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

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Page ix

... Centre Equation of the Asymptotes Condition for a rectangular Hyperbola

Conditions for a Circle All Circles pass through the same two points at infinity All

Conics ,

points ...

... Centre Equation of the Asymptotes Condition for a rectangular Hyperbola

Conditions for a Circle All Circles pass through the same two points at infinity All

Conics ,

**similar**and similarly situated to each other , intersect in the same twopoints ...

Page xii

Also into

effected in an infinite number of ways ib . 17 . Any two intersecting conics may be

projected into hyperbolas of any assigned eccentricity ib . 18 . Any two conics ...

Also into

**similar**and similarly situated curves 140 16 . These projections may beeffected in an infinite number of ways ib . 17 . Any two intersecting conics may be

projected into hyperbolas of any assigned eccentricity ib . 18 . Any two conics ...

Page 5

-a

the form 2 ( B - B2 ) ( 7. - Y ) + m ( Y. - Y ) ( Qz - Q ) + n ( az -22 ) ( B - B2 ) , dicular

to AB , PN , QN ' to AC . Draw Qm perpendicular to PM , Qn to PN , and join mn .

-a

**Similar**expressions may be found for ( B.-B. ) , ( Y. - Y ) . Hence , pa will be ofthe form 2 ( B - B2 ) ( 7. - Y ) + m ( Y. - Y ) ( Qz - Q ) + n ( az -22 ) ( B - B2 ) , dicular

to AB , PN , QN ' to AC . Draw Qm perpendicular to PM , Qn to PN , and join mn .

Page 6

44 % ab2c Similarly 442 abc 442 " abc Hence pa { a ( B.-B. ) ( y - 7 ) + b ( 7-7 ) ( a

, – Q. ) + c ( Qz - Q ) ( B.-B. ) } . This is one form of the expression for r . It may also

ke proved in a

44 % ab2c Similarly 442 abc 442 " abc Hence pa { a ( B.-B. ) ( y - 7 ) + b ( 7-7 ) ( a

, – Q. ) + c ( Qz - Q ) ( B.-B. ) } . This is one form of the expression for r . It may also

ke proved in a

**similar**manner that abc g2 447 { a cos A ( an - Qn ) + b cos B ... Page 7

Then by

equal to the area of the triangle ABC . Hence PG . AC = PH . AB , bB = cy . This is

a relation between the co - ordinates of any point on the line AD , it therefore is ...

Then by

**similar**triangles PG : DE :: PH : DF . But DE , AC = DF . AB , for each isequal to the area of the triangle ABC . Hence PG . AC = PH . AB , bB = cy . This is

a relation between the co - ordinates of any point on the line AD , it therefore is ...

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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