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

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Page 1

We shall usually denote the

letters A , B , C , the lengths of the sides respectively opposite to them by a , b , c ,

and the distances of any point from BC , .CA , AB respectively by the letters a , b ,

y .

We shall usually denote the

**angular points**of the triangle of reference by theletters A , B , C , the lengths of the sides respectively opposite to them by a , b , c ,

and the distances of any point from BC , .CA , AB respectively by the letters a , b ,

y .

Page 6

To find the equation of the straight line drawn through one of the

the triangle of reference , so as to bisect the opposite side . Let D be the middle

point of the side BC , we have then to investigate the equation of the straight line

...

To find the equation of the straight line drawn through one of the

**angular points**ofthe triangle of reference , so as to bisect the opposite side . Let D be the middle

point of the side BC , we have then to investigate the equation of the straight line

...

Page 7

In AD take any point P , and let a , B , y be its co - ordiFig . 5 . НА E B D nates . ... It

hence may be proved that the three straight lines , drawn through the

In AD take any point P , and let a , B , y be its co - ordiFig . 5 . НА E B D nates . ... It

hence may be proved that the three straight lines , drawn through the

**angular****points**of a triangle to bisect the opposite sides , intersect in a point . For these ... Page 8

To find the equation of the straight line drawn through one of the

the triangle of reference , perpendicular to the opposite side . sar Making a

construction similar to that in the last proposition , it will be seen that we have

here an ...

To find the equation of the straight line drawn through one of the

**angular points**ofthe triangle of reference , perpendicular to the opposite side . sar Making a

construction similar to that in the last proposition , it will be seen that we have

here an ...

Page 18

To find the inclinations of a straight line , drawn through one of the

of the triangle of reference , to the sides which intersect in that point . Let the

equation of the straight line AP be uß = vy , Fig . 8 . B D and let O be its inclination

to ...

To find the inclinations of a straight line , drawn through one of the

**angular points**of the triangle of reference , to the sides which intersect in that point . Let the

equation of the straight line AP be uß = vy , Fig . 8 . B D and let O be its inclination

to ...

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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