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 20
... hence , But , of the angles DCA + DCB = ECA + ECD + DCB ; ECD + DCB is equal to ECB ( A. 9 ) ; hence , DCA + DCB = ECA + ECB . The sum of the angles ECA and ECB , is equal to two right angles ; consequently , its equal , that is , the ...
... hence , But , of the angles DCA + DCB = ECA + ECD + DCB ; ECD + DCB is equal to ECB ( A. 9 ) ; hence , DCA + DCB = ECA + ECB . The sum of the angles ECA and ECB , is equal to two right angles ; consequently , its equal , that is , the ...
Page 22
... Hence , the proposition is proved . Cor . 1. If one of the angles about C all of the others will be right angles also . each of its adjacent angles will be a right angle ; and from the proposition just demonstrated , its opposite angle ...
... Hence , the proposition is proved . Cor . 1. If one of the angles about C all of the others will be right angles also . each of its adjacent angles will be a right angle ; and from the proposition just demonstrated , its opposite angle ...
Page 23
... Hence , the sum of the given angles is equal to four right angles . PROPOSITION III . THEOREM . If two straight lines have twc points in common , they will coincide throughout their whole extent , and form one and the same line . " Let ...
... Hence , the sum of the given angles is equal to four right angles . PROPOSITION III . THEOREM . If two straight lines have twc points in common , they will coincide throughout their whole extent , and form one and the same line . " Let ...
Page 26
... hence , the triangles coincide throughout ,, therefore equal in all their parts ( I. , D. ) ; which was to be proved . and are PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is greater than the third side . Let ABC ...
... hence , the triangles coincide throughout ,, therefore equal in all their parts ( I. , D. ) ; which was to be proved . and are PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is greater than the third side . Let ABC ...
Page 29
... Hence , in each case , BC is greater than EF ; which was to be proved . Conversely : If in two triangles ABC and DEF , the side AB is equal to the side DE , the side AC to DF , and BC greater than EF , then will the angle BAC be greater ...
... Hence , in each case , BC is greater than EF ; which was to be proved . Conversely : If in two triangles ABC and DEF , the side AB is equal to the side DE , the side AC to DF , and BC greater than EF , then will the angle BAC be greater ...
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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