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

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Page 22

Find the equations of the straight lines , drawn through the several angular points

of the triangle of reference ... middle point of the side BC , is parallel to the

straight line joining A with the

and ...

Find the equations of the straight lines , drawn through the several angular points

of the triangle of reference ... middle point of the side BC , is parallel to the

straight line joining A with the

**point of contact**of the circle touching BC externallyand ...

Page 35

Through the angular

EAF , FBD , DCE . ... of two tangents so as to bisect their chord of

also through the centre , 0 will be the centre of the conic . a -- - Now , at the

...

Through the angular

**points**A , B , C of the triangle of reference draw the tangentsEAF , FBD , DCE . ... of two tangents so as to bisect their chord of

**contact**passesalso through the centre , 0 will be the centre of the conic . a -- - Now , at the

**point**...

Page 40

It may be remarked , that the condition that the point ( 1 , m , n ) should lie in the

above conic , is the same as the condition that the straight line ( l , m , n ) should

touch ... Let D , E , F be the

.

It may be remarked , that the condition that the point ( 1 , m , n ) should lie in the

above conic , is the same as the condition that the straight line ( l , m , n ) should

touch ... Let D , E , F be the

**points of contact**of the sides BC , CA , AB respectively.

Page 46

If we put a = 0 , we get MB = + N ( -1 ) Ny , shewing that BC cuts the conic in two

imaginary

to ...

If we put a = 0 , we get MB = + N ( -1 ) Ny , shewing that BC cuts the conic in two

imaginary

**points**. ... Since the two tangents drawn through B meet the conic in**points**situated in the line CA , it follows that CA is the chord of**contact**of tangentsto ...

Page 52

To find the equation of the conic which touches two sides of the triangle of

reference in the points where they meet the third ... involves only one arbitrary

constant , as ought to be the case , since when a tangent and its

are given ...

To find the equation of the conic which touches two sides of the triangle of

reference in the points where they meet the third ... involves only one arbitrary

constant , as ought to be the case , since when a tangent and its

**point of contact**are given ...

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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