Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous Examples |
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Page 1
... perpendicular to the plane ; take any point D in the section and join OD , CD . Since OC is perpendicular to the plane , the angle OCD is a right angle ; therefore CD = √ ( OD- OC ) . Now O and C are fixed points , so that OC is ...
... perpendicular to the plane ; take any point D in the section and join OD , CD . Since OC is perpendicular to the plane , the angle OCD is a right angle ; therefore CD = √ ( OD- OC ) . Now O and C are fixed points , so that OC is ...
Page 2
... perpendicular to the plane of the circle ; the ex- tremities of the axis are called the poles of the circle . The poles of a great circle are equally distant from the plane of the circle . The poles of a small circle are not equally ...
... perpendicular to the plane of the circle ; the ex- tremities of the axis are called the poles of the circle . The poles of a great circle are equally distant from the plane of the circle . The poles of a small circle are not equally ...
Page 4
... perpendicular to OC , which is a straight line in the plane OCD ; and BO is perpendicular to OC , which is a straight line in the plane OCE ; therefore OC is perpen- dicular to the plane AOB ( Euclid , xI . 4 ) ; and therefore OC is ...
... perpendicular to OC , which is a straight line in the plane OCD ; and BO is perpendicular to OC , which is a straight line in the plane OCE ; therefore OC is perpen- dicular to the plane AOB ( Euclid , xI . 4 ) ; and therefore OC is ...
Page 6
... perpendicular to OP , because the planes aCb and AOB are perpendicular to OP ; therefore Ca is parallel to OA , and Cb is parallel to OB . Therefore the angle aCb the angle AOB ( Euclid , xI . 10 ) . Hence , ( Plane Trigonometry , Art ...
... perpendicular to OP , because the planes aCb and AOB are perpendicular to OP ; therefore Ca is parallel to OA , and Cb is parallel to OB . Therefore the angle aCb the angle AOB ( Euclid , xI . 10 ) . Hence , ( Plane Trigonometry , Art ...
Page 8
... perpendicular to OA , the angle bAc is the angle of inclination of the planes OAB and OAC . 20. The letters A , B , C are generally used to denote the angles of a spherical triangle , and the letters a , b , c are used to denote the ...
... perpendicular to OA , the angle bAc is the angle of inclination of the planes OAB and OAC . 20. The letters A , B , C are generally used to denote the angles of a spherical triangle , and the letters a , b , c are used to denote the ...
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Common terms and phrases
ambiguity angular points approximately arcs drawn arcs which join bisecting centre circular measure cos a cos cos² cos³ cosb cosines Crown 8vo deduce denote equation equilateral escribed circles example expression faces fixed points formulæ formulæ of Art greater Hence inscribed Legendre's Theorem less Let ABC lune meet middle point Napier's analogies Napier's Rules obtain octahedron opposite angle opposite sides parallelepiped Plane Geometry plane triangle Plane Trigonometry polar triangle pole polygon position preceding Article primitive triangle quadrant r₁ regular polyhedron respectively result right angles right-angled triangles shew shewn Similarly sin b cos sin b sin sin² sin³ sine small circle described solid angles solution sphere spherical excess spherical triangle Spherical Trigonometry ß³ straight lines subtended suppose surface tangent tetrahedron Trigono
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 49 - 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 12 - Any two sides of a spherical triangle are together greater than the third side.
Page 19 - Thus the sines of the angles of a spherical triangle are proportional to the sines of the opposite sides.
Page 30 - From this proposition, it is obvious that if one angle of a triangle be equal to the sum of the other two angles, that angle is a right angle, as is shewn in Euc.
Page 1 - A sphere is a solid bounded by a surface, every point of which is equally distant from a fixed point called the centre.
Page 62 - A circle which touches one side of a triangle and the other two sides produced, is called an escribed circle of the triangle.
Page 15 - If one angle of a spherical triangle be greater than another, the side opposite the greater angle is greater than the side opposite the less angle.