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

### From inside the book

Results 1-5 of 38

Page vii

Distance from a Point to a Straight Line

Definitions The Anharmonic Ratio of a Pencil is equal to that of the range in

which it is cut by any Transversal ib . Definition of an Harmonic Pencil 25 . 20 21 .

Distance from a Point to a Straight Line

**EXAMPLES**19 . ANHARMONIC RATIO .Definitions The Anharmonic Ratio of a Pencil is equal to that of the range in

which it is cut by any Transversal ib . Definition of an Harmonic Pencil 25 . 20 21 .

Page viii

... 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 of Tangency . Condition

for a Parabola . 27 . Co - ordinates of the Centre

19 .

... 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 of Tangency . Condition

for a Parabola . 27 . Co - ordinates of the Centre

**EXAMPLES**43 45 48 49 ib . 18 .19 .

Page ix

Pascal's Theorem

CONIC REPRESENTED BY THE GENERAL EQUATION OF THE SECOND

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

Line ...

Pascal's Theorem

**EXAMPLES**65 66 ib . IO . II . ib . 68 70 CHAPTER IV . ON THECONIC REPRESENTED BY THE GENERAL EQUATION OF THE SECOND

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

Line ...

Page x

Criterion to distinguish between an Ellipse and an Hyperbola

CHAPTER V. TRIANGULAR CO - ORDINATES . I. 94 2 . Definition of the

Triangular Co - ordinates of a Point Formulæ relating to Straight Lines Formulæ

relating ...

Criterion to distinguish between an Ellipse and an Hyperbola

**EXAMPLES**91 92CHAPTER V. TRIANGULAR CO - ORDINATES . I. 94 2 . Definition of the

Triangular Co - ordinates of a Point Formulæ relating to Straight Lines Formulæ

relating ...

Page xi

Circular points at infinity Conditions for a Circle

rectangular Co - ordinates 14 . Tangential polar Co - ordinates

126 IO . 127 ib . 128 129 130 132 ib . . CHAPTER VIII . ON THE INTERSECTION

...

Circular points at infinity Conditions for a Circle

**EXAMPLES**II - 13 . Tangentialrectangular Co - ordinates 14 . Tangential polar Co - ordinates

**EXAMPLES**125126 IO . 127 ib . 128 129 130 132 ib . . CHAPTER VIII . ON THE INTERSECTION

...

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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