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 . 29 21 37 3 6. On the sides BC , CA , AB of the triangle ABC , respectively , pairs of points are taken , B , C1 ; С ̧ , A ̧ ; A ̧ , B .; such that the points ...
... point of contact of the circle touching BC externally and AB , AC produced . 29 21 37 3 6. On the sides BC , CA , AB of the triangle ABC , respectively , pairs of points are taken , B , C1 ; С ̧ , A ̧ ; A ̧ , B .; such that the points ...
Page 35
... points A , B , C of the triangle of re- ference draw the tangents EAF , FBD , DCE . Bisect Fig . 14 . + ... contact passes also through the centre , O will be the centre of the conic . Now , at the point E , we have and 3-2 CENTRE OF THE ...
... points A , B , C of the triangle of re- ference draw the tangents EAF , FBD , DCE . Bisect Fig . 14 . + ... contact passes also through the centre , O will be the centre of the conic . Now , at the point E , we have and 3-2 CENTRE OF THE ...
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 ...
... 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 ...
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 MODERN GEOMETRY . 20 Equation ...
... 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 MODERN GEOMETRY . 20 Equation ...
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Common terms and phrases
a₁ aa+bB+cy Algebra angular points anharmonic ratio Arithmetic asymptotes auxiliary conic b₁ c₁ CAMBRIDGE CLASS BOOKS centre Chap chord cloth co-ordinates coefficients College common tangents condition conic passing conic section conics intersect Crown 8vo curve determine directrix ellipse find the equation fixed point focus four points given conic given point given straight line Hence hyperbola imaginary investigated line at infinity line joining locus meets the conic obtain pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact PQRS projection prove reciprocal polars represented respect right angles second degree Second Edition Similarly sin POS system of conics tangents tangents drawn theorem three points three straight lines touches the line Treatise triangle of reference U'bc ua² V'ca Vb² vß² W'ab wy² λα