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

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Page vii

Condition that Two Straight Lines may be

16 15 . Equation of a Straight Line , drawn through a given Point ,

given Straight Line 17 16 . Inclination of a Straight Line to a side of the Triangle of

...

Condition that Two Straight Lines may be

**parallel**to one another . Line at Infinity16 15 . Equation of a Straight Line , drawn through a given Point ,

**parallel**to agiven Straight Line 17 16 . Inclination of a Straight Line to a side of the Triangle of

...

Page 14

To find the condition that two straight lines may be

the equations of the two straight lines be la + mß + ny = 0 ......... ... ( 1 ) , l'a + m'ß +

ny = 0 ......... . ( 2 ) . Let ( f , g , h ) ( a , b , y ) be the co - ordinates of any two points

...

To find the condition that two straight lines may be

**parallel**to one another . Letthe equations of the two straight lines be la + mß + ny = 0 ......... ... ( 1 ) , l'a + m'ß +

ny = 0 ......... . ( 2 ) . Let ( f , g , h ) ( a , b , y ) be the co - ordinates of any two points

...

Page 17

... impossible , -in fact , a contradiction in terms ,and can only be admitted as a

limiting form to which possible equations may continually tend . 15. To find the

equation of a straight line , drawn through a given point ,

straight ...

... impossible , -in fact , a contradiction in terms ,and can only be admitted as a

limiting form to which possible equations may continually tend . 15. To find the

equation of a straight line , drawn through a given point ,

**parallel**to a givenstraight ...

Page 18

The general equation of a straight line

aa + b3 + cy ) , where k is an arbitrary constant . 16 . To find the inclinations of a

straight line , drawn through one of the angular points of the triangle of reference

...

The general equation of a straight line

**parallel**to ( l , m , n ) is la + mB + ny = k (aa + b3 + cy ) , where k is an arbitrary constant . 16 . To find the inclinations of a

straight line , drawn through one of the angular points of the triangle of reference

...

Page 19

Through A draw two straight lines

the equations ( ma – 16 ) B + ( na – lc ) y = 0 , ( m'a – 1'0 ) B + ( n'a— l'c ) y = 0 .

And these straight lines must be perpendicular to each other . If 0 , o be the ...

Through A draw two straight lines

**parallel**to them . These will be represented bythe equations ( ma – 16 ) B + ( na – lc ) y = 0 , ( m'a – 1'0 ) B + ( n'a— l'c ) y = 0 .

And these straight lines must be perpendicular to each other . If 0 , o be the ...

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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