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

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Page 10

B The property of the straight line , which we shall make the basis of our

investigation , is , that it is the locus of a point which

that the sum of the areas of the triangles PAQ , PAR is constant . Let AQ = 9 , AR

= r , then ...

B The property of the straight line , which we shall make the basis of our

investigation , is , that it is the locus of a point which

**moves**in such a manner ,that the sum of the areas of the triangles PAQ , PAR is constant . Let AQ = 9 , AR

= r , then ...

Page 57

A system of conics is described touching three straight lines ; prove that , if one of

the foci

triangle . Hence prove that the circle , which passes through the points of ...

A system of conics is described touching three straight lines ; prove that , if one of

the foci

**move**along a given straight line , the other will describe à conic about thetriangle . Hence prove that the circle , which passes through the points of ...

Page 98

... with regard to any conic ; and shews how from the properties of a curve ,

regarded as the locus of a

which is always touched by the polar of this

conic .

... with regard to any conic ; and shews how from the properties of a curve ,

regarded as the locus of a

**moving**point , may be deduced those of another curvewhich is always touched by the polar of this

**moving**point with regard to a fixedconic .

Page 100

hence the polar of any point on E is a tangent to L. That is , if a point

E , its polar will envelope L. In other words , L may be generated from E , as E

was from L. In this consists the reciprocity of the curves . The process of

generating ...

hence the polar of any point on E is a tangent to L. That is , if a point

**move**alongE , its polar will envelope L. In other words , L may be generated from E , as E

was from L. In this consists the reciprocity of the curves . The process of

generating ...

Page 103

If two of the angular points of a triangle

and each side pass through a fixed point , the three points lying in the same

straight line , the third angular point will

through the ...

If two of the angular points of a triangle

**move**each along a fixed straight line ,and each side pass through a fixed point , the three points lying in the same

straight line , the third angular point will

**move**along a straight line , passingthrough 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