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

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Page 17

therefore , to which the straight line ( 1 , m , n ) continually approaches , and with

which it ultimately

and ultimately

...

therefore , to which the straight line ( 1 , m , n ) continually approaches , and with

which it ultimately

**coincides**, when the ratios 1 : m : n continually approach to ,and ultimately

**coincide**with , the ratios a : b : c , is a straight line altogether at an...

Page 34

Hence the line 2 + 1 = 0 meets the conic in the points in which it meets the lines B

= 0 , x = 0 ; but these two points

passes through the point of intersection of B = 0 and y = o . Hence the straight

line ...

Hence the line 2 + 1 = 0 meets the conic in the points in which it meets the lines B

= 0 , x = 0 ; but these two points

**coincide**, since the line in question evidentlypasses through the point of intersection of B = 0 and y = o . Hence the straight

line ...

Page 48

Hence PQ , RS intersect in A. Similarly , PR , QS intersect in B , and PS , QR

intersect in C. Hence , the angular points of the triangle of reference

the intersections of the line joining each pair of points of intersection of the conics

...

Hence PQ , RS intersect in A. Similarly , PR , QS intersect in B , and PS , QR

intersect in C. Hence , the angular points of the triangle of reference

**coincide**withthe intersections of the line joining each pair of points of intersection of the conics

...

Page 52

Or , the centre of the circle , with respect to which the triangle of reference is self -

conjugate ,

angular points to the opposite sides . This is otherwise evident from geometrical ...

Or , the centre of the circle , with respect to which the triangle of reference is self -

conjugate ,

**coincides**with the intersection of the perpendiculars drawn from theangular points to the opposite sides . This is otherwise evident from geometrical ...

Page 69

... same straight line . But ( 2 ) and ( 3 ) are identical . Hence the proposition is

proved . From Pascal's Theorem many interesting consequences may be

deduced . Thus , if the point F

THEOREM .

... same straight line . But ( 2 ) and ( 3 ) are identical . Hence the proposition is

proved . From Pascal's Theorem many interesting consequences may be

deduced . Thus , if the point F

**coincide**with A , D with B , E with C , PASCAL'STHEOREM .

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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