An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 11
... fixed point D on the locus of the equation , a , ß , y those of any point P. Draw DE , PM perpendicular to AC , DF , PN perpendi- cular to AB . Also draw Dm , Dn , perpendicular respectively to PM , PN . Then Pm - B - g , Pn - y - h ...
... fixed point D on the locus of the equation , a , ß , y those of any point P. Draw DE , PM perpendicular to AC , DF , PN perpendi- cular to AB . Also draw Dm , Dn , perpendicular respectively to PM , PN . Then Pm - B - g , Pn - y - h ...
Page 98
... point , may be deduced those of another curve which is always touched by the polar of this moving point with regard to a fixed conic . The theory is especially valuable when the conic , with respect to which the poles and polars are ...
... point , may be deduced those of another curve which is always touched by the polar of this moving point with regard to a fixed conic . The theory is especially valuable when the conic , with respect to which the poles and polars are ...
Page 103
... fixed point , the three points lying in the same straight line , the third angular point will move along a straight line , passing through the intersection of the straight lines along which the other angu- lar points move . " The ...
... fixed point , the three points lying in the same straight line , the third angular point will move along a straight line , passing through the intersection of the straight lines along which the other angu- lar points move . " The ...
Page 104
... fixed straight lines , along which two of the angular points of the first triangle move , will be fixed points ... point , along which the angular points of the reciprocal triangle always move . Hence the data of the reciprocal proposition ...
... fixed straight lines , along which two of the angular points of the first triangle move , will be fixed points ... point , along which the angular points of the reciprocal triangle always move . Hence the data of the reciprocal proposition ...
Page 105
... point , " that is , the sides of the triangle themselves . This condition , therefore , reciprocates into itself ... fixed straight line Gʻ , the point P'Q ' along a fixed straight line H ' , the three straight lines F " , Gʻ , H ...
... point , " that is , the sides of the triangle themselves . This condition , therefore , reciprocates into itself ... fixed straight line Gʻ , the point P'Q ' along a fixed straight line H ' , the three straight lines F " , Gʻ , H ...
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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