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

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Page v

... the

great utility of these expressions in investigations connected with curves of the

notation.

... the

**Second Degree**. I have introduced a short Chapter on Determinants . Thegreat utility of these expressions in investigations connected with curves of the

**second degree**will , I hope , be a sufficient excuse for the employment of anotation.

Page viii

Every Equation of the

of the Conic described about the Triangle of Reference 4 . Position of the Centre .

Condition for a Parabola Condition of Tangency . Every Parabola touches the ...

Every Equation of the

**Second Degree**represents a Conic Section 2 , 3 . Equationof the Conic described about the Triangle of Reference 4 . Position of the Centre .

Condition for a Parabola Condition of Tangency . Every Parabola touches the ...

Page ix

ON THE CONIC REPRESENTED BY THE GENERAL EQUATION OF THE

a Straight Line , drawn in a given direction through a given Point of the Conic ,

meets ...

ON THE CONIC REPRESENTED BY THE GENERAL EQUATION OF THE

**SECOND DEGREE**. 2 . 3 . 4 , 5 . 6 . 72 73 74 76 7 . 8 . To find the Point in whicha Straight Line , drawn in a given direction through a given Point of the Conic ,

meets ...

Page 4

Then , gut will be a rational integral function of a , - og , B. - By , - Yg , of the

be the two given points . Join PQ , and draw PM , QM ' perpen . Again , since aa ,

+ ...

Then , gut will be a rational integral function of a , - og , B. - By , - Yg , of the

**second degree*** . * This , if not self - evident , may be proved as follows : Let P , Qbe the two given points . Join PQ , and draw PM , QM ' perpen . Again , since aa ,

+ ...

Page 5

... ( B1 - B2 ) + ( 71-72 ) 2 + 2 ( B1 – B2 ) ( 71-72 ) cos A whence ge sin ? A a

rational integral function of the

DISTANCE BETWEEN TWO POINTS . 5.

... ( B1 - B2 ) + ( 71-72 ) 2 + 2 ( B1 – B2 ) ( 71-72 ) cos A whence ge sin ? A a

rational integral function of the

**second degree**. 1 - ; also r = a . - whereDISTANCE BETWEEN TWO POINTS . 5.

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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