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

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Page viii

... of the Conic which touches two sides of the Triangle of Reference in the points

where they meet the third Any

Conic , any Point , and its Polar 23 Equation of a Line joining Two given Points .

... of the Conic which touches two sides of the Triangle of Reference in the points

where they meet the third Any

**Chord**of a Conic is divided harmonically by theConic , any Point , and its Polar 23 Equation of a Line joining Two given Points .

Page xi

If the four points of intersection be all real , all the common

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 ...

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 35

Then , since every straight line drawn through the intersection of two tangents so

as to bisect their

centre of the conic . a -- - Now , at the point E , 3-2 CENTRE OF THE CONIC . 35.

Then , since every straight line drawn through the intersection of two tangents so

as to bisect their

**chord**of contact passes also through the centre , 0 will be thecentre of the conic . a -- - Now , at the point E , 3-2 CENTRE OF THE CONIC . 35.

Page 46

... which shew that these tangents are imaginary , or that the point A lies within

the concavity of the conic . 14. Since the two tangents drawn through B meet the

conic in points situated in the line CA , it follows that CA is the

...

... which shew that these tangents are imaginary , or that the point A lies within

the concavity of the conic . 14. Since the two tangents drawn through B meet the

conic in points situated in the line CA , it follows that CA is the

**chord**of contact of...

Page 53

Or any

the

observe , that the two straight lines represented by the equations ka = wß , ka = 1

...

Or any

**chord**of a conic is divided harmonically by the conic itself , any point onthe

**chord**, and the polar of the point with respect to the conic . • NY , 22. We mayobserve , that the two straight lines represented by the equations ka = wß , ka = 1

...

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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