A treatise on plane and spherical trigonometry

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J. Smith, printer to the University, 1822 - Trigonometry - 264 pages
 

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Page 187 - 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 124 - THEOREM. Every section of a sphere, made by a plane, is a circle.
Page 125 - 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 140 - That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles.
Page 123 - 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 23 - 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 136 - ... 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 132 - The measure of the surface of a spherical triangle is the difference between the sum of its three angles and two right angles.
Page 125 - Cor. 2. Two great circles always bisect each other ; for their common intersection, passing through the centre, is a diameter. Cor. 3. Every great circle divides the sphere and its surface into two equal parts ; for, if the two hemispheres were separated, and afterwards placed on the common base, with their convexities turned the same way, the two surfaces would exactly coincide, no point of the one being nearer the centre than any...
Page 143 - ... is enabled to solve every case of right-angled triangles. These are known by the name of Napier's Rules for Circular Parts ; and it has been well observed by the late Professor Woodhouse, that, in the whole compass of mathematical science, there cannot be found rules which more completely attain that which is the proper object of all rules, namely, facility and brevity of computation.

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