## 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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acute adjacent altitude apparent azimuth bearing becomes calculated called centre circle column computed Corollary correction corresponding cosec cosine cotan course declination departure determined diff difference difference of latitude direction dist distance drawn earth eclipse equal equator error EXAMPLES formulas given gives greater Hence horizon hour angle increase interval known latitude less logarithm mean measured meridian method middle miles moon moon's motion Nautical Navigator nearly negative observer obtained obtuse opposite parallax parallel perpendicular plane pole position Problem proportion radius reduced right ascension right triangle Rules sailing shadow side sideral signs sine solar Solution spherical triangle star substituted sun's supposed Table taken tang tangent term transit true whence zenith

### Popular passages

Page 42 - 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 123 - II. The sine of the middle part is equal to the product of the cosines of the opposite parts.

Page 107 - 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 39 - 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 241 - 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 115 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.

Page 123 - 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 161 - 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 97 - 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 297 - Twilight begins and ends when the sun is about 18° below the horizon.