Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 26
... ( A. 5 ) , AC – BC < AB` ; as BC , for that is , the difference between any two sides of a triangle is Less than the third side . Scholium . In order that any three given lines may re present the sides of a triangle , the sum of 26 GEOMETRY .
... ( A. 5 ) , AC – BC < AB` ; as BC , for that is , the difference between any two sides of a triangle is Less than the third side . Scholium . In order that any three given lines may re present the sides of a triangle , the sum of 26 GEOMETRY .
Page 27
... difference of any two must be less than the third . PROPOSITION VIII . THEOREM . If from any point within a triangle two straight lines be drawn to the extremities of any side , their sum will be . less than that of the two remaining ...
... difference of any two must be less than the third . PROPOSITION VIII . THEOREM . If from any point within a triangle two straight lines be drawn to the extremities of any side , their sum will be . less than that of the two remaining ...
Page 69
... difference of HN and HM , at A -B M P D- -E N is equal to PQ , which is the difference of HQ and HP ( A. 3 ) ; which was to be proved . 2o . Let the secant AB and tangent DE , be parallel : then will the intercepted arcs MH and PH be ...
... difference of HN and HM , at A -B M P D- -E N is equal to PQ , which is the difference of HQ and HP ( A. 3 ) ; which was to be proved . 2o . Let the secant AB and tangent DE , be parallel : then will the intercepted arcs MH and PH be ...
Page 71
... difference , of their radii . Let the circumferences , whose centres are C and D , intersect at A : then will CD be less than the sum , and greater than the difference of the radii of the two circles . For , draw AC and AD , forming the ...
... difference , of their radii . Let the circumferences , whose centres are C and D , intersect at A : then will CD be less than the sum , and greater than the difference of the radii of the two circles . For , draw AC and AD , forming the ...
Page 72
... difference of their radii , one will be tangent to the other internally . Let C and D be the centres of two circles , and let the distance between these centres be equal to the difference of the radii then will the one be tangent to the ...
... difference of their radii , one will be tangent to the other internally . Let C and D be the centres of two circles , and let the distance between these centres be equal to the difference of the radii then will the one be tangent to the ...
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Common terms and phrases
AB² 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