A Treatise on Plane and Spherical Trigonometry

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J. Smith, 1819 - Plane trigonometry - 264 pages

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Page 191 - The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle.
Page 126 - THEOREM. Every section of a sphere, made by a plane, is a circle.
Page 127 - 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 142 - That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles.
Page 125 - A sphere is a solid terminated by a curved surface, all the points of which are equally distant from a point within called the centre.
Page 171 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Page 25 - It depends on the principle, that the difference of the squares of two quantities is equal to the product of the sum and difference of the quantities.
Page 138 - ... sun in the meridian. The arches being supposed semi-circular, it is required to find the curve terminating that part of the surface of the water which is illuminated by the sun's rays passing through any arch. 7- It is required to express the cosine of an angle of a spherical triangle in terms of the sines and cosines of the sides.
Page 134 - The measure of the surface of a spherical triangle is the difference between the sum of its three angles and two right angles.
Page 188 - From the logarithm of the area of the triangle, taken as a plane one, in feet, subtract the constant log 9-3267737, then the remainder is the logarithm of the excess above 180░, in seconds nearly.* 3.

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