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

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Page vii

Every Straight Line may be

Every Equation of the First Degree

Intersection of Two Straight Lines Equation of a Straight Line passing through

Two given ...

Every Straight Line may be

**represented**by an Equation of the First Degree 9 8 .Every Equation of the First Degree

**represents**a Straight Line 9 . Point ofIntersection of Two Straight Lines Equation of a Straight Line passing through

Two given ...

Page viii

Every Equation of the Second Degree

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

SECOND DEGREE . 2 . 3 . 4 , 5 . 6 . 72 73 74 76 7 . 8 . To find the Point in which

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 THESECOND DEGREE . 2 . 3 . 4 , 5 . 6 . 72 73 74 76 7 . 8 . To find the Point in which

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

meets ...

Page xi

An equation of the nth degree

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 3

Hence , twice the area PBC will be

have as before aa + b3 + cy = 2A . Thirdly , let P lie between AB , AC , produced

backwards ( fig . 3 ) , so that B , y are negative while a is positive . Twice Fig . 3 .

Hence , twice the area PBC will be

**represented**by — ad , and we shall thereforehave as before aa + b3 + cy = 2A . Thirdly , let P lie between AB , AC , produced

backwards ( fig . 3 ) , so that B , y are negative while a is positive . Twice Fig . 3 .

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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