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

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Page viii

Condition for a

Line at Infinity 6 . Equation of the Circumscribing Circle 7 . Equation of the Conic

touching the Three Sides of the Triangle of Reference 8 . Position of the Centre .

Condition for a

**Parabola**Condition of Tangency . Every**Parabola**touches theLine at Infinity 6 . Equation of the Circumscribing Circle 7 . Equation of the Conic

touching the Three Sides of the Triangle of Reference 8 . Position of the Centre .

Page ix

... Point in which a Straight Line , drawn in a given direction through a given Point

of the Conic , meets the Curve again Equation of the Tangent at a given Point

Condition that a given Straight Line may touch the Conic Condition for a

... Point in which a Straight Line , drawn in a given direction through a given Point

of the Conic , meets the Curve again Equation of the Tangent at a given Point

Condition that a given Straight Line may touch the Conic Condition for a

**Parabola**. Page x

Directrix of a

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

EXAMPLES 91 92 CHAPTER V. TRIANGULAR CO - ORDINATES . I. 94 2 .

Directrix of a

**Parabola**To find the magnitudes of the axes of the Conic To find thearea of the Conic . Criterion to distinguish between an Ellipse and an Hyperbola

EXAMPLES 91 92 CHAPTER V. TRIANGULAR CO - ORDINATES . I. 94 2 .

Page xi

Condition for a

EXAMPLES II - 13 . Tangential rectangular Co - ordinates 14 . Tangential polar

Co - ordinates EXAMPLES 125 126 IO . 127 ib . 128 129 130 132 ib . . CHAPTER

VIII .

Condition for a

**Parabola**9 . Circular points at infinity Conditions for a CircleEXAMPLES II - 13 . Tangential rectangular Co - ordinates 14 . Tangential polar

Co - ordinates EXAMPLES 125 126 IO . 127 ib . 128 129 130 132 ib . . CHAPTER

VIII .

Page 36

We may hence deduce the relation which must hold between , ui , v , in order that

the conic may be a bola . For , since the centre of a

distance , its co - ordinates will satisfy the equation as + b + cy = 0 . We hence

obtain ...

We may hence deduce the relation which must hold between , ui , v , in order that

the conic may be a bola . For , since the centre of a

**parabola**is at an infinitedistance , its co - ordinates will satisfy the equation as + b + cy = 0 . We hence

obtain ...

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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