Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page vii
... SPHERICAL TRIGONOMETRY . Spherical Trigonometry Defined , 73 ... General Principles , ..... 73 Formulas for Right - angled Triangles , 74-76 Napier's Circular Parts , 77 Solution of Right - angled Spherical Triangles , 80-83 Quadrantal ...
... SPHERICAL TRIGONOMETRY . Spherical Trigonometry Defined , 73 ... General Principles , ..... 73 Formulas for Right - angled Triangles , 74-76 Napier's Circular Parts , 77 Solution of Right - angled Spherical Triangles , 80-83 Quadrantal ...
Page 235
... - circumferences of two great circles . 5. A SPHERICAL WEDGE is a portion of a sphere bounded by a lune and two semicircles meeting in a diameter of the sphere . 6. A SPHERICAL PYRAMID is a portion of a sphere BOOK IX Spherical Geometry,
... - circumferences of two great circles . 5. A SPHERICAL WEDGE is a portion of a sphere bounded by a lune and two semicircles meeting in a diameter of the sphere . 6. A SPHERICAL PYRAMID is a portion of a sphere BOOK IX Spherical Geometry,
Page 236
... SPHERICAL PYRAMID is a portion of a sphere bounded by a spherical polygon and sectors of circles whose common centre ... triangle is less than the sum of Let ABC be a whose centre is 0 than the sum of the the other two . spherical triangle ...
... SPHERICAL PYRAMID is a portion of a sphere bounded by a spherical polygon and sectors of circles whose common centre ... triangle is less than the sum of Let ABC be a whose centre is 0 than the sum of the the other two . spherical triangle ...
Page 241
... spherical triangk , as poles , arcs be described forming a spherical triangle , the vertices of the angles of this second triangle will be respectively poles of the sides of the first . From the vertices A , B , C , as poles , let the ...
... spherical triangk , as poles , arcs be described forming a spherical triangle , the vertices of the angles of this second triangle will be respectively poles of the sides of the first . From the vertices A , B , C , as poles , let the ...
Page 243
... triangle thus formed will be equal to those of the given triangle , each to each . Let ABC be a spherical triangle situated on a sphere whose centre is 0 , CED and CFD arcs of circles described about B and A as poles , and let and let ...
... triangle thus formed will be equal to those of the given triangle , each to each . Let ABC be a spherical triangle situated on a sphere whose centre is 0 , CED and CFD arcs of circles described about B and A as poles , and let and let ...
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence