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

### From inside the book

Results 1-5 of 22

Page viii

... Any Chord of a Conic is divided harmonically by the Conic , any Point , and its

Polar 23 Equation of a Line joining Two given Points . 24 . Equation of the

Tangent at a given Point 25 .

Tangency .

... Any Chord of a Conic is divided harmonically by the Conic , any Point , and its

Polar 23 Equation of a Line joining Two given Points . 24 . Equation of the

Tangent at a given Point 25 .

**Pole**of a given Straight Line . 26 . Condition ofTangency .

Page ix

... 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

a given Straight Line Equation of the pair of Tangents , drawn to the Conic from a

...

... 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**ofa given Straight Line Equation of the pair of Tangents , drawn to the Conic from a

...

Page x

The anharmonic ratio of the Pencil , formed by four intersecting straight lines , is

the same as that of the range formed by their

respect to a Circle 18 . Polar reciprocal of one Circle with regard to another 19.

The anharmonic ratio of the Pencil , formed by four intersecting straight lines , is

the same as that of the range formed by their

**poles**15–17 . Reciprocation withrespect to a Circle 18 . Polar reciprocal of one Circle with regard to another 19.

Page xi

An equation of the nth degree represents a curve of the nth class 6. Equation of a

Conic , touching the three sides of the triangle of reference 7 . Equation of

circumscribed Conic 8 . Equation of the

centre .

An equation of the nth degree represents a curve of the nth class 6. Equation of a

Conic , touching the three sides of the triangle of reference 7 . Equation of

circumscribed Conic 8 . Equation of the

**Pole**of a given straight line , and of thecentre .

Page 46

Similarly , C , AB , stand to one another in the relation of

since the

that the line joining B and C is the polar of the point of intersection of AB , AC , i.e.

...

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 followsthat the line joining B and C is the polar of the point of intersection of AB , AC , i.e.

...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### 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