I made a modest attempt to create a working nb for the original Desargues' Theorem (before included) and I include this new one, however, since I am essentially a beginner in programming with Mathematica, I am not able to make the dashed red/blue lines invisible in the regions where they are not needed (accordingly to the original nb). I'd appreciate to receive some hints on this part and if one can write a shorter and better version of this new code.

Attachments:

K-Desargues'Theorem.nb

A bunch of the functions being used are undefined (Coordinates, Intersections, Sides, etc). I don't know if they were built in when that page of MathWorld was created and are now deprectated, or if there is some other notebook you need to download to get the definitions or if these functions live in some special context that wasn't called out explicitly.