Elements of Geometry and Trigonometry: With Notes |
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Page 163
... sphere ; for the two given points and the centre of the sphere make three points , which determine the position of a plane . But if the two given points were at the extremities of a diameter , these two points and the centre would then ...
... sphere ; for the two given points and the centre of the sphere make three points , which determine the position of a plane . But if the two given points were at the extremities of a diameter , these two points and the centre would then ...
Page 164
... spherical triangle is less than the circumference of a great circle . Let ABC be any spherical tri- angle ; produce the sides AB , AC till they meet again in D ... sphere , a solid angle may be conceived as formed at O by the. 164 GEOMETRY .
... spherical triangle is less than the circumference of a great circle . Let ABC be any spherical tri- angle ; produce the sides AB , AC till they meet again in D ... sphere , a solid angle may be conceived as formed at O by the. 164 GEOMETRY .
Page 166
... sphere ; and draw the radii CA , CD , CM . Since the angles ACD , MCD are right , the line CD is perpendicular to the two straight lines CA , CM ; hence it is perpendicular to their plane ; hence the point D is the pole of the arc AM ...
... sphere ; and draw the radii CA , CD , CM . Since the angles ACD , MCD are right , the line CD is perpendicular to the two straight lines CA , CM ; hence it is perpendicular to their plane ; hence the point D is the pole of the arc AM ...
Page 167
... sphere ; hence ( Def . 4. VII . ) it is a tangent . Scholium . In the same way it may be shewn , that two spheres have but one point in common , and therefore touch each other , when the distance between their centres is equal to the ...
... sphere ; hence ( Def . 4. VII . ) it is a tangent . Scholium . In the same way it may be shewn , that two spheres have but one point in common , and therefore touch each other , when the distance between their centres is equal to the ...
Page 169
... sphere is supposed to be at O , a solid angle may be conceived as D formed at O by the three plane angles AOB , AOC ... spherical triangle DAB are respectively equal to those of the triangle CAB , namely , DAB— BAC , DBA ABC , and ADB ...
... sphere is supposed to be at O , a solid angle may be conceived as D formed at O by the three plane angles AOB , AOC ... spherical triangle DAB are respectively equal to those of the triangle CAB , namely , DAB— BAC , DBA ABC , and ADB ...
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre A. M. Legendre No preview available - 2017 |
Common terms and phrases
AC² adjacent adjacent angles altitude angle ACB angle BAC centre chord circ circle circular sector circumference circumscribed common cone consequently construction continued fraction convex surface cos² cosine cylinder demonstration determined diagonal diameter draw drawn equal angles equation equivalent faces figure formulas frustum greater homologous sides hypotenuse inclination inscribed intersection isosceles join less likewise manner measure multiplied number of sides opposite parallel parallelepipedon parallelogram perpendicular plane MN polyedron prism PROBLEM Prop PROPOSITION quadrilateral quantities radii radius ratio rectangle rectilineal triangle regular polygon right angles right-angled triangle SABC Scholium sector segment shew shewn side BC similar sin² sines solid angle sphere spherical polygon spherical triangle square straight line suppose tang tangent THEOREM third side three angles three plane angles triangle ABC triangular pyramids vertex vertices
Popular passages
Page 152 - AMB be a section, made by a plane, in the sphere, whose centre is C. From the...
Page 24 - THEOREM. In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Page 22 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 62 - Similar triangles are to each other as the squares of their homologous sides.
Page 211 - If two angles of one triangle are equal to two angles of another triangle, the third angles are equal, and the triangles are mutually equiangular.
Page 187 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Page 140 - AT into equal parts .Ax, xy, yz, &c., each less than Aa, and let k be one of those parts : through the points of division pass planes parallel to the plane of the bases : the corresponding sections formed by these planes in the two pyramids will be respectively equivalent, namely, DEF to def, GHI to ghi, &c.
Page 150 - The radius of a sphere is a straight line, drawn from the centre to any point...
Page 168 - THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle.
Page 135 - XII.) ; in like manner, the two solids AQ, AK, having the same base, AOLE, are to each other as their altitudes AD, A M.