Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous Examples |
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Page 9
... less than a semicircle ; this is of course a convention , and it is adopted because it is found convenient . B F C D E Thus , in the figure , the arc ADEB is greater than a semicir- cumference , and we might , if we pleased , consider ...
... less than a semicircle ; this is of course a convention , and it is adopted because it is found convenient . B F C D E Thus , in the figure , the arc ADEB is greater than a semicir- cumference , and we might , if we pleased , consider ...
Page 11
... less than a quadrant ; and since A is a pole of B'C ' , and AA ' is less than a quadrant , A and A ' are on the same side of B'C ' . Similarly it may be shewn that B is a pole of C'A ' , and that B and B ' are on the same side of C'A ...
... less than a quadrant ; and since A is a pole of B'C ' , and AA ' is less than a quadrant , A and A ' are on the same side of B'C ' . Similarly it may be shewn that B is a pole of C'A ' , and that B and B ' are on the same side of C'A ...
Page 12
... two . 30. The sum of the three sides of a spherical triangle is less than the circumference of a great circle . ( See the figure of Art . 18. ) For the sum of the three plane angles which form 12 SPHERICAL GEOMETRY .
... two . 30. The sum of the three sides of a spherical triangle is less than the circumference of a great circle . ( See the figure of Art . 18. ) For the sum of the three plane angles which form 12 SPHERICAL GEOMETRY .
Page 13
... less than four right angles ( Euclid , XI . 21 ) ; therefore therefore , AB + BC CA + is less than 2π , OA OA ОА AB + BC + CA is less than 2 ′′ × ОA ; that is , the sum of the arcs is less than the circumference of a great circle . 31 ...
... less than four right angles ( Euclid , XI . 21 ) ; therefore therefore , AB + BC CA + is less than 2π , OA OA ОА AB + BC + CA is less than 2 ′′ × ОA ; that is , the sum of the arcs is less than the circumference of a great circle . 31 ...
Page 14
... less than quadrants ; if they are greater than quadrants the tangents to AC and BC will meet on CO produced through O instead of through C , and the demonstration may be completed as before . If AC and BC are quadrants , the angles at ...
... less than quadrants ; if they are greater than quadrants the tangents to AC and BC will meet on CO produced through O instead of through C , and the demonstration may be completed as before . If AC and BC are quadrants , the angles at ...
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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.