Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 26
... triangles coincide throughout , and are therefore equal in all their parts ( I. , D. 14 ) ; which was to be proved . · PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is greater than the third side . Let ABC be a triangle ...
... triangles coincide throughout , and are therefore equal in all their parts ( I. , D. 14 ) ; which was to be proved . · PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is greater than the third side . Let ABC be a triangle ...
Page 28
... triangle ABC , it may be on the side BC , or it may be within the tri- angle ABC . Each case will be considered separately . 1o . When G is A D without the triangle ABC . In the triangles GIC and AIB , we have , ( P. VII . ) , B4 C E GI ...
... triangle ABC , it may be on the side BC , or it may be within the tri- angle ABC . Each case will be considered separately . 1o . When G is A D without the triangle ABC . In the triangles GIC and AIB , we have , ( P. VII . ) , B4 C E GI ...
Page 29
... triangle ABC . From 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 ...
... triangle ABC . From 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 ...
Page 30
... triangles have the three sides of the one equal to the three sides of the other , each to each , the triangles will be equal in all their parts . then will the tri- In the triangles ABC and DEF , let AB be equal to DE AC to DF , and BC ...
... triangles have the three sides of the one equal to the three sides of the other , each to each , the triangles will be equal in all their parts . then will the tri- In the triangles ABC and DEF , let AB be equal to DE AC to DF , and BC ...
Page 31
... triangle are equal , the sides opposite to them are also equal , and consequently , the triangle is isos- celes . In the triangle ABC , let the angle ABC be equal to the angle ACB : then will AC be equal to AB , and consequently , the ...
... triangle are equal , the sides opposite to them are also equal , and consequently , the triangle is isos- celes . In the triangle ABC , let the angle ABC be equal to the angle ACB : then will AC be equal to AB , and consequently , 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