## 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

... 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

Condition of Tangency Equations of the Four Circles which touch the Three

of the Triangle of Reference 11–15 . Equation involving the Squares only of the

Variables 16 . Condition of Tangency 17 . Condition for a Parabola .

Condition of Tangency Equations of the Four Circles which touch the Three

**Sides**of the Triangle of Reference 11–15 . Equation involving the Squares only of the

Variables 16 . Condition of Tangency 17 . Condition for a Parabola .

Page xi

Equation of a Conic , touching the three

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 triangle of reference

, its

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

Page 2

1 . : Similarly bB = twice the area of PCA , cy = twice the area of PAB . Adding

these equations , we get aa + b3 + cy = 2A . Next , suppose P to lie between AB ,

AC produced , and on the

2 .

1 . : Similarly bB = twice the area of PCA , cy = twice the area of PAB . Adding

these equations , we get aa + b3 + cy = 2A . Next , suppose P to lie between AB ,

AC produced , and on the

**side**of BC remote from A ( fig . 2 ) . Then a will be Fig .2 .

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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