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abscissa angle xop arc-ordinate area swept axis celestial sphere centre circle computation coordinates cos0 cos2 cosecant cosp cot q cotangent difference of latitude difference of longitude direction draw ecliptic equal equator EXAMPLES figure formulae of th geom given angle horizon hour-angle hypothenuse LAW OF COSINES law of sines let xop log-sin logarithmic meridian miles minutes nat-sin nearer right negative angle oblique angle oblique triangle obtuse opposite ordinate perpendicular plane angle plane sailing polar pole positive angle less possible errors prime vertical projection q cot quarter radians radius radius-arcs ratios revolution right angles right ascension right spherical triangle right triangles sailing secant segment side sin b sin sin0 sin2 sinp Solve species spherical angle straight line subtended sun's supplement tan2 tangent terminal line Theor triangle abc trigonometric functions values vertex wherein
Seite 118 - 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...
Seite 113 - 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.
Seite 12 - 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.
Seite 67 - 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.
Seite 99 - 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...
Seite 80 - Each angle of a spherical triangle is greater than the difference between two right angles and the sum of the other two angles.
Seite 65 - 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...
Seite 12 - 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.
Seite 96 - ... 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.