Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 23
... PROPOSITION III . THEOREM . If two straight lines have two points in common , they will coincide throughout their whole extent , and form one and the same line . Let A and B be two points common to two lines : then will the lines ...
... PROPOSITION III . THEOREM . If two straight lines have two points in common , they will coincide throughout their whole extent , and form one and the same line . Let A and B be two points common to two lines : then will the lines ...
Page 24
... PROPOSITION V. THEOREM . If two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other , each to each , the triangles will be equal in all their parts . In the triangles ABC and ...
... PROPOSITION V. THEOREM . If two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other , each to each , the triangles will be equal in all their parts . In the triangles ABC and ...
Page 26
... PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is greater than the third side . Let ABC be a triangle : then will the sum of any two sides , as AB , BC , be greater than the third side For , the distance from A AC ...
... PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is greater than the third side . Let ABC be a triangle : then will the sum of any two sides , as AB , BC , be greater than the third side For , the distance from A AC ...
Page 27
... 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 sides of the triangle . A Let be any point within the ...
... 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 sides of the triangle . A Let be any point within the ...
Page 29
... Proposition VIII . , we have , BA + BC > GA + GC ; or , since GA = BA , and GC = EF , BA + BC > BA + EF . BC > we have , Taking away the common part AB , there remains , BC > EF A D B E F Hence , in each case , BC is greater than EF ...
... Proposition VIII . , we have , BA + BC > GA + GC ; or , since GA = BA , and GC = EF , BA + BC > BA + EF . BC > we have , Taking away the common part AB , there remains , BC > EF A D B E F Hence , in each case , BC is greater than EF ...
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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