Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 40
... intersect two parallel straight lines , the sum of the interior angles on the same side will be equal to two right angles . Let the parallels AB , CD , be cut by the secant line FE : then will the sum of HGB and GHD be equal to two ...
... intersect two parallel straight lines , the sum of the interior angles on the same side will be equal to two right angles . Let the parallels AB , CD , be cut by the secant line FE : then will the sum of HGB and GHD be equal to two ...
Page 41
... intersect a third 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 ...
... intersect a third 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 ...
Page 66
... intersection O , is the only point . that is equally distant from A , B , and C hence , one circumference may be made to pass through these points , and but one ; which was to be proved . Cor . Two circumferences cannot intersect in ...
... intersection O , is the only point . that is equally distant from A , B , and C hence , one circumference may be made to pass through these points , and but one ; which was to be proved . Cor . Two circumferences cannot intersect in ...
Page 70
... intersect each other , the points of in- tersection will be in a perpendicular to the line joining their centres , and at equal distances from it . Let the circumferences , whose centres are intersect at the points A and B : then will ...
... intersect each other , the points of in- tersection will be in a perpendicular to the line joining their centres , and at equal distances from it . Let the circumferences , whose centres are intersect at the points A and B : then will ...
Page 71
... intersect each other , the distance be- tween their centres will be less than the sum , and greater than the difference , of their radii . Let the circumferences , whose centres are C and D , intersect at A : then will CD be less than ...
... intersect each other , the distance be- tween their centres will be less than the sum , and greater than the difference , of their radii . Let the circumferences , whose centres are C and D , intersect at A : then will CD be less than ...
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Common terms and phrases
ABĀ² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following