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

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Page xi

CHAPTER VIII . ON THE INTERSECTION OF CONICS , ON PROJECTIONS ,

AND ON THE ERMINATION OF A CONIC FROM FIVE GIVEN GEOMETRICAL

CONDITIONS . 134 135 1-3 . Any two conics intersect in four points , real or

CHAPTER VIII . ON THE INTERSECTION OF CONICS , ON PROJECTIONS ,

AND ON THE ERMINATION OF A CONIC FROM FIVE GIVEN GEOMETRICAL

CONDITIONS . 134 135 1-3 . Any two conics intersect in four points , real or

**imaginary**... Page 31

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

Ferrers. If k * be positive , there will evidently be two such foci , one on each side

of O , if negative ( and k therefore

...

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

Ferrers. If k * be positive , there will evidently be two such foci , one on each side

of O , if negative ( and k therefore

**imaginary**) there will be no real foci . The point...

Page 33

Every curve represented by an equation of the second degree is cut by a straight

line in two points , real , coincident , or

second degree is represented by ua + up + wy ? + 2u ' By + 20'ya + 2w ' aß = 0 .

Every curve represented by an equation of the second degree is cut by a straight

line in two points , real , coincident , or

**imaginary**. The general equation of thesecond degree is represented by ua + up + wy ? + 2u ' By + 20'ya + 2w ' aß = 0 .

Page 46

If we put a = 0 , we get MB = + N ( -1 ) Ny , shewing that BC cuts the conic in two

satisfied here also . 13. We may next investigate the equations of the tangents

drawn ...

If we put a = 0 , we get MB = + N ( -1 ) Ny , shewing that BC cuts the conic in two

**imaginary**points . The analytical condition of harmonic section is , however ,satisfied here also . 13. We may next investigate the equations of the tangents

drawn ...

Page 47

It must here be borne in mind that one of the three quantities L , M , N is

essentially

as I'c + M ß2 + N'ye = 0 , L ' ? c ? + M " 2ß2 + N ' ? y = 0 , have important relations

to one ...

It must here be borne in mind that one of the three quantities L , M , N is

essentially

**imaginary**. 15. Any two conic sections represented by such equationsas I'c + M ß2 + N'ye = 0 , L ' ? c ? + M " 2ß2 + N ' ? y = 0 , have important relations

to one ...

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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