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 21
... intersect each other , they form four angles about the point of intersection , which have received different names , with respect to each other . 1o . ADJACENT ANGLES those which lie on the same side of one line , and on opposite sides ...
... intersect each other , they form four angles about the point of intersection , which have received different names , with respect to each other . 1o . ADJACENT ANGLES those which lie on the same side of one line , and on opposite sides ...
Page 23
... intersect in only one point . NOTE . The method of demonstration employed above , is called the reductio ad absurdum . It consists in assuming an hypothesis which is the contradictory of the proposition to be proved , and then ...
... intersect in only one point . NOTE . The method of demonstration employed above , is called the reductio ad absurdum . It consists in assuming an hypothesis which is the contradictory of the proposition to be proved , and then ...
Page 26
... intersection hence , the triangles coincide throughout , therefore equal in all their parts ( I. , D. 14 ) ; which was to be proved . 1 PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is greater than the third side ...
... intersection hence , the triangles coincide throughout , therefore equal in all their parts ( I. , D. 14 ) ; which was to be proved . 1 PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is greater than the third side ...
Page 37
... intersection have different names , with respect to each other . F 1o . INTERIOR ANGLES ON THE SAME SIDE , are those that lie on the same side of the secant and within the other two lines . Thus , BGH and GHD are interior angles on the ...
... intersection have different names , with respect to each other . F 1o . INTERIOR ANGLES ON THE SAME SIDE , are those that lie on the same side of the secant and within the other two lines . Thus , BGH and GHD are interior angles on the ...
Page 39
... Now , EGB and AGII are equal , because they are vertical ( P. II . ) ; and consequently , AGH and GHD are equal : hence , from Cor . 1 , AB and CD are parallel . PROPOSITION XX . THEOREM . La straight line intersect two BOOK I. 39.
... Now , EGB and AGII are equal , because they are vertical ( P. II . ) ; and consequently , AGH and GHD are equal : hence , from Cor . 1 , AB and CD are parallel . PROPOSITION XX . THEOREM . La straight line intersect two BOOK I. 39.
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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