Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
From inside the book
Results 1-5 of 11
Page 236
... POLE OF A CIRCLE is a point on the surface of the sphere , equally distant from all the points of the cir cumference of the circle . 8. A DIAGONAL of a spherical polygon is an arc of a great circle joining the vertices of any two angles ...
... POLE OF A CIRCLE is a point on the surface of the sphere , equally distant from all the points of the cir cumference of the circle . 8. A DIAGONAL of a spherical polygon is an arc of a great circle joining the vertices of any two angles ...
Page 238
... poles of that circle . Let C be the centre of a sphere , FNG any circle of the sphere , and DE a diameter of the sphere perpendicular to the plane of FNG : then will the extremities D and E , be poles of the circle FNG . The diameter DE ...
... poles of that circle . Let C be the centre of a sphere , FNG any circle of the sphere , and DE a diameter of the sphere perpendicular to the plane of FNG : then will the extremities D and E , be poles of the circle FNG . The diameter DE ...
Page 239
... pole of the circle ( D. 7 ) . In like manner , it may be shown that the point E is also a pole of the circle : hence , both D , and E , are poles of the circle FNG ; which was proved . Cor . 1. Let AMB be a great circle perpendicular to ...
... pole of the circle ( D. 7 ) . In like manner , it may be shown that the point E is also a pole of the circle : hence , both D , and E , are poles of the circle FNG ; which was proved . Cor . 1. Let AMB be a great circle perpendicular to ...
Page 240
... pole of the arc AM . Scholium . The properties of these poles enable us to describe arcs of a circle on the surface of a sphere , with the same facility as on a plane surface . For , by turning the arc DF about the point D , the ...
... pole of the arc AM . Scholium . The properties of these poles enable us to describe arcs of a circle on the surface of a sphere , with the same facility as on a plane surface . For , by turning the arc DF about the point D , the ...
Page 241
... poles , and included between their sides . A spherical angle can always be constructed equal to a given spherical angle . Cor . 2. Vertical angles , such as ACO and BCN are equal ... pole of the arc EF , the distance AE 16 BOOK IX . 241.
... poles , and included between their sides . A spherical angle can always be constructed equal to a given spherical angle . Cor . 2. Vertical angles , such as ACO and BCN are equal ... pole of the arc EF , the distance AE 16 BOOK IX . 241.
Other editions - View all
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