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

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Page 13

... v must

, λας + μβ , + νY , = 0 , whence , eliminating 2 , l , v , by cross multiplication , QB : 7

: - 0,337 , + aß.7 . – 2.B.72 + ax B.72 – QBxy = 0 , the required condition . 13 .

... v must

**satisfy**the following equations : aa , + uß , + 2y = 0 , 12 , + uß , + 272 = 0, λας + μβ , + νY , = 0 , whence , eliminating 2 , l , v , by cross multiplication , QB : 7

: - 0,337 , + aß.7 . – 2.B.72 + ax B.72 – QBxy = 0 , the required condition . 13 .

Page 16

... which is known to be a necessary condition of their parallelism , and also a

sufficient condition , since the two straight lines are in the same plane . Although ,

however , no values of Q , B , y exist which will

0 ...

... which is known to be a necessary condition of their parallelism , and also a

sufficient condition , since the two straight lines are in the same plane . Although ,

however , no values of Q , B , y exist which will

**satisfy**the equation au + bB + cy =0 ...

Page 36

We may hence deduce the relation which must hold between , ui , v , in order that

the conic may be a bola . For , since the centre of a parabola is at an infinite

distance , its co - ordinates will

obtain ...

We may hence deduce the relation which must hold between , ui , v , in order that

the conic may be a bola . For , since the centre of a parabola is at an infinite

distance , its co - ordinates will

**satisfy**the equation as + b + cy = 0 . We henceobtain ...

Page 37

... the parabola

b3 + cy = 0 . This is generally expressed by saying that every parabola touches

the line at infinity . 6. To investigate the equation of the circle , circumscribing the

...

... the parabola

**satisfies**the analytical condition of touching the straight line aa +b3 + cy = 0 . This is generally expressed by saying that every parabola touches

the line at infinity . 6. To investigate the equation of the circle , circumscribing the

...

Page 41

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

Ferrers. Let fi , 9 ,, h , be the co - ordinates of D. Then fi = 0 ; and 9 , he will be the

values of B , y , which

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

Ferrers. Let fi , 9 ,, h , be the co - ordinates of D. Then fi = 0 ; and 9 , he will be the

values of B , y , which

**satisfy**the equations M * ß * + N ? ya – 2 MNBy = 0 , MB ...### What people are saying - Write a review

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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