Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 47
... ABCD be a parallelogram : then will AB be equal to DC , and AD to BC . D C For , draw the diagonal BD . Then , because AB and DC are parallel , the A angle DBA is equal to its alternate angle BDC ( P. XX . , C. 2 ) and , because AD and ...
... ABCD be a parallelogram : then will AB be equal to DC , and AD to BC . D C For , draw the diagonal BD . Then , because AB and DC are parallel , the A angle DBA is equal to its alternate angle BDC ( P. XX . , C. 2 ) and , because AD and ...
Page 48
... ABCD , let AB be equal to DC , and AD to BC : then will it be a parallelogram . Draw the diagonal DB . Then , the triangles ADB and CBD , will have A D the sides of the one equal to the sides of the other , each to each ; and therefore ...
... ABCD , let AB be equal to DC , and AD to BC : then will it be a parallelogram . Draw the diagonal DB . Then , the triangles ADB and CBD , will have A D the sides of the one equal to the sides of the other , each to each ; and therefore ...
Page 49
... ABCD be a parallelogram , and AC , BD , its diagonals : then will AE be equal to EC , and BE BE to ED . For , the triangles BEC and AED , have the angles EBC and ADE equal B E X A ( P. XX . , C. 2 ) , the angles ECB and DAE equal , and ...
... ABCD be a parallelogram , and AC , BD , its diagonals : then will AE be equal to EC , and BE BE to ED . For , the triangles BEC and AED , have the angles EBC and ADE equal B E X A ( P. XX . , C. 2 ) , the angles ECB and DAE equal , and ...
Page 52
... A B C D ; whence , :: clearing of fractions , we have , BC AD ; B D = A C ; which was to be proved . Cor . If B is equal to C , there will be but three pro- case , the square of the mean is portional quantities ; in this equal to the ...
... A B C D ; whence , :: clearing of fractions , we have , BC AD ; B D = A C ; which was to be proved . Cor . If B is equal to C , there will be but three pro- case , the square of the mean is portional quantities ; in this equal to the ...
Page 79
... ABCD , are together equal to two right angles ; for the angle DAB is measured by half the arc DCB , the angle DCB by half the arc : D B DAB hence , the two angles , taken together , are mea- sured by half the circumference : hence ...
... ABCD , are together equal to two right angles ; for the angle DAB is measured by half the arc DCB , the angle DCB by half the arc : D B DAB hence , the two angles , taken together , are mea- sured by half the circumference : hence ...
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Common terms and phrases
ABĀ² 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