## 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 angular points of the triangle of reference by the

letters A , B , C , the lengths of the

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 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 .

Page 7

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

points of a triangle to bisect the

straight lines will be represented by the equations or b = oy , cy = an , αα = bß ,

and ...

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 thesestraight lines will be represented by the equations or b = oy , cy = an , αα = bß ,

and ...

Page 8

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

the triangle of reference , perpendicular to the

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

It will however be observed , that if Q and B lie on the same side of AC , Q and C

will lie on

have therefore gle wn B + y = 0 as the equation of the line AQ , which externally ...

It will however be observed , that if Q and B lie on the same side of AC , Q and C

will lie on

**opposite sides**of AB , and vice versa . Hence , if QK = B , QL = -9 . siWehave therefore gle wn B + y = 0 as the equation of the line AQ , which externally ...

Page 30

... respectively intersect the

and that the points in which the external bisector of any one angle and the

internal bisectors of the other two angles , intersect the

... respectively intersect the

**sides opposite**to them , lie in the same straight line ;and that the points in which the external bisector of any one angle and the

internal bisectors of the other two angles , intersect the

**sides**respectively**opposite**to ...### What people are saying - Write a review

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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