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

### From inside the book

Results 1-5 of 14

Page 2

Join PA , PB , PC , and draw PD

twice the area of the triangle PBC . Fig . 1 . : Similarly bB = twice the area of PCA ,

cy = twice the area of PAB . Adding these equations , we get aa + b3 + cy = 2A .

Join PA , PB , PC , and draw PD

**perpendicular**to BC . Then PD = a , and aa =twice the area of the triangle PBC . Fig . 1 . : Similarly bB = twice the area of PCA ,

cy = twice the area of PAB . Adding these equations , we get aa + b3 + cy = 2A .

Page 5

-a Similar expressions may be found for ( B.-B. ) , ( Y. - Y ) . Hence , pa will be of

the form 2 ( B - B2 ) ( 7. - Y ) + m ( Y. - Y ) ( Qz - Q ) + n ( az -22 ) ( B - B2 ) , dicular

to AB , PN , QN ' to AC . Draw Qm

-a Similar expressions may be found for ( B.-B. ) , ( Y. - Y ) . Hence , pa will be of

the form 2 ( B - B2 ) ( 7. - Y ) + m ( Y. - Y ) ( Qz - Q ) + n ( az -22 ) ( B - B2 ) , dicular

to AB , PN , QN ' to AC . Draw Qm

**perpendicular**to PM , Qn to PN , and join mn . Page 7

The Method of Reciprocal Polars, and the Theory Projections Norman Macleod

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

nates . From D , P draw DE , PG

AB ...

The Method of Reciprocal Polars, and the Theory Projections Norman Macleod

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

nates . From D , P draw DE , PG

**perpendicular**to AC , DF , PH**perpendicular**toAB ...

Page 8

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

the triangle of reference ,

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 of

the triangle of reference ,

**perpendicular**to the opposite side . sar Making aconstruction similar to that in the last proposition , it will be seen that we have

here an ...

Page 9

The Method of Reciprocal Polars, and the Theory Projections Norman Macleod

Ferrers. ре gh For the external bisector we proceed as follows . Let Q be any

point on the line , a , B , y its co - ordinates . Draw QK

AB .

The Method of Reciprocal Polars, and the Theory Projections Norman Macleod

Ferrers. ре gh For the external bisector we proceed as follows . Let Q be any

point on the line , a , B , y its co - ordinates . Draw QK

**perpendicular**to AC , QL toAB .

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### Common terms and phrases

angle angular points Arithmetic asymptotes auxiliary become BOOKS called Cambridge centre Chap chapter chord circle cloth co-ordinates coincide College condition conic conic section considered constant corresponding Crown 8vo curve denoted described determine directrix distance equal equation Examples expressed fixed point focus follows four points given conic given point given straight line gives harmonic Hence hyperbola imaginary line at infinity locus meet move obtain opposite sides pair parabola parallel passing pencil perpendicular plane point of intersection points of contact polar pole positive produced projection proposition prove ratio reciprocal relation represented respect result right angles satisfy Schools second degree seen sides similar Similarly suppose taken tangents term theorem third three points tion touch Treatise triangle of reference values whence writing written