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A System of Plane and Spherical Trigonometry: To Which Is Added A Treatise ...
No preview available - 2008
2cos 2cosa 2sin ad+bc addition arcs to radius centre chord circle circumference corresponding cos(a cosB cosC cosec 22 cosec a)2 cosine cot a)2 decimal differentiating dividing equal expressed factors find what values Firstly formulae become four right angles given greater or less hence hypothenuse imaginary quantities less than 90 logarithm magnitude multiplying Napier's rules nearly negative odd integer opposite perpendicular plane angles plane triangle polar triangle pole polyhedron positive integer Prob Prop proposition quadrant quadratic equation radius unity regular polyhedrons right angle right-angled triangle roots Similarly Sin2 sinB sine sines and cosines solid angle sphere spherical angle spherical polygon spherical triangle substituting sum the series suppose surface tangent theorem trigono trigonometric functions vanish vers
Page 197 - IF two triangles have two sides of the one equal to two sides of the other, each to each ; and have likewise the angles contained by those sides equal to one another ; they shall likewise have their bases, or third sides, equal ; and the two triangles shall be equal ; and their other angles shall be equal, each to each, viz.
Page 190 - 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 191 - THEOREM. The sum of the sides of a spherical polygon is less than the circumference of a great circle.
Page 181 - ... poles. 751. COR. 2. All great circles of a sphere are equal. 752. COR. 3. Every great circle bisects the sphere. For the two parts into which the sphere is divided can be .so placed that they .will coincide; otherwise there would be points on the surface unequally distant from the centre. 753. COR. 4. Two great circles bisect each other. For the intersection of their planes passes through the centre, and is, therefore, a diameter of each circle. 754.
Page 258 - A solid angle is that which is made by the meeting of more than two plane angles, which are not in the same plane, in one point. X. ' The tenth definition is omitted for reasons given in the notes.
Page 189 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 181 - An arc of a great circle may be drawn through any two points on the surface of a sphere.
Page 45 - Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...