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

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Page 4

This , if not self - evident , may be proved as

points . Join PQ , and draw PM , QM ' perpen . Again , since aa , + bß , + cy 4

MODERN GEOMETRY . 4-6 Investigation of Equations of certain Straight Lines.

This , if not self - evident , may be proved as

**follows**: Let P , Q be the two givenpoints . Join PQ , and draw PM , QM ' perpen . Again , since aa , + bß , + cy 4

MODERN GEOMETRY . 4-6 Investigation of Equations of certain Straight Lines.

Page 8

... the angle A , we shall have , making the same construction as before , PG = PH

. The straight line will be therefore represented by the equation B = y . ре gh For

the external bisector we proceed as

... the angle A , we shall have , making the same construction as before , PG = PH

. The straight line will be therefore represented by the equation B = y . ре gh For

the external bisector we proceed as

**follows**8 MODERN GEOMETRY . Page 9

The Method of Reciprocal Polars, and the Theory Projections Norman Macleod

Ferrers. ре gh For the external bisector we proceed as

point on the line , a , B , y its co - ordinates . Draw QK perpendicular to AC , QL to

AB .

The Method of Reciprocal Polars, and the Theory Projections Norman Macleod

Ferrers. ре gh For the external bisector we proceed as

**follows**. Let Q be anypoint on the line , a , B , y its co - ordinates . Draw QK perpendicular to AC , QL to

AB .

Page 27

It hence

= 0 , B - kry = 0 , x = 0 , B + kry = 0 , form an harmonic pencil . 24. Hence we

deduce a geometrical construction for the determination of the fourth harmonic to

...

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 we

deduce a geometrical construction for the determination of the fourth harmonic to

...

Page 31

It will also be determined if two pair of conjugate points be given ; as may be

seen as

any arbitrary point on the line , x the distance of the centre from the same point .

It will also be determined if two pair of conjugate points be given ; as may be

seen as

**follows**. Let p , p ' , q , be the respective distances of the four points fromany arbitrary point on the line , x the distance of the centre from the same point .

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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