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

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Page vii

ANHARMONIC

that of the range in which it is cut by any Transversal ib . Definition of an

Harmonic Pencil 25 . 20 21 . 23 20 . 21 . ARTS . PAGE 22 . The Bisectors of any

Angle.

ANHARMONIC

**RATIO**. Definitions The Anharmonic**Ratio**of a Pencil is equal tothat of the range in which it is cut by any Transversal ib . Definition of an

Harmonic Pencil 25 . 20 21 . 23 20 . 21 . ARTS . PAGE 22 . The Bisectors of any

Angle.

Page viii

Anharmonic

Lines 25 . Harmonic Relation of Points and Lines 26 . ON INVOLUTION .

Definitions 27—29 . Anharmonic Properties of Points and Lines in Involution 25

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 25

26 27 ...

Page x

The anharmonic

the same as that of the range formed by their poles 15–17 . Reciprocation with

respect to a Circle 18 . Polar reciprocal of one Circle with regard to another 19.

The anharmonic

**ratio**of the Pencil , formed by four intersecting straight lines , isthe same as that of the range formed by their poles 15–17 . Reciprocation with

respect to a Circle 18 . Polar reciprocal of one Circle with regard to another 19.

Page xii

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

pencil or range is unaltered by projection 142 Any two lines , which make an

angle A with each other , form with the lines joining the circular points at infinity to

their ...

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

**ratio**of anypencil or range is unaltered by projection 142 Any two lines , which make an

angle A with each other , form with the lines joining the circular points at infinity to

their ...

Page 1

In the system of which we are about to treat , the position of a point in a plane will

be determined by the

plane , these straight lines not passing through the same point . The triangle ...

In the system of which we are about to treat , the position of a point in a plane will

be determined by the

**ratios**of its distances from three given straight lines in thatplane , these straight lines not passing through the same point . The triangle ...

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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