Q describes a second conic as P varies on c.

The result can be stated in a way resembling the Maclaurin's construction of conics (see Maclaurin.html ):

If the triangle PEQ has the properties:

(i) Its side-lines pass through three fixed points {A,B,C} lying on a line M,

(ii) One vertex (E) moves on a fixed line L,

(iii) A second vertex (P) moves on a conic c,

then its third vertex moves also on a conic c'.

The proof follows easily by defining an appropriate projectivity F, and obtaining c' as the image F(c). The projectivity is uniquely defined by the properties:

1) F fixes all points of line L and also point A,

2) F maps point B to C.

It follows that line BE maps under F to line CE and point P maps to Q.

MaclaurinLike2.html

Perspectivity.html

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