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

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Page vii

Distance from a Point to a Straight Line EXAMPLES 19 . ANHARMONIC RATIO .

Definitions The Anharmonic Ratio of a Pencil is equal to that of the range in

which it is cut by any Transversal ib . Definition of an

Distance from a Point to a Straight Line EXAMPLES 19 . ANHARMONIC RATIO .

Definitions The Anharmonic Ratio of a Pencil is equal to that of the range in

which it is cut by any Transversal ib . Definition of an

**Harmonic**Pencil 25 . 20 21 . Page viii

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

Pencil 23 . Anharmonic Ratio of a given Pencil 24 . Fourth

given Straight Lines 25 .

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 Threegiven Straight Lines 25 .

**Harmonic**Relation of Points and Lines 26 . ONINVOLUTION .

Page 23

We shall introduce , in this place , a short account of

section , as a familiarity with this conception is useful in the higher geometrical

investigations . DEF . 1. If OP , OQ , OR , OS be four straight lines intersecting in a

...

We shall introduce , in this place , a short account of

**harmonic**and anharmonicsection , as a familiarity with this conception is useful in the higher geometrical

investigations . DEF . 1. If OP , OQ , OR , OS be four straight lines intersecting in a

...

Page 25

A pencil , of which the anharmonic ratio is unity , is called an

range , of which the anharmonic ratio is unity , is called an

the straight line , on which the range lies , is said to be divided harmonically ...

A pencil , of which the anharmonic ratio is unity , is called an

**harmonic**pencil . Arange , of which the anharmonic ratio is unity , is called an

**harmonic**range , andthe straight line , on which the range lies , is said to be divided harmonically ...

Page 27

It hence follows that the straight lines respectively represented by the equations B

= 0 , B - kry = 0 , x = 0 , B + kry = 0 , form an

deduce a geometrical construction for the determination of the fourth

...

It hence follows that the straight lines respectively represented by the equations B

= 0 , B - kry = 0 , x = 0 , B + kry = 0 , form an

**harmonic**pencil . 24. Hence wededuce a geometrical construction for the determination of the fourth

**harmonic**to...

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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