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 ... Polygon , 113 Area of a Regular Polygon , 114 ..... To find the Circumference of a Circle , 116 To find the Diameter of a ...
... SPHERICAL TRIGONOMETRY . Spherical Trigonometry Defined , ... General Principles , ...... Formulas for Right ... Polygon , 113 Area of a Regular Polygon , 114 ..... To find the Circumference of a Circle , 116 To find the Diameter of a ...
Page viii
... Sphere , 122 Area of a Zone , 122 Area of a Spherical Polygon , 123 Volume of a Prism , 124 Volume of a Pyramid , 124 Volume of the Frustum of a Pyramid , 125 Volume of a Sphere , 126 Volume of a Wedge , Volume of a Prismoid , ..... 127 ...
... Sphere , 122 Area of a Zone , 122 Area of a Spherical Polygon , 123 Volume of a Prism , 124 Volume of a Pyramid , 124 Volume of the Frustum of a Pyramid , 125 Volume of a Sphere , 126 Volume of a Wedge , Volume of a Prismoid , ..... 127 ...
Page 215
... sphere , the zone has but one base . 17. A SPHERICAL SEGMENT is a portion of a sphere in cluded between two parallel ... polygon . The convex surface of this prism will be equal to the perimeter of its base multiplied by its altitude ( B ...
... sphere , the zone has but one base . 17. A SPHERICAL SEGMENT is a portion of a sphere in cluded between two parallel ... polygon . The convex surface of this prism will be equal to the perimeter of its base multiplied by its altitude ( B ...
Page 235
... POLYGON is a portion of the surface of a sphere bounded by three or more arcs of great circles . The bounding arcs are called sides of the polygon ... SPHERICAL PYRAMID is a portion of a sphere BOOK IX Spherica! Geometry,
... POLYGON is a portion of the surface of a sphere bounded by three or more arcs of great circles . The bounding arcs are called sides of the polygon ... 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 is the centre of the sphere . The spherical polygon is called the base of the pyramid , and the centre of the sphere is ...
... SPHERICAL PYRAMID is a portion of a sphere bounded by a spherical polygon and sectors of circles whose common centre is the centre of the sphere . The spherical polygon is called the base of the pyramid , and the centre of the sphere is ...
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Common terms and phrases
ABē ACē 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