Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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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 . are 1o . ADJACENT ANGLES those which lie . on the same side of one line , and ' on ...
... intersect each other , they form four angles about the point of intersection , which have received different names , with respect to each other . are 1o . ADJACENT ANGLES those which lie . on the same side of one line , and ' on ...
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 , and are therefore equal in all their parts ( I. , D. 14 ) ; which was to be proved . · PROPOSITION VII . THEOREM . The sum of any two sides of a triangle is greater than the third ...
... intersection hence , the triangles coincide throughout , and are therefore equal in all their parts ( I. , D. 14 ) ; which was to be proved . · 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
... Now EGB and AGII are equal , because they are vertical ( P. II . ) ; and consequently , AGI and GIID are equal : hence , from Cor . 1 , AB and CD are parallel . PROPOSITION XX . THEOREM . If a straight line intersect BOOK I. 39.
... Now EGB and AGII are equal , because they are vertical ( P. II . ) ; and consequently , AGI and GIID 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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AB² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following