Spherical Trigonometry: For the Use of Colleges and SchoolsMacmillan and Company, 1914 - 275 páginas |
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Página xi
... SPHERICAL TRIANGLE . SPHERICAL EXCESS , . EXAMPLES IX , 96 105 • EXAMPLES X. , • · 107 EXAMPLES XI . , • VIII . VARIOUS PROPERTIES OF THE SPHERICAL TRIANGLE , IX . PROPERTIES OF CIRCLES ON THE SPHERE , 109 • 130 132 EXAMPLES XII ...
... SPHERICAL TRIANGLE . SPHERICAL EXCESS , . EXAMPLES IX , 96 105 • EXAMPLES X. , • · 107 EXAMPLES XI . , • VIII . VARIOUS PROPERTIES OF THE SPHERICAL TRIANGLE , IX . PROPERTIES OF CIRCLES ON THE SPHERE , 109 • 130 132 EXAMPLES XII ...
Página 96
... angle equal to four right angles , we have for a lune with an angle whose circular measure is A , area of lune surface of sphere A 27 Suppose r the radius of the sphere , then the VII AREA OF A SPHERICAL TRIANGLE SPHERICAL EXCESS,
... angle equal to four right angles , we have for a lune with an angle whose circular measure is A , area of lune surface of sphere A 27 Suppose r the radius of the sphere , then the VII AREA OF A SPHERICAL TRIANGLE SPHERICAL EXCESS,
Página 98
... Spherical excess . The expression A + B + C - T is called the spherical excess of the triangle ; and since ( A + B + C - π ) r2 . = A + B + C - T 4π 4πr2 , the result obtained may be enunciated thus : the area of a spherical triangle is ...
... Spherical excess . The expression A + B + C - T is called the spherical excess of the triangle ; and since ( A + B + C - π ) r2 . = A + B + C - T 4π 4πr2 , the result obtained may be enunciated thus : the area of a spherical triangle is ...
Página 99
... spherical excess of a spherical polygon is the excess of the sum of the angles of the polygon over the sum of the angles of a plane polygon having the same number of sides . The result just obtained shews that the area of a spherical ...
... spherical excess of a spherical polygon is the excess of the sum of the angles of the polygon over the sum of the angles of a plane polygon having the same number of sides . The result just obtained shews that the area of a spherical ...
Página 101
... excess , is necessarily positive and less than 2 ; hence C - E is positive and less than π . This justifies the assumption made above , that sin ( CE ) is always positive . 134. L'Huilier's theorem . * To shew that ... SPHERICAL EXCESS .
... excess , is necessarily positive and less than 2 ; hence C - E is positive and less than π . This justifies the assumption made above , that sin ( CE ) is always positive . 134. L'Huilier's theorem . * To shew that ... SPHERICAL EXCESS .
Otras ediciones - Ver todas
Spherical Trigonometry: For the Use of Colleges and Schools Isaac Todhunter Vista de fragmentos - 1949 |
Spherical Trigonometry: For the Use of Colleges and Schools Isaac Todhunter Vista de fragmentos - 1929 |
Términos y frases comunes
angle of intersection angular points approximately arcs drawn arcs which join b₁ bisecting centre CHAPTER circles touch coincide colunar triangle constant corresponding cos a cos cos TU cos² cosec cosines deduce DELAMBRE's analogies denote elements equal equation example expression fixed points formulae Geometry given greater Hence inscribed circle length less mutual power obtained octahedron opposite sides orthogonal parallelepiped perpendicular plane angles Plane Geometry plane triangle Plane Trigonometry polar triangle pole polygon preceding Article produced quadrant r₁ r₂ radii radius reciprocal regular polyhedron relation respectively result right angles right-angled triangles shew sin b sin sin c cos sin² sine small circle solid angles solution sphere spherical excess spherical tangents spherical triangle spherical triangle ABC Spherical Trigonometry substitution suppose surface