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 , ... General Principles , ...... Formulas for Right - angled Triangles , Napier's Circular Parts , Solution of Right - angled Spherical Triangles , Quadrantal Triangles ...
... , .... SPHERICAL TRIGONOMETRY . Spherical Trigonometry Defined , ... General Principles , ...... Formulas for Right - angled Triangles , Napier's Circular Parts , Solution of Right - angled Spherical Triangles , Quadrantal Triangles ...
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 Spherica! 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 Spherica! 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 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 ...
Page 244
... spherical angles ; consequently , the angle BAD is equal to BAC , the angle ABD to ABC , and the angle ADB to ACB : hence , the parts of the triangle ABD are equal to the parts of the triangle ACB , each to each ; which was to be proved ...
... spherical angles ; consequently , the angle BAD is equal to BAC , the angle ABD to ABC , and the angle ADB to ACB : hence , the parts of the triangle ABD are equal to the parts of the triangle ACB , each to each ; which was to be proved ...
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Common terms and phrases
AB² AC² 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 straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence