Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 31
... bisects the angle at the vertex , and is perpendicular to the base . PROPOSITION XII . THEOREM . If two angles of a triangle are equal , the sides opposite to them are also equal , and consequently , the triangle is isos- celes . In the ...
... bisects the angle at the vertex , and is perpendicular to the base . PROPOSITION XII . THEOREM . If two angles of a triangle are equal , the sides opposite to them are also equal , and consequently , the triangle is isos- celes . In the ...
Page 49
... bisect each other . Let ABCD be a parallelogram , and B AC , BD , its diagonals : then will AE be equal to EC , and BE to ED . For , the triangles BEC and AED , have the angles EBC and ADE equal E ( P. XX . , C. 2 ) , the angles ECB and ...
... bisect each other . Let ABCD be a parallelogram , and B AC , BD , its diagonals : then will AE be equal to EC , and BE to ED . For , the triangles BEC and AED , have the angles EBC and ADE equal E ( P. XX . , C. 2 ) , the angles ECB and ...
Page 64
... bisects that chord , and also the arc subtended by it . Let CG be the radius which is perpendicular to the chord AB : then will this radius bisect the chord AB , and also the arc AGB . For , draw the radii CA and CB . Then , the right ...
... bisects that chord , and also the arc subtended by it . Let CG be the radius which is perpendicular to the chord AB : then will this radius bisect the chord AB , and also the arc AGB . For , draw the radii CA and CB . Then , the right ...
Page 65
... bisects the chord AB , and also the arc AGB ; which was to be proved . Cor . A straight line , perpendicular to a chord ... bisect these lines by perpendiculars DE and FG : then will these perpendiculars 单 meet in some point 0. For , if ...
... bisects the chord AB , and also the arc AGB ; which was to be proved . Cor . A straight line , perpendicular to a chord ... bisect these lines by perpendiculars DE and FG : then will these perpendiculars 单 meet in some point 0. For , if ...
Page 81
... be proved . B The angle CAE , which is the difference of DAE and DAC is measured by half the difference of the arcs DCA and DC : or by half the arc CA. 6 PRACTICAL APPLICATIONS . PROBLEM I. To bisect a given straight BOOK III . 81.
... be proved . B The angle CAE , which is the difference of DAE and DAC is measured by half the difference of the arcs DCA and DC : or by half the arc CA. 6 PRACTICAL APPLICATIONS . PROBLEM I. To bisect a given straight BOOK III . 81.
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AB² AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence