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

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Page viii

... of the Conic which touches two sides of the Triangle of Reference in the points

where they meet the

Conic , any Point , and its Polar 23 Equation of a Line joining Two given Points .

... of the Conic which touches two sides of the Triangle of Reference in the points

where they meet the

**third**Any Chord of a Conic is divided harmonically by theConic , any Point , and its Polar 23 Equation of a Line joining Two given Points .

Page 15

m b m 7 C a a where it will be seen that the equality of any two members implies

that the

denominators of the several members of ( 3 ) by l , m ' , n ' and adding , we obtain

the ...

m b m 7 C a a where it will be seen that the equality of any two members implies

that the

**third**is equal to either of them . Multiplying the numerators anddenominators of the several members of ( 3 ) by l , m ' , n ' and adding , we obtain

the ...

Page 21

Find the equation of the straight line joining the middle points of two sides of the

triangle of reference ; and thence prove that it is parallel to the

the equations of the straight lines , drawn DISTANCE FROM A POINT TO A LINE

...

Find the equation of the straight line joining the middle points of two sides of the

triangle of reference ; and thence prove that it is parallel to the

**third**side . 2. Findthe equations of the straight lines , drawn DISTANCE FROM A POINT TO A LINE

...

Page 23

... ratio of the pencil OP , OQ , OR , OS , will be equal to that of the range P , Q , R ,

S. * This notation is due , I believe , to Dr. Salmon . See his Conic Sections , p .

273 (

... ratio of the pencil OP , OQ , OR , OS , will be equal to that of the range P , Q , R ,

S. * This notation is due , I believe , to Dr. Salmon . See his Conic Sections , p .

273 (

**third**edition ) . Fig . 9 . For sin POQ sin POQ sin ANHARMONIC RATIO . 23. Page 34

It may similarly be shewn to pass through the

μγα + ναβ = 0 , or , as it may also be written , a M + - = 0 , B n represents a conic ,

described about the triangle of reference . 3. Let us now inquire how the line By +

...

It may similarly be shewn to pass through the

**third**. Hence the equation λβη +μγα + ναβ = 0 , or , as it may also be written , a M + - = 0 , B n represents a conic ,

described about the triangle of reference . 3. Let us now inquire how the line By +

...

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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