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

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Page 11

M N m n B Let la + mß + ny = 0 be the general equation of the first degree , and

let f , g , h be the co - ordinates of any

a , b , u those of any point P. Draw DE , PM perpendicular to AC , DF , PN ...

M N m n B Let la + mß + ny = 0 be the general equation of the first degree , and

let f , g , h be the co - ordinates of any

**fixed point**D on the locus of the equation ,a , b , u those of any point P. Draw DE , PM perpendicular to AC , DF , PN ...

Page 98

... this chapter , discusses the relations which exist between systems of

and straight lines which are the poles and ... deduced those of another curve

which is always touched by the polar of this moving

conic .

... this chapter , discusses the relations which exist between systems of

**points**and straight lines which are the poles and ... deduced those of another curve

which is always touched by the polar of this moving

**point**with regard to a**fixed**conic .

Page 103

Hence it follows that parallel lines reciprocate into points lying on a straight line

passing through the centre of the ... If two of the angular points of a triangle move

each along a fixed straight line , and each side pass through a

Hence it follows that parallel lines reciprocate into points lying on a straight line

passing through the centre of 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 ... Page 104

Those of the fixed straight lines , along which two of the angular points of the first

triangle move , will be

will be “ Two of the sides of a triangle pass each through a

...

Those of the fixed straight lines , along which two of the angular points of the first

triangle move , will be

**fixed points**... Hence the data of the reciprocal propositionwill be “ Two of the sides of a triangle pass each through a

**fixed point**, and each...

Page 105

The three conics touching respectively each pair of the sides of a triangle at the

angular points where they meet the third side , will ... Then the reciprocal theorem

is that the side P ' will always pass through a

The three conics touching respectively each pair of the sides of a triangle at the

angular points where they meet the third side , will ... Then the reciprocal theorem

is that the side P ' will always pass through a

**fixed point**lying in the line Q ' .### What people are saying - Write a review

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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