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

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Page 8

To find the equation of the straight line drawn through one of the angular points of

the triangle of reference , perpendicular to the opposite side . sar Making a

construction similar to that in the last proposition , it will be

here an ...

To find the equation of the straight line drawn through one of the angular points of

the triangle of reference , perpendicular to the opposite side . sar Making a

construction similar to that in the last proposition , it will be

**seen**that we havehere an ...

Page 14

Its full geometrical meaning will be

investigations , speak of the straight line represented by the equation la + mß +

ny = 0 , as the straight line ( l , m , n ) . Adopting this phraseology , it will be

Its full geometrical meaning will be

**seen**hereafter . We shall sometimes , in futureinvestigations , speak of the straight line represented by the equation la + mß +

ny = 0 , as the straight line ( l , m , n ) . Adopting this phraseology , it will be

**seen**... Page 15

m b m 7 C a a where it will be

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 ...

m b m 7 C a a where it will be

**seen**that the equality of any two members impliesthat 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 16

By referring to the investigation of Art . ( 7 ) it will be

distances from A , of the points in which the straight line ( 1 , m , n ) cuts AC , AB

respectively , gra qr 1 , mi q = m , -q = n ; bc b с 3 C bc n whence - bc m = ar ī a a

...

By referring to the investigation of Art . ( 7 ) it will be

**seen**that , q , r , denoting thedistances from A , of the points in which the straight line ( 1 , m , n ) cuts AC , AB

respectively , gra qr 1 , mi q = m , -q = n ; bc b с 3 C bc n whence - bc m = ar ī a a

...

Page 25

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

harmonically , From what has been said above , it will be

harmonic pencil be cut by a transversal , the four points of section will form 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 anharmonic pencil be cut by a transversal , the four points of section will form an

harmonic range .

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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