 ° , which will be explained in a future chapter , this table corresponds precisely to the series of right triangles ...
... columns in Table XXVII , with which at present we have nothing to do , and the insertion of angles . greater than 90 ° , which will be explained in a future chapter , this table corresponds precisely to the series of right triangles ...
Page 73
... column of the table are the numbers of the tracks ; in the second and third columns are the courses and distances ; in the fourth and fifth columns are the differences of latitude , the column headed N. corresponding to the northerly ...
... column of the table are the numbers of the tracks ; in the second and third columns are the courses and distances ; in the fourth and fifth columns are the differences of latitude , the column headed N. corresponding to the northerly ...
Page 101
... column of the table are the successive sides of the field . In the second and third columns are the differences of latitude of the several sides ; the column headed N. corresponding to the sides running in a northerly direction , and ...
... column of the table are the successive sides of the field . In the second and third columns are the differences of latitude of the several sides ; the column headed N. corresponding to the sides running in a northerly direction , and ...
Page 102
... columns E. and W .; and every succeeding number in column Departure is obtained by adding the corresponding number in columns E. and W. , if it is of the same column with the first number in those two columns , to the previous number in ...
... columns E. and W .; and every succeeding number in column Departure is obtained by adding the corresponding number in columns E. and W. , if it is of the same column with the first number in those two columns , to the previous number in ...
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Common terms and phrases
A₁ aberration acute adjacent Aldebaran ascension and declination azimuth celestial equator celestial sphere circle computed Corollary corr correct central altitude correction of Table corresponding cosec cosine cotan denote departure diff difference of latitude difference of longitude dist earth ecliptic equal to 90 formulas gives Greenwich Hence horizon horizontal parallax hour angle hypothenuse included angle interval mean meridian altitude method middle latitude miles moon moon's motion Napier's Rules Nautical Almanac Navigator obliquity observer at Boston obtuse opposite parallax perpendicular plane pole position prime vertical Problem Prop R₁ radius rhumb right ascension sailing Scholium secant second member semidiameter sideral sideral day solar Solution solve the triangle spherical right triangle spherical triangle star star's sun's tang tangent Theorem transit Trig true latitude vernal equinox vertical whence zenith
Popular passages
Page 44 - 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 125 - II. The sine of the middle part is equal to the product of the cosines of the opposite parts.
Page 109 - 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 41 - 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 117 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 125 - 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 163 - 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 99 - 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 299 - Twilight begins and ends when the sun is about 18° below the horizon.