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

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Page v

A desire not unduly to increase the size of the book has prevented me from

proceeding beyond

Chapter on Determinants . The great utility of these expressions in investigations

...

A desire not unduly to increase the size of the book has prevented me from

proceeding beyond

**Curves**of the Second Degree . I have introduced a shortChapter on Determinants . The great utility of these expressions in investigations

...

Page ix

To find the Point in which a Straight Line , drawn in a given direction through a

given Point of the Conic , meets the

given Point Condition that a given Straight Line may touch the Conic Condition

for a ...

To find the Point in which a Straight Line , drawn in a given direction through a

given Point of the Conic , meets the

**Curve**again Equation of the Tangent at agiven Point Condition that a given Straight Line may touch the Conic Condition

for a ...

Page x

The degree of a

7. The polar reciprocal of a conic is a conic 8 . Equation of the Polar Reciprocal of

one Conic with regard to another Instances of Transformation Brianchon's ...

The degree of a

**curve**is the same as the class of its reciprocal , and vice versa 6 ,7. The polar reciprocal of a conic is a conic 8 . Equation of the Polar Reciprocal of

one Conic with regard to another Instances of Transformation Brianchon's ...

Page xi

An equation of the nth degree represents 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 the

centre .

An equation of the nth degree represents a

**curve**of the nth class 6. Equation of aConic , 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 the

centre .

Page xii

Also into similar and similarly situated

effected in an infinite number of ways ib . 17 . Any two intersecting conics may be

projected into hyperbolas of any assigned eccentricity ib . 18 . Any two conics ...

Also into similar and similarly situated

**curves**140 16 . These projections may beeffected in an infinite number of ways ib . 17 . Any two intersecting conics may be

projected into hyperbolas of any assigned eccentricity ib . 18 . Any two conics ...

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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