Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 235
... LUNE is a portion of the surface of a sphere bounded by semi - circumferences of two great circles . 5. A SPHERICAL WEDGE is a portion of a sphere bounded by a lune and two semicircles meeting in a diameter of the sphere . 6. A ...
... LUNE is a portion of the surface of a sphere bounded by semi - circumferences of two great circles . 5. A SPHERICAL WEDGE is a portion of a sphere bounded by a lune and two semicircles meeting in a diameter of the sphere . 6. A ...
Page 251
... two . denote the spherical excess by E , the sum of the If we angles by S , and the number of sides by n , we shall have , - E = S 2 ( n − 2 ) = S - 2n + 4 . PROPOSITION XV . THEOREM . Any lune , is to BOOK IX . 251.
... two . denote the spherical excess by E , the sum of the If we angles by S , and the number of sides by n , we shall have , - E = S 2 ( n − 2 ) = S - 2n + 4 . PROPOSITION XV . THEOREM . Any lune , is to BOOK IX . 251.
Page 252
... lune , is to the surface of the sphere , as the angle of the lune is to four right angles , or as the arc which measures that angle is to the circumference of a great circle . Let AMBN be a lune , and MCN the angle of the lune then will ...
... lune , is to the surface of the sphere , as the angle of the lune is to four right angles , or as the arc which measures that angle is to the circumference of a great circle . Let AMBN be a lune , and MCN the angle of the lune then will ...
Page 253
... lune is to four right angles , or as the arc which measures that angle is to the circumference of a great circle ... lune by L , and the angle of the lune by A , the right angle being denoted by 1 , we shall have , whence , L : 8T :: A ...
... lune is to four right angles , or as the arc which measures that angle is to the circumference of a great circle ... lune by L , and the angle of the lune by A , the right angle being denoted by 1 , we shall have , whence , L : 8T :: A ...
Page 255
... lune whose angle is equal to that formed by the circles . Let the circumferences AOB , COD , intersect on the surface of a hemis- phere : then will the sum of the oppo- site triangles AOC , BOD , be equal to the lune whose angle is BOD ...
... lune whose angle is equal to that formed by the circles . Let the circumferences AOB , COD , intersect on the surface of a hemis- phere : then will the sum of the oppo- site triangles AOC , BOD , be equal to the lune whose angle is BOD ...
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Common terms and phrases
AB² 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