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

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Page vii

EQUATION OF A

DEFINITION of Trilinear Co - ordinates Identical relation between the Trilinear Co

- ordinates of a Point ib . 3 . Distance between two

...

EQUATION OF A

**STRAIGHT LINE**. ARTE , PAGE I. I 2 . 4 II I 2 . 10 . II . I 2 . 13 .DEFINITION of Trilinear Co - ordinates Identical relation between the Trilinear Co

- ordinates of a Point ib . 3 . Distance between two

**given**Points 4-6 . Investigation...

Page viii

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

Pencil 23 . Anharmonic Ratio of a given Pencil 24 . Fourth Harmonic to Three

INVOLUTION .

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

Pencil 23 . Anharmonic Ratio of a given Pencil 24 . Fourth Harmonic to Three

**given Straight Lines**25 . Harmonic Relation of Points and Lines 26 . ONINVOLUTION .

Page ix

To find the Point in which a Straight Line , drawn in a given direction through a

given Point of the Conic , meets the Curve again Equation of the Tangent at a

given Point Condition that a

for a ...

To find the Point in which a Straight Line , drawn in a given direction through a

given Point of the Conic , meets the Curve again Equation of the Tangent at a

given Point Condition that a

**given Straight Line**may touch the Conic Conditionfor a ...

Page xi

An equation of the nth degree represents a curve of the nth class 6. 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

centre .

An equation of the nth degree represents a curve of the nth class 6. 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 thecentre .

Page xii

The anharmonic ratio of any pencil or range is unaltered by projection 142 Any

two lines , which make an angle A with ... 25 A system of Conics , passing

through four

145 ...

The anharmonic ratio of any pencil or range is unaltered by projection 142 Any

two lines , which make an angle A with ... 25 A system of Conics , passing

through four

**given**points , cut any**straight line**in a system of points in involution145 ...

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### Common terms and phrases

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