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 . 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 , For , if not , suppose CE to be the prolongation of AU , then will the sum of the angles equal to two right angles ( P. I. ) : have ( A. 1 ) , DCADCB = DCA + DCE ; Taking from both the common angle DCA , there re- mains ...
... consequently , For , if not , suppose CE to be the prolongation of AU , then will the sum of the angles equal to two right angles ( P. I. ) : have ( A. 1 ) , DCADCB = DCA + DCE ; Taking from both the common angle DCA , there re- mains ...
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 ...
... 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 ...
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 altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence