Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 7
... SPHERICAL TRIGONOMETRY . PAGE . 55 57-59 60-62 63 64-66 67 68-70 71 Spherical Trigonometry Defined , 73 General Principles , 73 Formulas for Right - angled Triangles , 74-76 .... Napier's Circular Parts , 77 Solution of Right - angled ...
... SPHERICAL TRIGONOMETRY . PAGE . 55 57-59 60-62 63 64-66 67 68-70 71 Spherical Trigonometry Defined , 73 General Principles , 73 Formulas for Right - angled Triangles , 74-76 .... Napier's Circular Parts , 77 Solution of Right - angled ...
Page 235
... spherical angle is the same as that of the diedral angle included between the planes of its sides . Spherical angles may be acute , right , or obtuse . 2. A SPHERICAL POLYGON is a portion of the surface of a sphere bounded by arcs of ...
... spherical angle is the same as that of the diedral angle included between the planes of its sides . Spherical angles may be acute , right , or obtuse . 2. A SPHERICAL POLYGON is a portion of the surface of a sphere bounded by arcs of ...
Page 236
... spherical polygon and sectors of circles whose common centre is the centre of the sphere . The spherical polygon is ... triangle is less than the sum of Let ABC be a whose centre is 0 the other two . spherical triangle situated on a ...
... spherical polygon and sectors of circles whose common centre is the centre of the sphere . The spherical polygon is ... triangle is less than the sum of Let ABC be a whose centre is 0 the other two . spherical triangle situated on a ...
Page 241
... spherical triangle 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 triangle 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 DA and DB ...
... 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 DA and DB ...
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Common terms and phrases
ABē ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following