A Treatise on Plane and Spherical TrigonometryJ. Smith, 1819 - 264 pàgines |
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a+b+c analytical arithmetical Asin chord circle circumference co-sec co-tan coefficient compute the sines consequently cos.³ COS.C cosine decimal deduced determined difference equal equation Euclid Example formula fraction given Hence horizontal angle included angle instance latter loga logarithmic sines multiple arcs natural sines nearly oblique oblique-angled obtained plane preceding method Prob PROBLEM Prop quadrant quantity rectilinear triangles required to express right angle right ascension rithm root Rule secant Sherwin's Tables sides similar similarly simple arc sin.² sin.³ sin.c sine and cosine sines of arcs solution spherical angle spherical excess spherical triangle Spherical Trigonometry substitute subtract supplemental triangle tangent Theorem Treatise Trigonometrical formulæ Trigonometrical Survey Trigonometrical Tables versed sine versin
Passatges populars
Pàgina 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.
Pàgina 126 - THEOREM. Every section of a sphere, made by a plane, is a circle.
Pàgina 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.
Pàgina 142 - That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles.
Pàgina 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.
Pàgina 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.
Pàgina 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.
Pàgina 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.
Pàgina 134 - The measure of the surface of a spherical triangle is the difference between the sum of its three angles and two right angles.
Pàgina 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.