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 26
... AC BC < AB ; - 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 .
... AC BC < AB ; - 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 , D H A -B M P N -E Ci 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 PHI be ...
... difference of HN and HM , D H A -B M P N -E Ci 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 PHI 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 ...
... 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 ...
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence