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
... ; - 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 .
... ; - 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 b drawn to the extremities of any side , their sum will be less than that of the two remaining sides ...
... difference of any two must be less than the third . PROPOSITION VIII . THEOREM . If from any point within a triangle two straight lines b drawn to the extremities of any side , their sum will be less than that of the two remaining sides ...
Page 69
... difference of HN and HM , D- A B M N E is equal to PQ , which is the difference of HQ and HP ( A. 3 ) ; which was to be proved . 2 ° . Let the secant AB and tangent DE , be parallel . then will the intercepted arcs MH and PH be equal ...
... difference of HN and HM , D- A B M N E is equal to PQ , which is the difference of HQ and HP ( A. 3 ) ; which was to be proved . 2 ° . Let the secant AB and tangent DE , be parallel . then will the intercepted arcs MH and PH be equal ...
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 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