## A Treatise on Trigonometry |

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abscissa algebraic arc-ordinate area swept axis biquadrantal celestial sphere centre circle computation cos0 cos2 cosecant cosp cot q cotangent course and distance difference of latitude difference of longitude direction draw ecliptic equal equator EXAMPLES formulae of th geom horizon hour-angle hypothenuse LAW OF COSINES law of sines let xop log-sin logarithmic meridian miles nat-sin nearer right negative angle oblique angle oblique triangle observer's obtuse opposite ordinate parallel perpendicular plane angle plane sailing pole positive and less positive angle possible errors prime vertical PROB projection q cot quarter radians radius ratios right angles right ascension right spherical triangle right triangles secant segment side sin b sin sin0 sin2 sinp Solve species spherical angle straight line subtended sun's supplement tan2 tangent terminal line thence Theor theorem triangle abc trigonometric functions values vertex vertical angle wherein

### Popular passages

Page 124 - There are in general use three different kinds of time, True Solar Time — also called Apparent Solar Time — Mean Solar Time, and Sidereal Time. True or Apparent Solar Time is measured by the diurnal motion of the Sun, the length of the day being the interval between two successive transits of the Sun over the same meridian, and the time of day being the hour-angle of the Sun westward from the meridian. Owing to the obliquity of the ecliptic and to the lack of uniformity of the motion of the Earth...

Page 119 - As to the horizon : The altitude of a star is its angular distance from the horizon measured on a vertical circle ; and the arc of the horizon intercepted between this circle and the south point of the horizon is the star's azimuth. Owing to the rotation of the celestial sphere, the horizon-coordinates change every moment.

Page 8 - The radian is the plane angle with its vertex at the center of a circle that is subtended by an arc equal in length to the radius.

Page 73 - Two observers on the same side of a balloon, and in the same vertical plane with it, are a mile apart, and find the angles of elevation to be 17° and 68° 25' respectively : what is its height ? [1836 feet.

Page 105 - The law of sines states that in any spherical triangle the sines of the sides are proportional to the sines of their opposite angles: sin a _ sin b __ sin c _ sin A sin B sin C...

Page 86 - Each angle of a spherical triangle is greater than the difference between two right angles and the sum of the other two angles.

Page 71 - A wall is surrounded by a ditch ; from the edge of this ditch the angle of elevation of a point on the top of the wall is found to be 35° ; and at a distance of 100 yards from the ditch the angle of elevation of the same point...

Page 18 - If the radius of a circle be divided in extreme and mean ratio, the greater segment is equal to one side of a regular inscribed decagon.

Page 102 - ... 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 40 - C = 1 + 4 sin £A sin £B sin £C. 37. tan A + tan B + tan C = tan A tan B tan C.