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

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Page 21

m : n approach to the ratios a : b : c , the less does the denominator of the above

fraction

line ; which is in accordance with the remark made in Art . ( 14 ) . EXAMPLES . 1.

m : n approach to the ratios a : b : c , the less does the denominator of the above

fraction

**become**, and the greater , therefore , the distance from the point to theline ; which is in accordance with the remark made in Art . ( 14 ) . EXAMPLES . 1.

Page 39

For , if they be taken otherwise , the left - hand member of the equation of the

conic will

the conic will degenerate into a straight line , or rather into two coincident straight

...

For , if they be taken otherwise , the left - hand member of the equation of the

conic will

**become**a perfect square , as may be ascertained by substitution , andthe conic will degenerate into a straight line , or rather into two coincident straight

...

Page 40

Taking then the double signs all negatively , and writing for convenience , L , M ,

N , instead of u , v , w , the equation of the conic which touches the three sides of

the triangle of reference

Taking then the double signs all negatively , and writing for convenience , L , M ,

N , instead of u , v , w , the equation of the conic which touches the three sides of

the triangle of reference

**becomes**L'a ? + M * ß * + N ? y - 2 MNBy – 2NLya - 2 ... Page 43

... employment of the equations for the determination of the centre , obtained in

Art . 8 . Thus , let it be required to find the ratios of L , M , N in order that the conic

may

know ...

... employment of the equations for the determination of the centre , obtained in

Art . 8 . Thus , let it be required to find the ratios of L , M , N in order that the conic

may

**become**the inscribed circle . At the centre of this circle we have , as weknow ...

Page 49

Since every parabola satisfies the analytical condition of touching the line aa + b

+ cy = 0 , the required condition

co - ordinates of the centre . Let B , B , be the points in which the conic is cut by ...

Since every parabola satisfies the analytical condition of touching the line aa + b

+ cy = 0 , the required condition

**becomes**a ? 72 C + LT MTN + -0 . 18. To find theco - ordinates of the centre . Let B , B , be the points in which the conic is cut by ...

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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