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

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Page vii

through Two given Points ib . Equation of a Line passing through the

the ...

**Point of Intersection**of Two Straight Lines Equation of a Straight Line passingthrough Two given Points ib . Equation of a Line passing through the

**Point of****Intersection**of Two Given Straight Lines 13 Condition that Three Points may lie inthe ...

Page x

Locus of the

of a Parabola To ... Definition of the Triangular Co - ordinates of a

relating to Straight Lines Formulæ relating to Conics 95 3 : 96 CHAPTER VI .

Locus of the

**intersection**of two Tangents at right angles to one another . Directrixof a Parabola To ... Definition of the Triangular Co - ordinates of a

**Point**Formulærelating to Straight Lines Formulæ relating to Conics 95 3 : 96 CHAPTER VI .

Page xi

Circular

rectangular Co - ordinates 14 . Tangential polar Co - ordinates EXAMPLES 125

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

...

Circular

**points**at infinity Conditions for a Circle EXAMPLES II - 13 . Tangentialrectangular Co - ordinates 14 . Tangential polar Co - ordinates EXAMPLES 125

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

**INTERSECTION**...

Page xii

The anharmonic ratio of any pencil or range is unaltered by projection 142 Any

two lines , which make an angle A with each other , form with the lines joining the

circular points at infinity to their

The anharmonic ratio of any pencil or range is unaltered by projection 142 Any

two lines , which make an angle A with each other , form with the lines joining the

circular points at infinity to their

**point of intersection**a pencil of which the ... Page 12

Hence , the ratio of Pm to Pn is constant , whatever point on the locus P may

represent . This can only be true when that locus is a straight line . 9. To find the

co - ordinates of the

equations ...

Hence , the ratio of Pm to Pn is constant , whatever point on the locus P may

represent . This can only be true when that locus is a straight line . 9. To find the

co - ordinates of the

**point of intersection**of two given straight lines . Let theequations ...

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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