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

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Page 3

The importance of the above

any equation in a form homogeneous with respect to the trilinear co - ordinates of

any point to which it relates . Any locus may be represented , as in the ordinary ...

The importance of the above

**proposition**arises from its enabling us to expressany equation in a form homogeneous with respect to the trilinear co - ordinates of

any point to which it relates . Any locus may be represented , as in the ordinary ...

Page 7

For these straight lines will be represented by the equations or b = oy , cy = an ,

αα = bß , and , therefore , all pass through the point for which aa = bß = cy . ! In

the next three

BISECTORS ...

For these straight lines will be represented by the equations or b = oy , cy = an ,

αα = bß , and , therefore , all pass through the point for which aa = bß = cy . ! In

the next three

**propositions**the reader will easily EQUATIONS OF THEBISECTORS ...

Page 8

In the next three

himself , by comparison with fig . ... to the opposite side . sar Making a

construction similar to that in the last

here an DE.

In the next three

**propositions**the reader will easily be able to draw a figure forhimself , by comparison with fig . ... to the opposite side . sar Making a

construction similar to that in the last

**proposition**, it will be seen that we havehere an DE.

Page 10

... in the most general form of the equation of the first degree between two

variables . Putting gra qr = 1 , -q = m , 4 - r = n , bc the equation may be written la

+ mß + ny = 0 . C 8. We shall next establish the converse

MODERN ...

... in the most general form of the equation of the first degree between two

variables . Putting gra qr = 1 , -q = m , 4 - r = n , bc the equation may be written la

+ mß + ny = 0 . C 8. We shall next establish the converse

**proposition**, that 10MODERN ...

Page 11

We shall next establish the converse

degree represents a straight line . Fig . 7 . M N m n B Let la + mß + ny = 0 be the

general equation of the first degree , and let f , g , h be the co - ordinates of any ...

We shall next establish the converse

**proposition**, that every equation of the firstdegree represents a straight line . Fig . 7 . M N m n B Let la + mß + ny = 0 be the

general equation of the first degree , and let f , g , h be the co - ordinates of any ...

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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