Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 11
... consequently . 5. The general truths of Geometry are deduced by a course of logical reasoning , the premises being definitions and principles previously established . The course of reasoning employed in establishing any truth or ...
... consequently . 5. The general truths of Geometry are deduced by a course of logical reasoning , the premises being definitions and principles previously established . The course of reasoning employed in establishing any truth or ...
Page 20
... consequently , its equal , that is , the sum of the angles DCA and DCB , must also be equal to two right angles ; which was to be proved . Cor . 1. If one of the angles DCA , DCB , is a right angle , the other must also be a right angle ...
... consequently , its equal , that is , the sum of the angles DCA and DCB , must also be equal to two right angles ; which was to be proved . Cor . 1. If one of the angles DCA , DCB , is a right angle , the other must also be a right angle ...
Page 24
... consequently , DCA + DCB = DCA + DCE ; Taking from both the common angle DCA , there re- mains , DCB = DCE , which is impossible , since a part cannot be equal to the whole ( A. 8 ) . Hence , CB must be the prolongation of AC ; which ...
... consequently , DCA + DCB = DCA + DCE ; Taking from both the common angle DCA , there re- mains , DCB = DCE , which is impossible , since a part cannot be equal to the whole ( A. 8 ) . Hence , CB must be the prolongation of AC ; which ...
Page 25
... consequently , the side BC will coincide with the side EF ( A. 11 ) . The two triangles , therefore , coincide throughout , and are consequently equal in all their parts ( I. , D. 14 ) ; which was to be proved . PROPOSITION VI . THEOREM ...
... consequently , the side BC will coincide with the side EF ( A. 11 ) . The two triangles , therefore , coincide throughout , and are consequently equal in all their parts ( I. , D. 14 ) ; which was to be proved . PROPOSITION VI . THEOREM ...
Page 28
... consequently , GC is equal to EF ( P. V. ) . Now , the point G may be without the 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 ...
... consequently , GC is equal to EF ( P. V. ) . Now , the point G may be without the 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 ...
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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