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

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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 3

Any

between two coordinates , ß and y for example , and this may be made homoaa +

bB + oy geneous in a , b , y by multiplying each term by 24 raised to a suitable ...

Any

**locus**may be represented , as in the ordinary system , by means of a relationbetween two coordinates , ß and y for example , and this may be made homoaa +

bB + oy geneous in a , b , y by multiplying each term by 24 raised to a suitable ...

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B The property of the straight line , which we shall make the basis of our

investigation , is , that it is the

that the sum of the areas of the triangles PAQ , PAR is constant . Let AQ = 9 , AR

= r , then ...

B The property of the straight line , which we shall make the basis of our

investigation , is , that it is the

**locus**of a point which moves in such a manner ,that the sum of the areas of the triangles PAQ , PAR is constant . Let AQ = 9 , AR

= r , then ...

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... and let f , g , h be the co - ordinates of any fixed point D on the

equation , a , b , u those of any point P. Draw DE , PM perpendicular to AC , DF ,

PN perpendicular to AB . Also draw Dm , Dn , perpendicular respectively to PM ,

PN .

... and let f , g , h be the co - ordinates of any fixed point D on the

**locus**of theequation , a , b , u those of any point P. Draw DE , PM perpendicular to AC , DF ,

PN perpendicular to AB . Also draw Dm , Dn , perpendicular respectively to PM ,

PN .

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

represent . This can only be true when that

co - ordinates of the point of intersection of two given straight lines . Let the

equations ...

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

**locus**P mayrepresent . This can only be true when that

**locus**is a straight line . 9. To find theco - ordinates of the point of intersection of two given straight lines . Let the

equations ...

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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