An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 22
... point of contact of the circle touching BC externally and AB , AC produced . On the sides BC , CA , AB of the triangle ABC , respectively , pairs of points are taken , B , C1 ; С2 , A ̧ ; A ̧ , B .; such that the points of intersection ...
... point of contact of the circle touching BC externally and AB , AC produced . On the sides BC , CA , AB of the triangle ABC , respectively , pairs of points are taken , B , C1 ; С2 , A ̧ ; A ̧ , B .; such that the points of intersection ...
Page 35
... points A , B , C of the triangle of reference draw the tangents EAF , FBD , DCE . Bisect Fig . 14 . I H B a AC , AB ... contact passes also through the centre , O will be the centre of the conic . Now , at the point E , we have α 3-2 ...
... points A , B , C of the triangle of reference draw the tangents EAF , FBD , DCE . Bisect Fig . 14 . I H B a AC , AB ... contact passes also through the centre , O will be the centre of the conic . Now , at the point E , we have α 3-2 ...
Page 40
... points of contact of the sides BC , CA , AB respectively . Join EF , FD , DE , bisect FD , DE in H , I , join BH , CI , and produce them to meet in O. Then O will be the centre of the conic ( see p . 32 ) . We have then to find the ...
... points of contact of the sides BC , CA , AB respectively . Join EF , FD , DE , bisect FD , DE in H , I , join BH , CI , and produce them to meet in O. Then O will be the centre of the conic ( see p . 32 ) . We have then to find the ...
Page 46
... points . The analytical condition of harmonic section is , however , satisfied here also . 13. We may next investigate the equations of the tan- gents drawn through the points A , B , C. If in the equation of the conic we put La Ny , we ...
... points . The analytical condition of harmonic section is , however , satisfied here also . 13. We may next investigate the equations of the tan- gents drawn through the points A , B , C. If in the equation of the conic we put La Ny , we ...
Page 52
... points to the opposite sides . This is otherwise evident from geometri- cal considerations . 20. To find the ... contact are given , the conic is thus subjected to two conditions , and , therefore , when two 52 TRILINEAR CO - ORDINATES .
... points to the opposite sides . This is otherwise evident from geometri- cal considerations . 20. To find the ... contact are given , the conic is thus subjected to two conditions , and , therefore , when two 52 TRILINEAR CO - ORDINATES .
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Common terms and phrases
angular points asymptotes ax+bB+cy b₁ b₂ C₁ Cambridge centre Chap co-ordinates coefficients College common tangents conic section Crown 8vo determinant directrix Edition equation Fcap find the equation fixed point follows four points given conic given point given straight line Hence imaginary investigated Let the equation line at infinity line joining locus meets the conic nine-point circle numerous Illustrations obtain opposite sides Owens College pair parabola Pascal's Theorem perpendicular point f points of intersection pole Professor prove radical axis ratios rectangular hyperbola represented respect right angles second degree shewn similar and similarly sin POS tangents tangents drawn term a,b,c theorem three straight lines tion touches the line triangle of reference Ua² ux² V'ca v'f+u'g+wh va² values Vb² vß² W. K. CLIFFORD W'ab whence wy² λα