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acute adjacent angle Aldebaran ambiguous angle opposite Answer apparent altitude azimuth base centre complement construction cosec cosine degrees diff draw ecliptic equator Euclid find the angle find the side formulae given angle given side greater Greenwich half the sum Hence horizon horizontal parallax hypoth less mean arc measure meridian moon's Naut Nautical Almanac noon North observed obtuse opposite angle parallel perpendicular plane sailing plane triangle Plate pole PRACTICAL EXAMPLES prime vertical primitive proposition quadrant rad2 radius rhumb line right ascension right-angled spherical triangle right-angled triangle rule scale of chords SCHOLIUM secant semi-tangents semidiameter side ac side opposite sin2 sine of half species sphere spherical angle spherical triangle abc spherical trigonometry star star's subtract sun's declination supplement Tang tangent of half three angles three sides Trigonometry versed sine zenith distance
Side 109 - C' (89) (90) (91) (92) (93) 112. 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.
Side iii - An INTRODUCTION to the THEORY and PRACTICE of PLANE and SPHERICAL TRIGONOMETRY, and the Stereographic Projection of the Sphere, including the Theory of Navigation ; comprehending a variety of Rules, Formulae, &c.
Side 33 - An angle at the circumference of a circle is measured by half the arc that subtends it. Let BAC be an angle at the circumference : it has for its measure half the arc "BC, which subtends it.
Side 29 - The sine, or right sine, of an arc, is the line drawn from one extremity of the arc, perpendicular to the diameter passing through the other extremity. Thus, BF is the sine of the arc AB, or of the arc BDE.
Side 258 - The HORIZON is a great circle which separates the visible half of the heavens from the invisible ; the earth being considered as a point in the centre of the sphere of the fixed stars.
Side 116 - C = sin. A sin. B sin. C; dividing both sides of this equation by cos. A cos. B cos. C, we have sin. A sin. B sin. C _ sin.
Side 362 - Now it is plain, that if any great circle of the sphere (as 1, 2, 3.) be divided into any number of equal parts, and through the points of division...
Side 23 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...