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angle of elevation azimuth bearing Calculation celestial concave celestial equator celestial meridian circle of altitude colat colatitude cosec course and distance decl dist draw ecliptic Eule EXAMPLES feet find angle find the angle find the latitude formula given angle given sides given the side Given the sun's given the three haversines heavenly body hence horizon hour-angle included angle logarithm longitude meridian altitude miles natural number natural versine Nautical Navigation observed parallel perpendicular plane triangle ABC point of Aries pole prime vertical Prob problem quantities required angle required the height required the latitude right ascension right-angled triangle Rule sailing sextant ship sine solved spherical triangle Spherical Trigonometry station subtended subtract tangent third side three sides triangle ABC Trig whence yards zenith
Page 62 - EULE VIII. — SECOND METHOD, WITHOUT HAVERSINES. Three sides of a spherical triangle being given, to find an angle. Put down the two sides containing the required angle, * A spherical triangle is that part of the surface of a sphere which is bounded by arcs of three great circles, that is, three circles whose planes pass through the centre of the sphere. The three arcs are the sides of the triangles ; and any one of its angles is the same as the inclination of the planes of the r.ides containing...
Page 180 - AB describe a segment of a circle containing an angle equal to the given angle, (in.
Page 10 - Hence, if we find the logarithm of the dividend, and from it subtract the logarithm of the divisor, the remainder will be the logarithm of the quotient. This additional caution may be added. The difference of the logarithms, as here used, means the algebraic difference ; so that, if the logarithm of the divisor...
Page 60 - RULE. from half the sum of the three sides, subtract each side separately; multiply the half sum and the three remainders together, and the square root of the product will be the area required.
Page 125 - The hour angle of a heavenly body, is the angle at the pole between the celestial meridian and the circle of declination passing through the place of the body ; thus, zpx is the hour angle of x.
Page 174 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 59 - Heath,* believe that he probably discovered the theorem that bears his name, to the effect that, in a right-angled triangle, the square on the side opposite the right angle is equal to the sum of the squares on the other two sides.
Page 16 - The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor.