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a/sin acute angle broken line celestial sphere centre circle co-line coincides computation congruent Construct cos2 cosb cosecant cosine cotangent diedral difference directed lines distance draw ecliptic equal equations face angles figure following angles formulae given horizontal hypotenuse ideal triangle initial line latitude law of cosines law of sines length log-sin logarithm longitude maj-proj mantissa measure meridian miles minor projections motion negative normal opposite parallel perigon perpendicular plane angle plane sailing plane triangle proj quadrant radians radius right angles right ascension right triangle abc sailing sec f secant segment side sin2 sine solution Solve species sphere spherical triangle subtended subtracting sun's tan2 tanA tangent terminal line theor tion triedral angle Trigonometric Functions trigonometric ratios values vertex vertical
Page 48 - A a = sin (a + 2) sin a cos sin (a + ft) = sin a cos ft + cos a sin ft sin (a — ft) = sin a cos /? — cos a sin /? cos (a + ft) = cos a cos ft — sin a sin ft...
Page 110 - The projection of a point on a plane is the foot of the perpendicular from the point to the plane. The projection of a figure upon a plane is the locus of the projections of all the points of the figure upon the plane. Thus, A'B' represents the projection of AB upon plane MN.
Page 165 - 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 129 - That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles.
Page 5 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 5 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log
Page 62 - The sine of the difference of any two arcs or angles is equal to the sine of the first into the cosine of the second, minus the cosine of the first into the sine of the second.
Page 17 - 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?
Page 173 - To any observer the sensible horizon is a plane touching the earth's surface at the point of observation ; and a plane parallel to this plane through the earth's centre traces out on the celestial sphere the rational horizon, whose poles, zenith and nadir, are the traces of a vertical line, and whose secondaries are vertical circles. One of the vertical circles is also an hour-circle, the observer's celestial meridian, and passes through his zenith a'nd nadir, and the north and south poles of the...
Page 174 - ... sphere ; the hour-angle changes every moment. 2. As to the ecliptic : The latitude of a star is its angular distance from the ecliptic measured on a secondary ; and the arc of the ecliptic intercepted between the vernal equinox and this secondary, measured eastward, is the star's longitude. 3. 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...