Elements of Geometry and Trigonometry |
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Page 26
... ) , ACBC 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 .
... ) , ACBC 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 -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 , D- H A B M P -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
ABCD ACĀ² 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 line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence