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

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Page ix

... touch the Conic Condition for a Parabola . Condition that the Conic may break

up into Two Straight Lines . Equation of the Polar of a given Point Co - ordinates

of the Pole of a given Straight Line Equation of the

...

... touch the Conic Condition for a Parabola . Condition that the Conic may break

up into Two Straight Lines . Equation of the Polar of a given Point Co - ordinates

of the Pole of a given Straight Line Equation of the

**pair**of Tangents , drawn to the...

Page xi

If the four points of intersection be all real , all the common chords are real ; if not ,

one

Projection to infinity 10-12 . Any quadrilateral may be projected , in an infinite

number of ...

If the four points of intersection be all real , all the common chords are real ; if not ,

one

**pair**only is real ON PROJECTIONS . 8 . Definition of Projections 9 .Projection to infinity 10-12 . Any quadrilateral may be projected , in an infinite

number of ...

Page 22

On the sides BC , CA , AB of the triangle ABC , respectively ,

taken , B. , C ; C ,, 4 ,; 45 , B .; such that the points of intersection of BC with B , C ,,

of ČA with C , A ,, and of AB with 4 B lie in a straight line ; BC , CB , intersect in L ...

On the sides BC , CA , AB of the triangle ABC , respectively ,

**pairs**of points aretaken , B. , C ; C ,, 4 ,; 45 , B .; such that the points of intersection of BC with B , C ,,

of ČA with C , A ,, and of AB with 4 B lie in a straight line ; BC , CB , intersect in L ...

Page 31

It will also be determined if two

seen as follows . Let p , p ' , q , be the respective distances of the four points from

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 beseen as follows . Let p , p ' , q , be the respective distances of the four points from

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

Page 32

Conversely , if there be a system of

each

the ...

Conversely , if there be a system of

**pairs**of points in a straight line , such thateach

**pair**forms , with two given points , an harmonic range , the aggregate of the**pairs**of points will form a system in involution , of which the two given points arethe ...

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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