Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous Examples |
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Page 9
... greater than two right angles . Then suppose D to denote the point at which the arc BC , if produced , will meet AE ; then BED is a semicircle by Art . 10 , and therefore BEA is greater than a semicircle ; thus the proposed triangle is ...
... greater than two right angles . Then suppose D to denote the point at which the arc BC , if produced , will meet AE ; then BED is a semicircle by Art . 10 , and therefore BEA is greater than a semicircle ; thus the proposed triangle is ...
Page 12
... greater than the third ( Euclid , x1 . 20 ) . Therefore any two of the arcs AB , BC , CA , are together greater than the third . From this proposition it is obvious that any side of a spherical triangle is greater than the difference of ...
... greater than the third ( Euclid , x1 . 20 ) . Therefore any two of the arcs AB , BC , CA , are together greater than the third . From this proposition it is obvious that any side of a spherical triangle is greater than the difference of ...
Page 13
... greater than AC + CD , and à fortiori greater than AD , Again , if there be any polygon which has each of its angles less than two right angles , the sum of its sides will be less than the circumference of a great circle . This follows ...
... greater than AC + CD , and à fortiori greater than AD , Again , if there be any polygon which has each of its angles less than two right angles , the sum of its sides will be less than the circumference of a great circle . This follows ...
Page 14
... 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 the base are right angles by Arts ...
... 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 the base are right angles by Arts ...
Page 15
... greater angle is greater than the side opposite the less angle . A B C D Let ABC be a spherical triangle , and let the angle ABC be greater than the angle BAC : then the side AC will be greater than the side BC . At B make the angle ABD ...
... greater angle is greater than the side opposite the less angle . A B C D Let ABC be a spherical triangle , and let the angle ABC be greater than the angle BAC : then the side AC will be greater than the side BC . At B make the angle ABD ...
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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.