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 are also equal , and consequently , the triangle is isosceles . 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 are also equal , and consequently , the triangle is isosceles . In the ...
Page 49
... bisect each other . Let ABCD be a parallelogram , and AC , BD , its diagonals : then AE is equal to EC , and BE to ... bisect each other at right angles . EXERCISES . 1. Show that the lines which bisect ( BOOK I. 49.
... bisect each other . Let ABCD be a parallelogram , and AC , BD , its diagonals : then AE is equal to EC , and BE to ... bisect each other at right angles . EXERCISES . 1. Show that the lines which bisect ( BOOK I. 49.
Page 50
... bisect ( halve ) two verti- cal angles , form one and the same straight line . 2. Given two lines , BE and AD ; join B ... bisects the exterior vertical angle of an isos- celes triangle is parallel to the base of the triangle . ( P. XXV ...
... bisect ( halve ) two verti- cal angles , form one and the same straight line . 2. Given two lines , BE and AD ; join B ... bisects the exterior vertical angle of an isos- celes triangle is parallel to the base of the triangle . ( P. XXV ...
Page 51
... bisect the angles of any quadrilateral form , by their in- tersection , another quadrilateral , the opposite angles of which are supplements of each other . [ Twice the angle B is equal to the sum of the angles CDE and DEF . ] B BOOK II ...
... bisect the angles of any quadrilateral form , by their in- tersection , another quadrilateral , the opposite angles of which are supplements of each other . [ Twice the angle B is equal to the sum of the angles CDE and DEF . ] B BOOK II ...
Page 66
... bisects that chord , and also the arc subtended by it . Let CG be the radius which is perpendicular to the chord AB : then this radius bisects 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 this radius bisects the chord AB , and also the arc AGB . For , draw the radii CA and CB . Then , the right ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence