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 ... Angle ,. Area of a Trapezoid , Area of a Quadrilateral , Area of a Polygon , 105 106 106 108 112 112 113 114 . Area of a ...
... SPHERICAL TRIGONOMETRY . PAGE . 55 57-59 60-62 63 64-66 67 68-70 71 Spherical Trigonometry Defined , 73 General ... Angle ,. Area of a Trapezoid , Area of a Quadrilateral , Area of a Polygon , 105 106 106 108 112 112 113 114 . Area of a ...
Page 235
... SPHERICAL ANGLE is an angle included between the arcs of two great circles of a sphere meeting at a point . The arcs are called sides of the angle , and the point at which they meet is called the vertex of the angle . The measure of a ...
... SPHERICAL ANGLE is an angle included between the arcs of two great circles of a sphere meeting at a point . The arcs are called sides of the angle , and the point at which they meet is called the vertex of the angle . The measure of a ...
Page 236
... spherical polygon and sectors of circles whose common centre is the centre of the sphere . The spherical polygon is ... angle whose vertex is 0 , and the plane angles included between them are measured by the arcs AB , AC , and BC ( B. III .
... spherical polygon and sectors of circles whose common centre is the centre of the sphere . The spherical polygon is ... angle whose vertex is 0 , and the plane angles included between them are measured by the arcs AB , AC , and BC ( B. III .
Page 239
... spherical angle DMA , is a right - angle ; that is , if any point , in the circumference of a great circle , be joined with either pole by the arc of a great circle , such arc will be perpendicular to the circumference of the given ...
... spherical angle DMA , is a right - angle ; that is , if any point , in the circumference of a great circle , be joined with either pole by the arc of a great circle , such arc will be perpendicular to the circumference of the given ...
Page 241
... angles of spherical triangles may be com- pared by means of the arcs of great circles described from their vertices as poles , and included between their sides . A spherical angle can always be constructed equal to a given spherical angle ...
... angles of spherical triangles may be com- pared by means of the arcs of great circles described from their vertices as poles , and included between their sides . A spherical angle can always be constructed equal to a given spherical angle ...
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Common terms and phrases
ABĀ² 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