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 37
... third straight line , they will be parallel . Let the two lines AC , BD , be perpendicular to AB : then will they be parallel . For , if they could meet in a point 0 , there would be two perpendiculars OA , OB , drawn from the same ...
... third straight line , they will be parallel . Let the two lines AC , BD , be perpendicular to AB : then will they be parallel . For , if they could meet in a point 0 , there would be two perpendiculars OA , OB , drawn from the same ...
Page 38
... third straight line , making the sum of the interior angles on the same side equal to two right angles , the two lines will be parallel . Let the lines KC and HD meet the line BA , making the sum of the angles BAC and ABD equal to two ...
... third straight line , making the sum of the interior angles on the same side equal to two right angles , the two lines will be parallel . Let the lines KC and HD meet the line BA , making the sum of the angles BAC and ABD equal to two ...
Page 39
... third straight line , making the alternate angles equal to each other , the two straight lines will be parallel . Let the angle HGA be equal E to GHD . Adding to both , the A angle HGB , we have , -B HGA + HGB = GHD + HGB . -D But the ...
... third straight line , making the alternate angles equal to each other , the two straight lines will be parallel . Let the angle HGA be equal E to GHD . Adding to both , the A angle HGB , we have , -B HGA + HGB = GHD + HGB . -D But the ...
Page 41
... third straight line , making the sum of the interior angles on the same side less than two right angles , the two lines will meet if sufficiently produced . Let the two lines CD , IL , meet the line EF , making the sum of the interior ...
... third straight line , making the sum of the interior angles on the same side less than two right angles , the two lines will meet if sufficiently produced . Let the two lines CD , IL , meet the line EF , making the sum of the interior ...
Page 42
... third line , they arc parallel to each other . Let AB and CD be respectively parallel to EF : then will they be par- allel to each other . E R F D A P B For , draw PR perpendicular to C EF ; then will it be perpendicular to AB , and ...
... third line , they arc parallel to each other . Let AB and CD be respectively parallel to EF : then will they be par- allel to each other . E R F D A P B For , draw PR perpendicular to C EF ; then will it be perpendicular to AB , and ...
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Common terms and phrases
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