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

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Page 1

The triangle formed by these three straight lines is

, its sides , lines of reference , and the distances of a point from its three sides will

be

The triangle formed by these three straight lines is

**called**the triangle of reference, its sides , lines of reference , and the distances of a point from its three sides will

be

**called**the trilinear co - ordinates of that point . We shall usually denote the ... Page 17

It is , however , desirable that attention should be

equation aa + b3 + cy = 0 is , in itself , impossible , -in fact , a contradiction in

terms ,and can only be admitted as a limiting form to which possible equations

may ...

It is , however , desirable that attention should be

**called**to the fact , that theequation aa + b3 + cy = 0 is , in itself , impossible , -in fact , a contradiction in

terms ,and can only be admitted as a limiting form to which possible equations

may ...

Page 23

If OP , OQ , OR , OS be four straight lines intersecting in a point , the ratio sin POQ

.sin ROS sin POS.sin QOR is

OR , OS , and is expressed by the notation { 0. PQRS ) * . DEF . 2. If P , Q , R , S ...

If OP , OQ , OR , OS be four straight lines intersecting in a point , the ratio sin POQ

.sin ROS sin POS.sin QOR is

**called**the anharmonic ratio of the pencil OP , OQ ,OR , OS , and is expressed by the notation { 0. PQRS ) * . DEF . 2. If P , Q , R , S ...

Page 25

A range , of which the anharmonic ratio is unity , is

and the straight line , on which the range lies , is said to be divided harmonically ,

From what has been said above , it will be seen that , if an harmonic pencil be cut

...

A range , of which the anharmonic ratio is unity , is

**called**an harmonic range ,and the straight line , on which the range lies , is said to be divided harmonically ,

From what has been said above , it will be seen that , if an harmonic pencil be cut

...

Page 30

The point P , and the line DEF , may be

respect to the triangle ABC . By combining the proposition last proved with that

proved in Art . ( 22 ) , we shall obtain a demonstration of the statements made in

Art . 6 ...

The point P , and the line DEF , may be

**called**harmonics of one another withrespect to the triangle ABC . By combining the proposition last proved with that

proved in Art . ( 22 ) , we shall obtain a demonstration of the statements made in

Art . 6 ...

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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