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

### From inside the book

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Page vii

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

...

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

Anharmonic Ratio of

Lines 25 . Harmonic Relation of

Definitions 27—29 . Anharmonic Properties of

26 27 ...

Anharmonic Ratio of

**a given**Pencil 24 . Fourth Harmonic to Three**given**StraightLines 25 . Harmonic Relation of

**Points**and Lines 26 . ON INVOLUTION .Definitions 27—29 . Anharmonic Properties of

**Points**and Lines in Involution 2526 27 ...

Page ix

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

124 Definition of the Tangential Co - ordinates of a Straight Line Interpretation of

the Negative Sign . Equation of

Identical relation between the co - ordinates of any straight Line 5 . An equation

of ...

124 Definition of the Tangential Co - ordinates of a Straight Line Interpretation of

the Negative Sign . Equation of

**certain points**3 . General Equation of**a Point**.Identical relation between the co - ordinates of any straight Line 5 . An equation

of ...

Page xii

Any system of Points in involution projects into a system in involution , and the

foci of one system project into the foci of the ... 25 A system of Conics , passing

through four

145 ...

Any system of Points in involution projects into a system in involution , and the

foci of one system project into the foci of the ... 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