Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous Examples |
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Page 10
... is the triangle which is known under the name of the polar triangle . The triangle ABC is called the primitive triangle with respect to the triangle A'B'C ' . 26. If one triangle be the polar triangle of another ( 10 ) Spherical Geometry.
... is the triangle which is known under the name of the polar triangle . The triangle ABC is called the primitive triangle with respect to the triangle A'B'C ' . 26. If one triangle be the polar triangle of another ( 10 ) Spherical Geometry.
Page 32
... the right - angled triangle : here two elements , in addition to the right angle , will be supposed known . 62. The formulæ requisite for the solution of right - 32 SOLUTION OF RIGHT - ANGLED TRIANGLES . Solution of Right-angled Triangles "
... the right - angled triangle : here two elements , in addition to the right angle , will be supposed known . 62. The formulæ requisite for the solution of right - 32 SOLUTION OF RIGHT - ANGLED TRIANGLES . Solution of Right-angled Triangles "
Page 46
... known . ( 2 ) Suppose among the given elements of a triangle there are two equal sides or two equal angles . By drawing an arc from the vertex to the middle point of the base , the triangle is divided into two equal right - angled ...
... known . ( 2 ) Suppose among the given elements of a triangle there are two equal sides or two equal angles . By drawing an arc from the vertex to the middle point of the base , the triangle is divided into two equal right - angled ...
Page 48
... known . Again , by Art . 62 , cos c = cos AD cos DB = cos DB . cos b cos CD this finds c . It is obvious that CD is what was denoted by 0 in the former part of the Article . By Art . 62 , tan AD = tan C sin CD , and tan AD = tan ABD sin ...
... known . Again , by Art . 62 , cos c = cos AD cos DB = cos DB . cos b cos CD this finds c . It is obvious that CD is what was denoted by 0 in the former part of the Article . By Art . 62 , tan AD = tan C sin CD , and tan AD = tan ABD sin ...
Page 49
... known . Again , by Art . 62 , = cos AD sin CAD = cos C , and cos AD sin BAD = cos B ; therefore COS C cos B sin CAD sin BAD this finds C. It is obvious that DAB is what was denoted by in the former part of the Article , T. S. T. E By ...
... known . Again , by Art . 62 , = cos AD sin CAD = cos C , and cos AD sin BAD = cos B ; therefore COS C cos B sin CAD sin BAD this finds C. It is obvious that DAB is what was denoted by in the former part of the Article , T. S. T. E 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.