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A Treatise On Spherical Trigonometry, by W.J. M'Clelland and T. Preston
William John M'Clelland
No preview available - 2023
ambiguity Analogies Apply base base angles calculate called centre Chap connecting corresponding cos b cos cos(a cosē cosc cosines denote determine difference distance divides Draw drawn equal equation Exam Examples expression external find the locus follows formula geometrically given Given the base greater Hence hypotenuse internal bisector intersection L cos latitude length less meet middle points obtained once opposite sides passes perpendicular plane plano polar pole preceding Prove quadrant quadrilateral radius ratio reduces relation remaining respectively right-angled triangle Science and Art secondaries segments similar Similarly sin b sin sin c cos sinē sines small circle solution sphere spherical triangle substituting subtended supplemental surface tana tangents theorem vertex vertical angle
Page 78 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 17 - The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides.
Page 28 - Show that any side of a triangle is greater than the difference between the other two sides.
Page 37 - C . cos. a . sin. 6 . cos. c _ — 2 . sin. A . sin. B . sin. C . sin. a . sin. b . sin. c I — 2 sin.
Page 99 - BG; that is, the base is to the sum of the sides as the difference of the sides is to the sum or difference of the segments of the base made by the perpendicular from the vertex, according as the...
Page 114 - 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 39 - Thus the sines of the angles of a spherical triangle are proportional to the sines of the opposite sides.
Page 18 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal.