This means that one can find another tripple of lines {g,g

To show this, start with the three reflexions on lines {e,e

S

This means that one can find another tripple of lines {g,g

In fact, this case reduces immediately to the previous one by turning the system of the two first lines {e

Next section handles the very same case handled here but relates it to the triangle ABC formed by the three lines {e

Taking into account the fact that the altitudes of ABC are bisectors of the angles of the orthic triangle DEF we find first the image F'' of F under the successive application of reflexions on the sides {F

Join an arbitrary point X with F and the projection G on line FE to form triangle FGX. Then reflect again successively by the above three reflexions to obtain correspondingly the equal triangles {FG'X', F'G''X'', F''HS(X)}. The reflected F''HX* of the last triangle with respect to line FE is a parallel translate of the orginal triangle FGX and this proves the claim.

Given three non-concurrent straight lines L

By the previous discussion T is a glide reflexion and it is a trivial property of every glide reflexion that T

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