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

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Page viii

... Any Chord of a Conic is divided harmonically by the Conic , any Point , and its

Polar 23 Equation of a Line joining Two given Points . 24 . Equation of the

Tangency .

... Any Chord of a Conic is divided harmonically by the Conic , any Point , and its

Polar 23 Equation of a Line joining Two given Points . 24 . Equation of the

**Tangent**at a given Point 25 . Pole of a given Straight Line . 26 . Condition ofTangency .

Page ix

... meets the Curve again Equation of the

a given Straight Line may touch the ... of a given Point Co - ordinates of the Pole

of a given Straight Line Equation of the pair of

... meets the Curve again Equation of the

**Tangent**at a given Point Condition thata given Straight Line may touch the ... of a given Point Co - ordinates of the Pole

of a given Straight Line Equation of the pair of

**Tangents**, drawn to the Conic ... Page x

Locus of the intersection of two

of a Parabola To find the magnitudes of the axes of the Conic To find the area of

the Conic . Criterion to distinguish between an Ellipse and an Hyperbola ...

Locus of the intersection of two

**Tangents**at right angles to one another . Directrixof a Parabola To find the magnitudes of the axes of the Conic To find the area of

the Conic . Criterion to distinguish between an Ellipse and an Hyperbola ...

Page xi

8 . Definition of Projections 9 . Projection to infinity 10-12 . Any quadrilateral may

be projected , in an infinite number of ways , into a parallelogram of which the

angles are of any magnitude 13 . Projection of

14 .

8 . Definition of Projections 9 . Projection to infinity 10-12 . Any quadrilateral may

be projected , in an infinite number of ways , into a parallelogram of which the

angles are of any magnitude 13 . Projection of

**Tangents**, of Poles , and Polars14 .

Page xii

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

be given , two conics can be drawn If three points and two

four conics can be drawn If two points and three

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

**tangent**be given , two conics can be drawn If three points and two

**tangents**be given ,four conics can be drawn If two points and three

**tangents**be given , four conics ...### What people are saying - Write a review

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### Common terms and phrases

angle angular points Arithmetic asymptotes auxiliary become BOOKS called Cambridge centre Chap chapter chord circle cloth co-ordinates coincide College condition conic conic section considered constant corresponding Crown 8vo curve denoted described determine directrix distance equal equation Examples expressed fixed point focus follows four points given conic given point given straight line gives harmonic Hence hyperbola imaginary line at infinity locus meet move obtain opposite sides pair parabola parallel passing pencil perpendicular plane point of intersection points of contact polar pole positive produced projection proposition prove ratio reciprocal relation represented respect result right angles satisfy Schools second degree seen sides similar Similarly suppose taken tangents term theorem third three points tion touch Treatise triangle of reference values whence writing written