An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page viii
... respect to which the Triangle of Reference is self - conjugate • · Equation of the Conic which touches two sides of the Triangle of Reference in the points where they meet the third Any Chord of a Conic is divided harmonically by the ...
... respect to which the Triangle of Reference is self - conjugate • · Equation of the Conic which touches two sides of the Triangle of Reference in the points where they meet the third Any Chord of a Conic is divided harmonically by the ...
Page x
... that of the range formed by their poles • · 113 15 . Any straight line drawn through a given point A is divided harmonically by any Conic Section and the polar of A with respect to it 115 ARTS . 17 . 18 . 20 . 23 . CONTENTS .
... that of the range formed by their poles • · 113 15 . Any straight line drawn through a given point A is divided harmonically by any Conic Section and the polar of A with respect to it 115 ARTS . 17 . 18 . 20 . 23 . CONTENTS .
Page xi
... respect to a Circle Reciprocation with respect to a Point • PAGE If four straight lines form an harmonic pencil , either pair will be its own polar reciprocal with respect to the other 116 Condition that two pairs of straight lines may ...
... respect to a Circle Reciprocation with respect to a Point • PAGE If four straight lines form an harmonic pencil , either pair will be its own polar reciprocal with respect to the other 116 Condition that two pairs of straight lines may ...
Page 3
... respect to the trilinear co - ordinates of any point to which it relates . Any locus may be represented , as in the ordinary system , by means of a relation between two co- ordinates , B and y for example , and this may be made homo- az ...
... respect to the trilinear co - ordinates of any point to which it relates . Any locus may be represented , as in the ordinary system , by means of a relation between two co- ordinates , B and y for example , and this may be made homo- az ...
Page 30
... respect to the triangle ABC . By combining the proposition last proved with that proved in Art . ( 22 ) , we shall obtain a demonstration of the statements made in Art . 6 ; that the points in which the external bisectors of each angle ...
... respect to the triangle ABC . By combining the proposition last proved with that proved in Art . ( 22 ) , we shall obtain a demonstration of the statements made in Art . 6 ; that the points in which the external bisectors of each angle ...
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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