Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 23
... until the assumed hypothesis is shown to be false . Its contradictory is thus proved to be true . This method of demonstration is often used in Geometry . PROPOSITION IV . THEOREM . If a straight line meet BOOK I. 23.
... until the assumed hypothesis is shown to be false . Its contradictory is thus proved to be true . This method of demonstration is often used in Geometry . PROPOSITION IV . THEOREM . If a straight line meet BOOK I. 23.
Page 27
... , we have , BD + DC < BA + AC . But it was shown that BO + OC is less than BD + DC ; still more , then , is BO + 00 less than BA + AC ; which was to be proved . PROPOSITION IX . THEOREM . If two triangles have two BOOK I. 27.
... , we have , BD + DC < BA + AC . But it was shown that BO + OC is less than BD + DC ; still more , then , is BO + 00 less than BA + AC ; which was to be proved . PROPOSITION IX . THEOREM . If two triangles have two BOOK I. 27.
Page 35
... shown , as in the first case , that AD is equal to DF . Then , because the point triangle ADF , the sum of the lines AD Clies within the and DF will be greater than the sum of the lines AC and CF ( P. VIII . ) : hence , AD , the half of ...
... shown , as in the first case , that AD is equal to DF . Then , because the point triangle ADF , the sum of the lines AD Clies within the and DF will be greater than the sum of the lines AC and CF ( P. VIII . ) : hence , AD , the half of ...
Page 36
... shown , DA and DB will be equal ; but IB is less than the sum of ID and DB ( P. VII . ) ; and because the sum of ID and DB is equal to the sum of ID and DA , or IA , we have IB less than IA : hence , I is unequally distant from A and B ...
... shown , DA and DB will be equal ; but IB is less than the sum of ID and DB ( P. VII . ) ; and because the sum of ID and DB is equal to the sum of ID and DA , or IA , we have IB less than IA : hence , I is unequally distant from A and B ...
Page 39
... shown , AB and CD are parallel . Cor . 2. If two lines are cut by a third , making the oppo- site exterior and interior angles equal , the two lines will be parallel . Let the angles EGB and GHD be equal : Now EGB and AGII are equal ...
... shown , AB and CD are parallel . Cor . 2. If two lines are cut by a third , making the oppo- site exterior and interior angles equal , the two lines will be parallel . Let the angles EGB and GHD be equal : Now EGB and AGII are equal ...
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Common terms and phrases
ABē 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