## An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |

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Page vii

Condition that Three Straight Lines may intersect in a Point 14 14 . Condition that

Two Straight Lines may be parallel to one another .

Equation of a Straight Line , drawn through a given Point , parallel to a given

Straight ...

Condition that Three Straight Lines may intersect in a Point 14 14 . Condition that

Two Straight Lines may be parallel to one another .

**Line at Infinity**16 15 .Equation of a Straight Line , drawn through a given Point , parallel to a given

Straight ...

Page viii

The Bisectors of any Angle form , with the Lines containing it , an Harmonic

Pencil 23 . Anharmonic Ratio ... Anharmonic Properties of Points and Lines in

Involution 25 26 27 29 30 ib . ... Every Parabola touches the

Equation ...

The Bisectors of any Angle form , with the Lines containing it , an Harmonic

Pencil 23 . Anharmonic Ratio ... Anharmonic Properties of Points and Lines in

Involution 25 26 27 29 30 ib . ... Every Parabola touches the

**Line at Infinity**6 .Equation ...

Page ix

Sign changed by interchange of two Consecutive Lines or Columns 9 . ... All

Circles pass through the same two points at infinity All Conics , similar and

similarly situated to each other , intersect in the same two points in the

Sign changed by interchange of two Consecutive Lines or Columns 9 . ... All

Circles pass through the same two points at infinity All Conics , similar and

similarly situated to each other , intersect in the same two points in the

**line at****infinity**ib . ib . Page xi

Equation of a Conic , touching the three sides of the triangle of reference 7 .

Equation of circumscribed Conic 8 . Equation of the Pole of a given straight

and of the centre . Condition for a Parabola 9 . Circular points at

Conditions for ...

Equation of a Conic , touching the three sides of the triangle of reference 7 .

Equation of circumscribed Conic 8 . Equation of the Pole of a given straight

**line**,and of the centre . Condition for a Parabola 9 . Circular points at

**infinity**Conditions for ...

Page xii

Projection of the foci and directrices of a Conic ib . The anharmonic ratio of any

pencil or range is unaltered by projection 142 Any two

angle A with each other , form with the

their ...

Projection of the foci and directrices of a Conic ib . The anharmonic ratio of any

pencil or range is unaltered by projection 142 Any two

**lines**, which make anangle A with each other , form with the

**lines**joining the circular points at**infinity**totheir ...

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### Common terms and phrases

angle angular points appears Author become BOOKS called Cambridge centre Chap chapter chord circle cloth co-ordinates coefficients coincide College common condition conic conic section considered constant corresponding Crown 8vo curve denoted described determine distance draw drawn eliminating equal equation Examples expressed find the equation fixed point focus follows given point given straight line gives harmonic Hence imaginary line at infinity locus meet observed obtained opposite sides pair parabola parallel passing pencil perpendicular point of intersection points of contact polar pole positive produced projection prove ratio reciprocal relation represented respect result right angles satisfy Schools second degree sides similar Similarly student taken tangents term theorem third three points tion touch Treatise triangle of reference values whence writing written