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 27
... remaining sides of the triangle . Let O be any point within the triangle BAC , and let the lines OB , OC , be drawn to the extremities of any side , as BC : then the sum of BO BO and OC is less than the sum of the sides BA and AC . B4 ...
... remaining sides of the triangle . Let O be any point within the triangle BAC , and let the lines OB , OC , be drawn to the extremities of any side , as BC : then the sum of BO BO and OC is less than the sum of the sides BA and AC . B4 ...
Page 51
... remaining angles are equal each to each . 16. Show that if two sides of a quadrilateral are par- allel and two opposite angles equal , the figure is a paral- lelogram . 17. Show that if the opposite angles of a quadrilateral are equal ...
... remaining angles are equal each to each . 16. Show that if two sides of a quadrilateral are par- allel and two opposite angles equal , the figure is a paral- lelogram . 17. Show that if the opposite angles of a quadrilateral are equal ...
Page 63
... remaining common ; then will they coincide ; otherwise there would be some points in either one or the other of the curves unequally distant from the centre ; which is impossible ( D. 1 ) : hence , AB divides the circle , and also its ...
... remaining common ; then will they coincide ; otherwise there would be some points in either one or the other of the curves unequally distant from the centre ; which is impossible ( D. 1 ) : hence , AB divides the circle , and also its ...
Page 131
... remaining segment of the second is to the remain- ing segment of the first . For , draw CA and BD . ODB and OAC are equal , Then the angles because each is measured by half of the arc CB ( B. III . , P. XVIII . ) . The angles OBD and ...
... remaining segment of the second is to the remain- ing segment of the first . For , draw CA and BD . ODB and OAC are equal , Then the angles because each is measured by half of the arc CB ( B. III . , P. XVIII . ) . The angles OBD and ...
Page 141
... remaining segment . 13. Two circles , whose radii are 6 feet and 10 feet , intersect , and the line joining their points of intersection is 8 feet ; find the distance between their centres . 14. Find the area of a triangle whose sides ...
... remaining segment . 13. Two circles , whose radii are 6 feet and 10 feet , intersect , and the line joining their points of intersection is 8 feet ; find the distance between their centres . 14. Find the area of a triangle whose sides ...
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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