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

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Page 15

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 and

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

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 and

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

**obtain**the ...

Page 30

By combining the proposition last proved with that proved in Art . ( 22 ) , we shall

the external bisectors of each angle of a triangle respectively intersect the sides ...

By combining the proposition last proved with that proved in Art . ( 22 ) , we shall

**obtain**a demonstration of the statements made in Art . 6 ; that the points in whichthe external bisectors of each angle of a triangle respectively intersect the sides ...

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 satisfy the equation as + b + cy = 0 . We hence

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 hence

**obtain**... Page 37

If the conic be touched by the straight line ( 1 , m , n ) , the two values of the ratio

B : ' ,

mß + ny = 0 , must be coincident . The equation which determines these is - NlBy

...

If the conic be touched by the straight line ( 1 , m , n ) , the two values of the ratio

B : ' ,

**obtained**by eliminating a between the equations λβη + μγα + ναβ = 0 , la +mß + ny = 0 , must be coincident . The equation which determines these is - NlBy

...

Page 39

The condition that the conic ua + op + wys + 2u ' By + 2u'rya + 2w'aß = 0 , may

touch the line a = 0 ) is , that the left - hand member of the equation

writing a = 0 in the above may be a perfect square . This requires that u ' ? = vw ,

or ...

The condition that the conic ua + op + wys + 2u ' By + 2u'rya + 2w'aß = 0 , may

touch the line a = 0 ) is , that the left - hand member of the equation

**obtained**bywriting a = 0 in the above may be a perfect square . This requires that u ' ? = vw ,

or ...

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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