A Treatise on Spherical Trigonometry: With Applications to Spherical Geometry and Numerous Examples, Volume 1 |
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A Treatise On Spherical Trigonometry: With Applications to Spherical ... Thomas Preston,William J M'Clelland No preview available - 2022 |
Common terms and phrases
analogous angular distances angular radius anharmonic ratio arc joining B₁ b₂ base angles bisectors chordal triangle circle passing circular segment circumcircle coaxal colunar triangle concurrent concyclic corresponding cos a cos cos(a cos² cosb cosc cosec cosines cot² curve denote diagonals drawn equal equation Exam Examples external bisectors find the locus fixed point formula Geometrical Given the base Hence hypotenuse in-circle inverse joining the middle middle points opposite angles opposite sides pair perpendicular plane triangle plano points of contact polar triangle pole polygon prove quadrant r₁ r₂ radical axis radii relation respectively right-angled triangle segments Similarly sin b sin sin² sines small circle solid angle sphere spherical excess spherical triangle subtended supplemental surface tan² tana tanc triangle ABC vertex vertical angle
Popular passages
Page 86 - 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 146 - 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 109 - 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 6 - Thus, on a terrestrial globe the meridians and equator are great circles ; the parallels of latitude are small circles. The Axis of a circle of a sphere is the diameter of the sphere perpendicular to the plane of the circle ; the extremities of the axis are called the Poles of the circle and any of its arcs. Thus, in Fig. 4, Art. 5, N and S are the poles of the circle ABD and of the arcs AB and BD. It is obvious that all circles made by the intersections of parallel planes with a sphere have the...
Page 72 - Angles of the point, and the cosines of these angles are called the Direction Cosines of the point.
Page 42 - ... of the spherical excess the corresponding angle of the plane triangle, the sides of which are of the same length as the arcs of the spherical triangle.
Page 120 - A = - cos B cos C + sin B sin C cos a. Similarly cos B = - cos C...
Page 153 - Circle. [For the common tangents are b + c, b - c, c + a, c - a, a + b, a...
Page 1 - Each side of a spherical triangle is less than the sum of 'the other two sides. 48. The sum of the sides of a spherical polygon is less than 360°. 49. The sum of the angles of a spherical triangle is greater than 180° and less tha'n 540°.
Page 24 - 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.