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

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Page 1

... to them by a , b , c , and the distances of any point from BC , .CA , AB

respectively by the letters a , b , y . When two points lie on opposite sides of a line

of reference , the distance of one of these points from that line may be

...

... to them by a , b , c , and the distances of any point from BC , .CA , AB

respectively by the letters a , b , y . When two points lie on opposite sides of a line

of reference , the distance of one of these points from that line may be

**considered**...

Page 43

CONDITION OF TOUCHING A GIVEN STRAIGHT LINE . 43 Eliminating a , we

then get L ( mB + ny ) +7 { ( MB ) * + ( Ny ) ] = 0 , ( Im + M1 ) B + ( In + Nl ) y 21 (

MNBr ) } = 0 , or 2100 and , if the roots of this ,

equal ...

CONDITION OF TOUCHING A GIVEN STRAIGHT LINE . 43 Eliminating a , we

then get L ( mB + ny ) +7 { ( MB ) * + ( Ny ) ] = 0 , ( Im + M1 ) B + ( In + Nl ) y 21 (

MNBr ) } = 0 , or 2100 and , if the roots of this ,

**considered**as a quadratic in beequal ...

Page 73

The two roots of this equation ,

points where the line meets the conic . Now , since ( f , g , h ) is , by supposition ,

a point on the conic , it follows that $ ( f , g , h ) must be itself = 0 . Hence , one of ...

The two roots of this equation ,

**considered**as a quadratic in s , determine the twopoints where the line meets the conic . Now , since ( f , g , h ) is , by supposition ,

a point on the conic , it follows that $ ( f , g , h ) must be itself = 0 . Hence , one of ...

Page 94

In the system which we are about to explain , the position of a point P is

PAB , to the triangle of reference ABC . If these quantities be denoted by the

letters x , y , z ...

In the system which we are about to explain , the position of a point P is

**considered**as determined by the ratios of the areas of the triangles PBC , PCA ,PAB , to the triangle of reference ABC . If these quantities be denoted by the

letters x , y , z ...

Page 103

... sides of the given triangle will be three points , which may be

angles of a triangle , which may be called the reciprocal triangle . Those of the

angular points of the first triangle will be TRANSFORMATION OF THEOREMS .

... sides of the given triangle will be three points , which may be

**considered**as theangles of a triangle , which may be called the reciprocal triangle . Those of the

angular points of the first triangle will be TRANSFORMATION OF THEOREMS .

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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