## A Treatise on Trigonometry |

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abscissa arc-ordinate area swept axis celestial sphere centre circle computed cos0 cos2 cosb cosc cosecant cosp cosq cot q cotangent difference of latitude difference of longitude direction draw ecliptic equal equator formulae of th geom given horizon hour-angle hypothenuse LAW OF COSINES law of sines let xop log-sin log-tan meridian miles nearer right negative angle oblique angle oblique triangle observer's obtuse opposite ordinate perpendicular plane angle plane sailing plane triangle polar pole positive and less positive angle possible errors prime vertical PROB projection quarter radians radius ratio right angles right ascension right spherical triangle right triangles sailing secant segment side sin0 sin2 sinB sinp small angles Solve species spherical angle straight line subtended sun's tangent tanp terminal line thence Theor theorem triangle abc trigonometric functions values vernal equinox vertex vertical angle wherein

### Popular passages

Page 117 - Greenwich) ; so, the position of a star at any instant on the celestial sphere may be defined in either of three ways : 1. As to the celestial equator : The declination of a star is its angular distance (north or south) from the celestial equator measured upon its hour-circle ; and the arc of the equator intercepted between this circle and the vernal equinox is the star's right ascension ; it is reckoned eastward from the vernal equinox from 0° to 360°.

Page 122 - 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 152 - 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 117 - 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 71 - 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 84 - Each angle of a spherical triangle is greater than the difference between two right angles and the sum of the other two angles.

Page 41 - Thus in page 69, the sine of 5° 30' is .09585. The cosine of 5° 30' „ .99540. Sine of 40° 25' (page 73) „ .64834. Cosine of 40° 25' „ .76135. When the angle exceeds 45°, the degrees are found at the bottom of the page, and the minutes are counted upwards in the right hand column of the page, as in the table of logarithmic sines. Thus, sine of 84° 20

Page 104 - PM = sm b' = sm c, - = coa c> - = cos * 5 substituting these values, we have, cos a — sin b sin c cos A = cos J cos c ; and by transposing, cos a = cos b cos c + sin 6 sin c cos A.

Page 85 - From the mid-point O of a straight line AB a straight line OC is drawn; if OC = OA, /.ACB is a right angle.

Page 71 - From the top of a hill I observe two successive milestones in the plain below, and in a straight line before me, and find their angles of depression to be 5° 30', 14° 20' : what is the height of the hill ? [815.85 feet.