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

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Page ix

Signs of the several

two Consecutive Lines or Columns 9 . Multiplication of a Determinant by a given

Quantity Minors of a Determinant Condition that a Quadratic Function may be ...

Signs of the several

**Terms**of a Determinant 8 . Sign changed by interchange oftwo Consecutive Lines or Columns 9 . Multiplication of a Determinant by a given

Quantity Minors of a Determinant Condition that a Quadratic Function may be ...

Page 3

Any locus may be represented , as in the ordinary system , by means of a relation

between two coordinates , ß and y for example , and this may be made homoaa +

bB + oy geneous in a , b , y by multiplying each

Any locus may be represented , as in the ordinary system , by means of a relation

between two coordinates , ß and y for example , and this may be made homoaa +

bB + oy geneous in a , b , y by multiplying each

**term**by 24 raised to a suitable ... Page 4

...

ordinates of two given points , r the distance between them . Then , gut will be a

rational integral function of a , - og , B. - By , - Yg , of the second degree * . * This ,

if ...

...

**terms**of their trilinear co - ordinates . Let 04 , B. , % ; Qg , B2 , yz , be the co -ordinates of two given points , r the distance between them . Then , gut will be a

rational integral function of a , - og , B. - By , - Yg , of the second degree * . * This ,

if ...

Page 17

... desirable that attention should be called to the fact , that the equation aa + b3 +

cy = 0 is , in itself , impossible , -in fact , a contradiction in

admitted as a limiting form to which possible equations may continually tend .

... desirable that attention should be called to the fact , that the equation aa + b3 +

cy = 0 is , in itself , impossible , -in fact , a contradiction in

**terms**,and can only beadmitted as a limiting form to which possible equations may continually tend .

Page 25

The line OS is said to be a fourth harmonic to the pencil OP , OQ , OR ; and the

point S to be a fourth harmonic to the range P , Q , R. The

employed on account of the circumstance , that if the points P , Q , R , S form what

is ...

The line OS is said to be a fourth harmonic to the pencil OP , OQ , OR ; and the

point S to be a fourth harmonic to the range P , Q , R. The

**term**harmonic isemployed on account of the circumstance , that if the points P , Q , R , S form what

is ...

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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