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 are those which lie on the same side of one line , and on opposite ...
... 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 are those which lie on the same side of one line , and on opposite ...
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 D ( P. III . , C. ) : hence , the triangles coincide throughout , and are therefore equal in all respects ( I. , D. 15 ) ; which was to be proved . PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is ...
... intersection D ( P. III . , C. ) : hence , the triangles coincide throughout , and are therefore equal in all respects ( I. , D. 15 ) ; which was to be proved . PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is ...
Page 37
... intersect two other straight lines AB and CD , it is called a secant , with respect to them . The eight angles formed about the points of intersection have different names , with respect to each other . 1o . INTERIOR ANGLES ON THE SAME ...
... intersect two other straight lines AB and CD , it is called a secant , with respect to them . The eight angles formed about the points of intersection have different names , with respect to each other . 1o . INTERIOR ANGLES ON THE SAME ...
Page 41
... intersect a third straight line , making the sum of the interior angles on the same side less than two right angles , the two lines will meet if suffi- ciently produced . Let the two lines CD , IL , meet the line EF , making the sum of ...
... intersect a third straight line , making the sum of the interior angles on the same side less than two right angles , the two lines will meet if suffi- ciently produced . Let the two lines CD , IL , meet the line EF , making the sum of ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence