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

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Page viii

... with

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 the

Conic ...

... with

**respect**to which the Triangle of Reference is self - conjugate Equation ofthe 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 the

Conic ...

Page x

Reciprocation with

regard to another 19. Reciprocation with

Transformation of Theorems by Reciprocation with

Corresponding Points ...

Reciprocation with

**respect**to a Circle 18 . Polar reciprocal of one Circle withregard to another 19. Reciprocation with

**respect**to a Point Instances ofTransformation of Theorems by Reciprocation with

**respect**to a circleCorresponding Points ...

Page 3

The importance of the above proposition arises from its enabling us to express

any equation in a form homogeneous with

any point to which it relates . Any locus may be represented , as in the ordinary ...

The importance of the above proposition arises from its enabling us to express

any equation in a form homogeneous with

**respect**to the trilinear co - ordinates ofany point to which it relates . Any locus may be represented , as in the ordinary ...

Page 30

The point P , and the line DEF , may be called harmonics of one another with

proved in Art . ( 22 ) , we shall obtain a demonstration of the statements made in

Art . 6 ...

The point P , and the line DEF , may be called harmonics of one another with

**respect**to the triangle ABC . By combining the proposition last proved with thatproved in Art . ( 22 ) , we shall obtain a demonstration of the statements made in

Art . 6 ...

Page 46

... or that CA is the polar of B , and B_ the pole of CA with

Similarly , C , AB , stand to one another in the relation of pole and polar . Again ,

since the pole of AB is the point C , and the pole of AC is the point B , it follows

that ...

... or that CA is the polar of B , and B_ the pole of CA with

**respect**to the conic .Similarly , C , AB , stand to one another in the relation of pole and polar . Again ,

since the pole of AB is the point C , and the pole of AC is the point B , it follows

that ...

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### Common terms and phrases

angle angular points Arithmetic asymptotes auxiliary become BOOKS called Cambridge centre Chap chapter chord circle cloth co-ordinates coincide College condition conic conic section considered constant corresponding Crown 8vo curve denoted described determine directrix distance equal equation Examples expressed fixed point focus follows four points given conic given point given straight line gives harmonic Hence hyperbola imaginary line at infinity locus meet move obtain opposite sides pair parabola parallel passing pencil perpendicular plane point of intersection points of contact polar pole positive produced projection proposition prove ratio reciprocal relation represented respect result right angles satisfy Schools second degree seen sides similar Similarly suppose taken tangents term theorem third three points tion touch Treatise triangle of reference values whence writing written