## Plane and Spherical Trigonometry: With Stereographic Projections |

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a₁ angle angle increases applies base bearing body called celestial center of projection CHAPTER Check circle colog column complex numbers computation construct cosine cotangent course curve declination denoted Derive determined diameter difference direction Dividing draw drawn earth equal equations example EXERCISE expression figure formulae functions give given greater haversine Hence horizon hour illustration intersect latitude length less locate logarithm means measure meridian method miles minute negative observer obtain opposite passing perpendicular plane pole positive projection Prove quadrant radians radius ratios relation representing respectively right triangle rule secant Show sides Similarly sine solution Solve sphere spherical triangle given surface taken tangent trigonometric true units vector vertical write

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Page 147 - The axis of a circle of a sphere is the diameter of the sphere which is perpendicular to the plane of the circle. The ends of the axis are called the poles of the circle.

Page 188 - HA) of any point on the celestial sphere is the angle at the pole between the meridian of the observer and the hour circle passing through the point ; it is measured by the arc of the celestial equator intercepted between those circles.

Page 147 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.

Page 4 - X _ y toga— = m — n = loga x — log0 y, (4) showing that the logarithm of the quotient of two numbers is equal to the logarithm of the numerator minus the logarithm of the denominator.

Page 188 - Azimuth of a star is the angle at the zenith formed by the meridian of the observer and the vertical circle passing through the star, and is measured therefore by an arc of the horizon.

Page 8 - The characteristic of the logarithm of a number greater than 1 is a positive integer or zero, and is one less than the number of digits to the left of the decimal point.

Page 148 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...

Page 160 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts. II. The sine of the middle part is equal to the product of the cosines of the opposite parts.

Page 107 - In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other side upon it.

Page 188 - The Zenith Distance of any point is its angular distance from the zenith, measured upon the vertical circle passing through the point; the zenith distance of any point which is above the horizon of an observer must therefore equal 90° minus the altitude.