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

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Page xii

... with the lines joining the circular points at infinity to their point of intersection a

pencil of which the anharmonic ratio is e ( - 2A ) V - 1 143 The anharmonic ratio

of any four points on , or any four tangents to , a conic , is

... with the lines joining the circular points at infinity to their point of intersection a

pencil of which the anharmonic ratio is e ( - 2A ) V - 1 143 The anharmonic ratio

of any four points on , or any four tangents to , a conic , is

**constant**144 23 , 24. 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 moves in such a manner ,

that the sum of the areas of the triangles PAQ , PAR is

= 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 11

... bl • Hence , the ratio of Pm to Pn is

DEGREE . 11 Every Equation of the First Degree represents a Straight Line.

... bl • Hence , the ratio of Pm to Pn is

**constant**EQUATION OF THE FIRSTDEGREE . 11 Every Equation of the First Degree represents a Straight Line.

Page 12

Hence , the ratio of Pm to Pn is

represent . This can only be true when that locus is a straight line . 9. To find the

co - ordinates of the point of intersection of two given straight lines . Let the

equations ...

Hence , the ratio of Pm to Pn is

**constant**, whatever point on the locus P mayrepresent . This can only be true when that locus is a straight line . 9. To find the

co - ordinates of the point of intersection of two given straight lines . Let the

equations ...

Page 13

... where k is an arbitrary

equations of the given straight lines are both satisfied , and , being of the first

degree , it represents a straight line . It is therefore the equation of a straight line

passing ...

... where k is an arbitrary

**constant**. For this equation is satisfied when theequations of the given straight lines are both satisfied , and , being of the first

degree , it represents a straight line . It is therefore the equation of a straight line

passing ...

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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