Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous Examples |
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... Arcs drawn to fixed points on the Surface of a Sphere 96 114 125 XV . Miscellaneous Propositions • XVI . Numerical Solution of Spherical Triangles 135 149 LIBRA . OF TEE MACRON IBRAR LI OF THE UNIVERSITY CALIFORNIA SPHERICAL ...
... Arcs drawn to fixed points on the Surface of a Sphere 96 114 125 XV . Miscellaneous Propositions • XVI . Numerical Solution of Spherical Triangles 135 149 LIBRA . OF TEE MACRON IBRAR LI OF THE UNIVERSITY CALIFORNIA SPHERICAL ...
Page 2
... drawn through two given points , the great circle is unequally divided at the two points ; we shall for brevity speak of the shorter of the two arcs as the arc of a great circle joining the two points . 5. The axis of any circle of a ...
... drawn through two given points , the great circle is unequally divided at the two points ; we shall for brevity speak of the shorter of the two arcs as the arc of a great circle joining the two points . 5. The axis of any circle of a ...
Page 3
... arc of a great circle intercepted between the points . 7. The arc of a great circle which is drawn from a pole of a great circle to any point in its circumference is a quadrant . P B C A Let P be a pole of the great circle ABC ; then the ...
... arc of a great circle intercepted between the points . 7. The arc of a great circle which is drawn from a pole of a great circle to any point in its circumference is a quadrant . P B C A Let P be a pole of the great circle ABC ; then the ...
Page 4
... arc of a great circle which joins the poles of two great circles is equal to the inclination of the planes of the ... Draw a great circle through A and B , meeting CD and CE at M and N respectively . Then AO is perpendicular to OC ...
... arc of a great circle which joins the poles of two great circles is equal to the inclination of the planes of the ... Draw a great circle through A and B , meeting CD and CE at M and N respectively . Then AO is perpendicular to OC ...
Page 5
... drawn two arcs of great circles , not parts of the same great circle , the planes of which are at right angles to the plane of a given circle , that point is a pole of the given circle . For , since the planes of these arcs are at right ...
... drawn two arcs of great circles , not parts of the same great circle , the planes of which are at right angles to the plane of a given circle , that point is a pole of the given circle . For , since the planes of these arcs are at right ...
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Common terms and phrases
A+B+C ambiguity angular points approximately arcs drawn arcs which join bisecting centre circular measure cos b cos COS TU cos² cos³ cosb cosc cosines cot a sin Crown 8vo deduce denote equation equilateral escribed circles example expression faces fixed points formed formula formulæ formulæ of Art greater Hence inscribed less Let ABC lune meet middle point Napier's analogies Napier's Rules obtain opposite sides parallelepiped perpendicular plane triangle Plane Trigonometry polar triangle pole polygon position preceding Article quadrant r₁ regular polyhedron respectively result right angles right-angled triangles shew shewn Similarly sin b sin sin C cos sin² sin³ sine small circle described solid angles solution sphere spherical excess spherical triangle Spherical Trigonometry straight lines subtended suppose surface tangent tetrahedron µ³