An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page vii
The Method of Reciprocal Polars, and the Theory of Projections Norman Macleod Ferrers. CONTENTS . CHAPTER I. TRILINEAR CO - ORDINATES . EQUATION OF A STRAIGHT LINE . ARTS . PAGE 1 . DEFINITION of Trilinear Co - ordinates 1 2 . 3 ...
The Method of Reciprocal Polars, and the Theory of Projections Norman Macleod Ferrers. CONTENTS . CHAPTER I. TRILINEAR CO - ORDINATES . EQUATION OF A STRAIGHT LINE . ARTS . PAGE 1 . DEFINITION of Trilinear Co - ordinates 1 2 . 3 ...
Page viii
... The Bisectors of any Angle form , with the Lines containing it , an Harmonic Pencil 25 · 23 . Anharmonic Ratio of a given Pencil 26 24 . Fourth Harmonic to Three given Straight Lines 27 · 25 . Harmonic Relation of Points and Lines 29 26 ...
... The Bisectors of any Angle form , with the Lines containing it , an Harmonic Pencil 25 · 23 . Anharmonic Ratio of a given Pencil 26 24 . Fourth Harmonic to Three given Straight Lines 27 · 25 . Harmonic Relation of Points and Lines 29 26 ...
Page xi
... the other 116 Condition that two pairs of straight lines may form an har- . monic pencil ib . 118 • 119 24 , Foci of a quadrilateral 25 . 28 . 29 . 30 . The three circles described on the diagonals of a complete quadrilateral as ...
... the other 116 Condition that two pairs of straight lines may form an har- . monic pencil ib . 118 • 119 24 , Foci of a quadrilateral 25 . 28 . 29 . 30 . The three circles described on the diagonals of a complete quadrilateral as ...
Page 1
The Method of Reciprocal Polars, and the ... STRAIGHT LINE . 1. IN the system of co - ordinates ordinarily used , the position of a point in a plane is determined by means of its distances from two given straight lines ... three given straight ...
The Method of Reciprocal Polars, and the ... STRAIGHT LINE . 1. IN the system of co - ordinates ordinarily used , the position of a point in a plane is determined by means of its distances from two given straight lines ... three given straight ...
Page 7
... the area of the triangle ABC . Hence PG.AC - PH.AB , or bB = cy . This is a relation between the co - ordinates of any point on the line AD , it therefore is the equation of that line . COR . It hence may be proved that the three straight ...
... the area of the triangle ABC . Hence PG.AC - PH.AB , or bB = cy . This is a relation between the co - ordinates of any point on the line AD , it therefore is the equation of that line . COR . It hence may be proved that the three straight ...
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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