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

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Page vii

... Straight Lines may be parallel to one another . Line at Infinity 16 15 . Equation

of a Straight Line , drawn through a given Point , parallel to a given Straight Line

17 16 . Inclination of a Straight Line to a side of the

... Straight Lines may be parallel to one another . Line at Infinity 16 15 . Equation

of a Straight Line , drawn through a given Point , parallel to a given Straight Line

17 16 . Inclination of a Straight Line to a side of the

**Triangle of Reference**18 17 . Page viii

Equation of the Conic described about the

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

touches the Line at Infinity 6 . Equation of the Circumscribing Circle 7 . Equation

of ...

Equation of the Conic described about the

**Triangle of Reference**4 . Position ofthe Centre . Condition for a Parabola Condition of Tangency . Every Parabola

touches the Line at Infinity 6 . Equation of the Circumscribing Circle 7 . Equation

of ...

Page xi

Equation of a Conic , touching the three sides of the

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 1

The triangle formed by these three straight lines is called the

, its sides , lines of reference , and the distances of a point from its three sides will

be called the trilinear co - ordinates of that point . We shall usually denote the ...

The triangle formed by these three straight lines is called the

**triangle of reference**, its sides , lines of reference , and the distances of a point from its three sides will

be called the trilinear co - ordinates of that point . We shall usually denote the ...

Page 2

The Method of Reciprocal Polars, and the Theory Projections Norman Macleod

Ferrers. the

perpendicular to BC . Then PD = a , and aa = twice the area of the triangle PBC .

Fig .

The Method of Reciprocal Polars, and the Theory Projections Norman Macleod

Ferrers. the

**triangle of reference**( fig . 1 ) . Join PA , PB , PC , and draw PDperpendicular to BC . Then PD = a , and aa = twice the area of the triangle PBC .

Fig .

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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