On a given line, if two ranges I and II are defined, then we can assign a point on the line to either range.
Consider a projection I → II, where at the same time
A → A'
A' → A
Then {A, A'} are referred to as a [i]conjugate pair.[/i]
If, in a projection two pairs of corresponding points are conjugate, then every pair is conjugate (Desargues). The projection is determined, but what is it? Given conjugate pairs {A, A'}, {B, B'}, and an arbitrary point C on the same line, where is C'?
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Double Point -- Let C and C' coincide: [url]http://www.geogebratube.org/material/show/id/243957[/url]
