Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous Examples |
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Page 119
... tetrahedron . A tetrahedron is one - sixth of a parallelepiped which has the same altitude and its base double that of the tetrahedron ; thus if the edges and their inclinations are given we can take one - sixth of the expression for ...
... tetrahedron . A tetrahedron is one - sixth of a parallelepiped which has the same altitude and its base double that of the tetrahedron ; thus if the edges and their inclinations are given we can take one - sixth of the expression for ...
Page 120
... tetrahedron we have 144 V2 = 2ao . 159. If the vertex of a tetrahedron be supposed to be situ- ated at any point in the plane of its base , the volume vanishes ; hence if we equate to zero the expression on the right - hand side of the ...
... tetrahedron we have 144 V2 = 2ao . 159. If the vertex of a tetrahedron be supposed to be situ- ated at any point in the plane of its base , the volume vanishes ; hence if we equate to zero the expression on the right - hand side of the ...
Page 121
... tetrahedron in terms of its six edges . , Let a , b , c be the lengths of the sides of a triangle ABC forming one face of the tetrahedron , which we may call its base ; let a ' , b ' , c ' be the lengths of the straight lines which join ...
... tetrahedron in terms of its six edges . , Let a , b , c be the lengths of the sides of a triangle ABC forming one face of the tetrahedron , which we may call its base ; let a ' , b ' , c ' be the lengths of the straight lines which join ...
Page 122
... tetrahedron as in Art . 161. Let the sphere be supposed to be circumscribed about the tetrahedron , and draw on the sphere the six arcs of great circles joining the angular points of the tetrahedron . Then the relation given in Art ...
... tetrahedron as in Art . 161. Let the sphere be supposed to be circumscribed about the tetrahedron , and draw on the sphere the six arcs of great circles joining the angular points of the tetrahedron . Then the relation given in Art ...
Page 123
... tetrahedron and the other three faces produced : find its radius . 4. If a and b are the radii of the spheres inscribed in and described about a regular tetrahedron , shew that b = 3a . 5. If a is the radius of a sphere inscribed in a ...
... tetrahedron and the other three faces produced : find its radius . 4. If a and b are the radii of the spheres inscribed in and described about a regular tetrahedron , shew that b = 3a . 5. If a is the radius of a sphere inscribed in a ...
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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.