A Treatise on Plane and Spherical Trigonometry
J. Smith, 1819 - Plane trigonometry - 264 pages
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A.cos according already angles application arithmetical assign b.cos base calculation called chord circle circumference common computed consequently convenient corresponding deduced definition determined difference divide drawn equal equation error Example excess expression figures former formula fraction given greater Hence instance introduce involving latter less logarithms manner means measure method multiply Naper's nearly negative object observed obtained operation opposite places plane powers preceding principle Prob Problem Prop properties proportion Proposition quadrant quantity radius reduced represent right angle root rules sides similar similarly simple sine sine and cosine solution solved sphere spherical triangle Student substitute subtract supplemental supposed surface Tables tangent Theorem third Trigonometrical true
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.