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

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Page viii

Equation of the Conic

Position of the Centre . Condition for a Parabola 9 . Condition of Tangency

Equations of the Four Circles which

Reference ...

Equation of the Conic

**touching**the Three Sides of the Triangle of Reference 8 .Position of the Centre . Condition for a Parabola 9 . Condition of Tangency

Equations of the Four Circles which

**touch**the Three Sides of the Triangle ofReference ...

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 Curve again Equation of the Tangent at a

given Point Condition that a given Straight Line may

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 a

given Point Condition that a given Straight Line may

**touch**the Conic Conditionfor a ...

Page xi

Equation of a Conic ,

Equation of circumscribed Conic 8 . Equation of the Pole of a given straight line ,

and of the centre . Condition for a Parabola 9 . Circular points at infinity

Conditions for ...

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 the centre . Condition for a Parabola 9 . Circular points at infinity

Conditions for ...

Page 22

... joining the centre of the circle inscribed in the triangle ABC , with the middle

point of the side BC , is parallel to the straight line joining A with the point of

contact of the circle

sides BC ...

... joining the centre of the circle inscribed in the triangle ABC , with the middle

point of the side BC , is parallel to the straight line joining A with the point of

contact of the circle

**touching**BC externally and AB , AC produced . 6 . On thesides BC ...

Page 34

... but these two points coincide , since the line in question evidently passes

through the point of intersection of B = 0 and y = o . Hence the straight line and

the conic meet one another in coincident points , that is , they

at the ...

... but these two points coincide , since the line in question evidently passes

through the point of intersection of B = 0 and y = o . Hence the straight line and

the conic meet one another in coincident points , that is , they

**touch**one anotherat the ...

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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