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 11
... consequently . The symbols , 1o , 2o , etc. , mean , 1st , 2d , etc. deduced by a 5. The general truths of Geometry are course of logical reasoning , the premises being definitions and principles previously established . The course of ...
... consequently . The symbols , 1o , 2o , etc. , mean , 1st , 2d , etc. deduced by a 5. The general truths of Geometry are course of logical reasoning , the premises being definitions and principles previously established . The course of ...
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. ) ; 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. ) ; 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 without the ...
... 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 without 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