Elements of Geometry and Trigonometry |
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Page 11
... consequently . The symbols , 1o , 2o , etc. , mean , 1st , 2d , etc. 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 ...
... consequently . The symbols , 1o , 2o , etc. , mean , 1st , 2d , etc. 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 ...
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 , have ( A. 1 ) , 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 ...
... consequently , have ( A. 1 ) , 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 ...
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
ABCD ACĀ² 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 line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence