An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page viii
... touching the Three Sides of the Tri- angle of Reference 39 8 . Position of the Centre . Condition for a Parabola 40 9 . Condition of Tangency 42 10 . · Equations of the Four Circles which touch the Three Sides of the Triangle of ...
... touching the Three Sides of the Tri- angle of Reference 39 8 . Position of the Centre . Condition for a Parabola 40 9 . Condition of Tangency 42 10 . · Equations of the Four Circles which touch the Three Sides of the Triangle of ...
Page ix
... touch the Conic Condition for a Parabola 76 • 78 7 . Condition that the Conie may break up into Two Straight Lines ib . 8 . Equation of the Polar of a given Point ib . 9 . Co - ordinates of the Pole of a given Straight Line 10 ...
... touch the Conic Condition for a Parabola 76 • 78 7 . Condition that the Conie may break up into Two Straight Lines ib . 8 . Equation of the Polar of a given Point ib . 9 . Co - ordinates of the Pole of a given Straight Line 10 ...
Page xi
... touch four given straight lines have a common radical axis Polar reciprocal of a Circle with regard to any point ... touching the three sides of the triangle of reference ib . 8 . Equation of circumscribed Conic 138 · 9 . Equation of the ...
... touch four given straight lines have a common radical axis Polar reciprocal of a Circle with regard to any point ... touching the three sides of the triangle of reference ib . 8 . Equation of circumscribed Conic 138 · 9 . Equation of the ...
Page 22
... 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 of BC with B , C ,, of CA with ...
... 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 of BC with B , C ,, of CA with ...
Page 34
... = 0 and y = 0. Hence the straight line and the conic meet one another in coincident points , that is , they touch one another at the point A. Similarly , the equations of the tangents at B and 34 TRILINEAR CO - ORDINATES . ence.
... = 0 and y = 0. Hence the straight line and the conic meet one another in coincident points , that is , they touch one another at the point A. Similarly , the equations of the tangents at B and 34 TRILINEAR CO - ORDINATES . ence.
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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