An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page xiv
... points , forming a con- jugate triad PAGE 171 · 173 · 18 . 19 . Envelope of a side of an inscribed triangle whose ... point Locus of a vertex of a circumscribed triangle , whose other ver- tices move each along a fixed straight line ...
... points , forming a con- jugate triad PAGE 171 · 173 · 18 . 19 . Envelope of a side of an inscribed triangle whose ... point Locus of a vertex of a circumscribed triangle , whose other ver- tices move each along a fixed straight line ...
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 PmB - g , Pn - y - h . Also ...
... 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 PmB - g , Pn - y - h . Also ...
Page 104
... 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 109
... 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 110
... 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 ...
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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