Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous Examples |
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Page 3
... distance of a pole of a circle from every point of the circumference of the circle is constant , whether that distance be measured by the straight line joining the points , or by the arc of a great circle intercepted between the points ...
... distance of a pole of a circle from every point of the circumference of the circle is constant , whether that distance be measured by the straight line joining the points , or by the arc of a great circle intercepted between the points ...
Page 30
... distance of its middle point from the opposite angle . 3. When does the polar triangle coincide with the primitive triangle ? 4. If D be the middle point of AB , shew that cos AC + cos BC = 2 cos AB cos CD . 5. If two angles of a ...
... distance of its middle point from the opposite angle . 3. When does the polar triangle coincide with the primitive triangle ? 4. If D be the middle point of AB , shew that cos AC + cos BC = 2 cos AB cos CD . 5. If two angles of a ...
Page 32
... distance in sailing from one to the other on the great circle , instead of sailing due East or West , is 2r { λ cos - sin1 ( sin à cos 7 ) } , A being expressed in circular measure , and r being the radius of the Earth . 18. If a ship ...
... distance in sailing from one to the other on the great circle , instead of sailing due East or West , is 2r { λ cos - sin1 ( sin à cos 7 ) } , A being expressed in circular measure , and r being the radius of the Earth . 18. If a ship ...
Page 57
... distances of P from the great circle ( see Art . 59 ) . Thus the figure supposes A and b each less than π 2 · If a be less than the arc which is represented by PD there is no triangle ; if a be between PD and PA in magnitude , there are ...
... distances of P from the great circle ( see Art . 59 ) . Thus the figure supposes A and b each less than π 2 · If a be less than the arc which is represented by PD there is no triangle ; if a be between PD and PA in magnitude , there are ...
Page 91
... 215 ) . 127. In geodetical operations it is sometimes required to de- termine the horizontal angle between two points , which are at a small angular distance from the horizon , the angle which GEODETICAL OPERATIONS . 91.
... 215 ) . 127. In geodetical operations it is sometimes required to de- termine the horizontal angle between two points , which are at a small angular distance from the horizon , the angle which GEODETICAL OPERATIONS . 91.
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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.