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 , .. 76 General Principles , 76 ....... Formulas for Right - angled Triangles , .... 77-80 Napier's Circular Parts , ....... 80 Solution of Right - angled Spherical Triangles , 84 ...
... SPHERICAL TRIGONOMETRY . Spherical Trigonometry Defined , .. 76 General Principles , 76 ....... Formulas for Right - angled Triangles , .... 77-80 Napier's Circular Parts , ....... 80 Solution of Right - angled Spherical Triangles , 84 ...
Page 249
... sphere is 5 feet ; find the area of the zone and the volume of the corresponding spherical sector . 13. Find the surface and the volume of a sphere whose radius is 4 feet . 14. The radius of a sphere is 5 feet ; how many cubic feet in a ...
... sphere is 5 feet ; find the area of the zone and the volume of the corresponding spherical sector . 13. Find the surface and the volume of a sphere whose radius is 4 feet . 14. The radius of a sphere is 5 feet ; how many cubic feet in a ...
Page 250
... two great circles . 5. A SPHERICAL WEDGE is a portion of a sphere bound- ed by a lune and two semicircles which intersect in a diameter of the sphere . 6. A SPHERICAL PYRAMID is a portion of a sphere BOOK IX Spherical Geometry,
... two great circles . 5. A SPHERICAL WEDGE is a portion of a sphere bound- ed by a lune and two semicircles which intersect in a diameter of the sphere . 6. A SPHERICAL PYRAMID is a portion of a sphere BOOK IX Spherical Geometry,
Page 251
... 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 the two others . Let ABC be a spherical triangle situated on a sphere whose centre ...
... 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 the two others . Let ABC be a spherical triangle situated on a sphere whose centre ...
Page 256
... spherical triangle , as poles , arcs be described forming a second spherical triangle , the vertices of the angles of this second triangle are respectively poles of the sides of the first . From the vertices A , B , C , as poles , let ...
... spherical triangle , as poles , arcs be described forming a second spherical triangle , the vertices of the angles of this second triangle are respectively poles of the sides of the first . From the vertices A , B , C , as poles , let ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence