Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous Examples |
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Page 9
... 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 not one of those which we consider . III . SPHERICAL GEOMETRY . 24. The relations between ...
... 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 not one of those which we consider . III . SPHERICAL GEOMETRY . 24. The relations between ...
Page 11
... produced if necessary , meet the arcs AB , AC , produced if necessary , at the points D and E respectively ; then since A is a pole of B'C ' , the spherical angle A is measured by the arc DE ( Art . 12 ) . But B'E and C'D are each ...
... produced if necessary , meet the arcs AB , AC , produced if necessary , at the points D and E respectively ; then since A is a pole of B'C ' , the spherical angle A is measured by the arc DE ( Art . 12 ) . But B'E and C'D are each ...
Page 14
... produced at the same point S , and AS will be equal to BS . Draw tangents AT , BT at the points A , B to the arc AB ; then AT = TB ; join TS . In the two triangles SAT , SBT the sides SA , AT , TS are equal to SB , BT , TS respectively ...
... produced at the same point S , and AS will be equal to BS . Draw tangents AT , BT at the points A , B to the arc AB ; then AT = TB ; join TS . In the two triangles SAT , SBT the sides SA , AT , TS are equal to SB , BT , TS respectively ...
Page 16
... produced at E , and let the tangent at A to the arc AB meet OB produced at D ; join ED . Thus the angle EAD is the angle A of the spherical triangle , and the angle EOD measures the side a . From the triangles ADE and ODE we have DE AD2 ...
... produced at E , and let the tangent at A to the arc AB meet OB produced at D ; join ED . Thus the angle EAD is the angle A of the spherical triangle , and the angle EOD measures the side a . From the triangles ADE and ODE we have DE AD2 ...
Page 17
... produced . We must now shew that the formula obtained is true when these sides are not less than quad- rants . This ... Produce BA and BC to meet at B ' ; and put AB ′ = c ' , CB ′ = a ' . B A B C Then we have from the triangle ABC , by ...
... produced . We must now shew that the formula obtained is true when these sides are not less than quad- rants . This ... Produce BA and BC to meet at B ' ; and put AB ′ = c ' , CB ′ = a ' . B A B C Then we have from the triangle ABC , by ...
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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.