Elements of Geometry and Trigonometry |
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Page 7
... SPHERICAL Spherical Trigonometry Defined , General Principles , .... TRIGONOMETRY . Formulas for Right - angled Triangles , Napier's Circular Parts , Solution of Right - angled Spherical Triangles , Quadrantal Triangles , Formulas for ...
... SPHERICAL Spherical Trigonometry Defined , General Principles , .... TRIGONOMETRY . Formulas for Right - angled Triangles , Napier's Circular Parts , Solution of Right - angled Spherical Triangles , Quadrantal Triangles , Formulas for ...
Page 235
... TRIANGLE is a spherical polygon of three sides . Spherical triangles are classified in the same manner as plane triangles . 4. A LUNE is a portion of the surface of a ... SPHERICAL PYRAMID is a portion of a sphere BOOK IX Spherical Geometry,
... TRIANGLE is a spherical polygon of three sides . Spherical triangles are classified in the same manner as plane triangles . 4. A LUNE is a portion of the surface of a ... SPHERICAL PYRAMID is a portion of a sphere BOOK IX Spherical Geometry,
Page 236
Adrien Marie Legendre. 6. A SPHERICAL PYRAMID is a portion of a sphere bounded by a spherical polygon and sectors of ... triangle is less than the sum of the other two . Let ABC be a spherical triangle situated on a sphere whose centre is ...
Adrien Marie Legendre. 6. A SPHERICAL PYRAMID is a portion of a sphere bounded by a spherical polygon and sectors of ... triangle is less than the sum of the other two . Let ABC be a spherical triangle situated on a sphere whose centre is ...
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
ABCD ACĀ² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence