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 , called the reductio ad absurdum . It consists in assuming an hypothesis which is the contradictory of the proposition to be proved , and then continuing ...
... intersect in only one point . NOTE . The method of demonstration employed above , called the reductio ad absurdum . It consists in assuming an hypothesis which is the contradictory of the proposition to be proved , and then continuing ...
Page 26
... intersection 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 ...
... intersection 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 ...
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
... AGH are equal , because they are verti- cal angles ( P. II . ) ; and consequently , AGII and GHD are equal : hence , from Cor . 1 , AB and CD are parallel . PROPOSITION XX . THEOREM . If a straight line intersect BOOK I. 39.
... AGH are equal , because they are verti- cal angles ( P. II . ) ; and consequently , AGII and GHD are equal : hence , from Cor . 1 , AB and CD are parallel . PROPOSITION XX . THEOREM . If a straight line intersect BOOK I. 39.
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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