Plane and Spherical Trigonometry

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Page 2 - The sum is the segment extending from the initial point of the first to the terminal point of the second.
Page 3 - BOC, and AOC. 2. Definitions. Two angles are equal when one can be superposed upon the other, so that the vertices shall coincide and the sides of the first shall fall along the sides of the second. Two angles are added by placing them in the same plane with their vertices together and a side in common, care being taken that neither of the angles is superposed upon the other. The angle formed by the exterior sides of the two angles is their sum. 3. A clear notion of the magnitude of an angle will...
Page 70 - If a straight line rotates about one of its points, remaining always in the same plane, it generates an angle. The angle is measured by the amount of rotation by which the line is brought from its original position into its terminal position. For the small rotation leading to acute and obtuse angles this definition agrees with the customary elementary definition, the knowledge of which has been presupposed in the foregoing chapters. As in Art. 3, counterclockwise rotation generates positive angles...
Page 120 - Reduce to the degree system : 4─, -6▀, l´?, ^f, -lif. 3 о 2 5. Find the lengths of the arcs subtended by the following angles at the center of a circle of radius 6 : 45░, 120░, 270░, —, —, — • 483 6. A polygon of n sides is inscribed in a circle of radius r. Find the length of the arc subtended by one side. Compute the numerical values if r = 10 and n = 3, 4, 5, 6, 8. 7. Taking the radius of the earth to be 4000 miles, find the difference in latitude of two points on the same meridian...
Page 29 - The Logarithm of a number to a given base is the index of the power to which the base must be raised to give the number. Thus if m = a", x is called the logarithm of m to the base a.
Page 106 - We have then the law that the absolute value of the product of two complex numbers equals the product of their absolute values, while the amplitude of the product equals the sum of their amplitudes.
Page 131 - The sum of any two sides of a spherical triangle is greater than the third side, and their difference is less than the third side. DEM.— Let ABC be any spherical triangle; then l3 BO' < BA + AC, and BC - AC < BA ; and the same is true of the sides in any order.
Page 131 - The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle; produce the sides AB, AU, till they meet again in D.
Page 27 - Halma ; of. the reproduction in Cantor's Oesch. d. Mathematik, I. (1894), p. 389). Ptolemy's object is to connect by an equation the lengths of the chord of an arc and the chord of half the arc. Substantially his procedure is as follows. Suppose AP, PQ to be equal arcs, AB the diameter through A ; and let AP, PQ, AQ, PB, QB be joined. Measure BD along BA equal to BQ. The perpendicular PN is now drawn, and it is proved that PA =PD, and AN= ND.

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