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

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Page ix

... Centre Equation of the Asymptotes Condition for a rectangular Hyperbola

Conditions for a Circle All Circles pass through the same two points at infinity All

Conics , similar and

points ...

... Centre Equation of the Asymptotes Condition for a rectangular Hyperbola

Conditions for a Circle All Circles pass through the same two points at infinity All

Conics , similar and

**similarly**situated to each other , intersect in the same twopoints ...

Page xii

Also into similar and

effected in an infinite number of ways ib . 17 . Any two intersecting conics may be

projected into hyperbolas of any assigned eccentricity ib . 18 . Any two conics ...

Also into similar and

**similarly**situated curves 140 16 . These projections may beeffected in an infinite number of ways ib . 17 . Any two intersecting conics may be

projected into hyperbolas of any assigned eccentricity ib . 18 . Any two conics ...

Page 1

We shall consider a , the distance of a point from the line BC , as positive if the

point lie on the same side of that line as the point A does , negative if on the other

side ; and

We shall consider a , the distance of a point from the line BC , as positive if the

point lie on the same side of that line as the point A does , negative if on the other

side ; and

**similarly**for 7 . It thus appears that the trilinear co - ordinates of any ... Page 2

equations , we get aa + b3 + cy = 2A . Next , suppose P to lie between AB , AC

produced , and on the side of BC remote from A ( fig . 2 ) . Then a will be Fig . 2 .

**Similarly**bB = twice the area of PCA , cy = twice the area of PAB . Adding theseequations , we get aa + b3 + cy = 2A . Next , suppose P to lie between AB , AC

produced , and on the side of BC remote from A ( fig . 2 ) . Then a will be Fig . 2 .

Page 6

44 % ab2c

, – Q. ) + c ( Qz - Q ) ( B.-B. ) } . This is one form of the expression for r . It may also

ke proved in a similar manner that abc g2 447 { a cos A ( an - Qn ) + b cos B ...

44 % ab2c

**Similarly**442 abc 442 " abc Hence pa { a ( B.-B. ) ( y - 7 ) + b ( 7-7 ) ( a, – Q. ) + c ( Qz - Q ) ( B.-B. ) } . This is one form of the expression for r . It may also

ke proved in a similar manner that abc g2 447 { a cos A ( an - Qn ) + b cos B ...

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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