Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous Examples |
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... Relations between the Trigonometrical Functions of the Sides and the Angles of a Spherical Triangle V. Solution of Right - angled Triangles " VI . Solution of Oblique - angled Triangles VII . Circumscribed and Inscribed Circles VIII ...
... Relations between the Trigonometrical Functions of the Sides and the Angles of a Spherical Triangle V. Solution of Right - angled Triangles " VI . Solution of Oblique - angled Triangles VII . Circumscribed and Inscribed Circles VIII ...
Page 6
... relations which subsist between the angles of the plane faces which form a solid angle and the angles at which the plane faces are inclined to each other . 16. Suppose that the angular point of a solid angle SPHERICAL TRIANGLES ...
... relations which subsist between the angles of the plane faces which form a solid angle and the angles at which the plane faces are inclined to each other . 16. Suppose that the angular point of a solid angle SPHERICAL TRIANGLES ...
Page 9
... 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 the SPHERICAL TRIANGLES . 9.
... 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 the SPHERICAL TRIANGLES . 9.
Page 10
With Numerous Examples Isaac Todhunter. III . SPHERICAL GEOMETRY . 24. The relations between the sides and angles of a Spherical Triangle , which are investigated in treatises on Spherical Trigono- metry , are chiefly such as involve the ...
With Numerous Examples Isaac Todhunter. III . SPHERICAL GEOMETRY . 24. The relations between the sides and angles of a Spherical Triangle , which are investigated in treatises on Spherical Trigono- metry , are chiefly such as involve the ...
Page 15
... formulæ of the next Chapter sup- ply an easy method of investigating the theorems of Spherical Geometry . See Arts . 56 , 57 , and 58 . IV . RELATIONS BETWEEN THE TRIGONOMETRICAL FUNCTIONS OF THE SIDES SPHERICAL GEOMETRY . 15.
... formulæ of the next Chapter sup- ply an easy method of investigating the theorems of Spherical Geometry . See Arts . 56 , 57 , and 58 . IV . RELATIONS BETWEEN THE TRIGONOMETRICAL FUNCTIONS OF THE SIDES SPHERICAL GEOMETRY . 15.
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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.