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

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Page viii

Anharmonic Ratio of a

Lines 25 . Harmonic Relation of Points and Lines 26 . ... Every Equation of the

Second Degree represents a

described ...

Anharmonic Ratio of a

**given**Pencil 24 . Fourth Harmonic to Three**given**StraightLines 25 . Harmonic Relation of Points and Lines 26 . ... Every Equation of the

Second Degree represents a

**Conic**Section 2 , 3 . Equation of the**Conic**described ...

Page ix

ON THE

SECOND DEGREE . 2 . 3 . 4 , 5 . 6 . 72 73 74 76 7 . 8 . To find the Point in which

a Straight Line , drawn in a

meets ...

ON THE

**CONIC**REPRESENTED BY THE GENERAL EQUATION OF THESECOND DEGREE . 2 . 3 . 4 , 5 . 6 . 72 73 74 76 7 . 8 . To find the Point in which

a Straight Line , drawn in a

**given**direction through a**given**Point of the**Conic**,meets ...

Page xi

Equation of a

Equation of circumscribed

and of the centre . Condition for a Parabola 9 . Circular points at infinity

Conditions for ...

Equation of a

**Conic**, touching the three sides of the triangle of reference 7 .Equation of circumscribed

**Conic**8 . Equation of the Pole of a**given**straight line ,and of the centre . Condition for a Parabola 9 . Circular points at infinity

Conditions for ...

Page xii

ON THE DETERMINATION OF A

CONDITIONS . 146 28 . 29 . 147 30 . ib . . 31 . If five points be

only can be drawn If four points and one tangent be

drawn ...

ON THE DETERMINATION OF A

**CONIC**FROM FIVE**GIVEN**GEOMETRICALCONDITIONS . 146 28 . 29 . 147 30 . ib . . 31 . If five points be

**given**, one**conic**only can be drawn If four points and one tangent be

**given**, two**conics**can bedrawn ...

Page 23

If four

points P , Q , R , S , the anharmonic ratio of the pencil OP , OQ , OR , OS , will be

equal to that of the range P , Q , R , S. * This ... See his

If four

**given**straight lines , intersecting in a point O , be cut by a transversal in thepoints P , Q , R , S , the anharmonic ratio of the pencil OP , OQ , OR , OS , will be

equal to that of the range P , Q , R , S. * This ... See his

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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