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 38
... parallel . Let the lines KC and HD meet the line BA , making the sum of the angles BAC and ABD equal to two right angles ; then KC and HD are parallel . Through G , the middle point of AB , draw GF perpendicular to KC , and prolong it ...
... parallel . Let the lines KC and HD meet the line BA , making the sum of the angles BAC and ABD equal to two right angles ; then KC and HD are parallel . Through G , the middle point of AB , draw GF perpendicular to KC , and prolong it ...
Page 39
... parallel . 1 E Let the angle HGA be equal to GHD . Adding to both the angle HGB , we have , A- B H HGA + HGB = GHD + ... parallel . Cor . 2. If two straight lines are cut by a third , making the opposite exterior and interior angles ...
... parallel . 1 E Let the angle HGA be equal to GHD . Adding to both the angle HGB , we have , A- B H HGA + HGB = GHD + ... parallel . Cor . 2. If two straight lines are cut by a third , making the opposite exterior and interior angles ...
Page 40
... parallel straight lines , the sum of the interior angles on the same side is equal to two right angles . Let the parallels AB , CD , be cut by the secant line FE : then the sum of HGB and GHD is equal to two right angles . For , if the ...
... parallel straight lines , the sum of the interior angles on the same side is equal to two right angles . Let the parallels AB , CD , be cut by the secant line FE : then the sum of HGB and GHD is equal to two right angles . For , if the ...
Page 41
... parallel ( D. 16 ) . But , if they were parallel , the sum of the interior angles HGL , GHD , would be equal to two right angles ( P. XX . ) , which contradicts the E hypothesis : hence , IL , CD , will meet if sufficiently pro- duced ...
... parallel ( D. 16 ) . But , if they were parallel , the sum of the interior angles HGL , GHD , would be equal to two right angles ( P. XX . ) , which contradicts the E hypothesis : hence , IL , CD , will meet if sufficiently pro- duced ...
Page 42
... parallel to a third line , they are parallel to each other . Let AB and CD be respectively parallel to EF : then are they par- allel to each other . For , draw PR perpendicular to EF ; then is it perpendicular to AB , and also to CD ( P ...
... parallel to a third line , they are parallel to each other . Let AB and CD be respectively parallel to EF : then are they par- allel to each other . For , draw PR perpendicular to EF ; then is it perpendicular to AB , and also to CD ( P ...
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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