Elements of Geometry and Trigonometry: With Notes |
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Page 167
... spherical triangles may be compared to- gether , by means of the arcs of great circles described from their vertices as poles and included between their sides : hence it is easy to make an angle of this kind equal to a given angle ...
... spherical triangles may be compared to- gether , by means of the arcs of great circles described from their vertices as poles and included between their sides : hence it is easy to make an angle of this kind equal to a given angle ...
Page 169
... triangle , which is distinguished from the other three by the circumstance ... triangle ABC being given , if from the pole A , with a distance AC , the arc DEC ... spherical triangle DAB are respectively equal to those of the triangle CAB ...
... triangle , which is distinguished from the other three by the circumstance ... triangle ABC being given , if from the pole A , with a distance AC , the arc DEC ... spherical triangle DAB are respectively equal to those of the triangle CAB ...
Page 171
... spherical triangle , the angles opposite the equal sides are equal ; and conversely , if two angles of a spherical triangle are equal , the triangle will be isosceles . First . Suppose the side AB - AC ; we shall have the angle C = B ...
... spherical triangle , the angles opposite the equal sides are equal ; and conversely , if two angles of a spherical triangle are equal , the triangle will be isosceles . First . Suppose the side AB - AC ; we shall have the angle C = B ...
Page 172
... spherical triangle to the middle of the base , is at right angles to that base , and bisects the opposite angle . PROPOSITION XVI . THEOREM . In a spherical triangle ABC , if the angle A is greater than the angle B , the side BC ...
... spherical triangle to the middle of the base , is at right angles to that base , and bisects the opposite angle . PROPOSITION XVI . THEOREM . In a spherical triangle ABC , if the angle A is greater than the angle B , the side BC ...
Page 174
With Notes Adrien Marie Legendre. triangle DEF is equal in all its parts to AHG ; hence it is also equal to the triangle ABC , and we have AB - DE , AC = DF , BC - EF ; hence if two spherical triangles are mutually equi- angular , the ...
With Notes Adrien Marie Legendre. triangle DEF is equal in all its parts to AHG ; hence it is also equal to the triangle ABC , and we have AB - DE , AC = DF , BC - EF ; hence if two spherical triangles are mutually equi- angular , the ...
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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.