Application of Desargues' theorem for constructions

Question

I found this interesting document (german) on the internet. On page 8 it says:

"Draw a line segment between two given points only using compass and ruler, while the distance between the two points is larger then the length of the ruler"

Now I have two questions:

1. Has someone heard about this problem and can give an other source?
2. I know there are two versions of Desargues' Theorem, an affine and a projective one. Is the problem stated above an application of the affine or of a projective version?

Any help is appreciated and if more translation is necessary please let me know.

Answer 1

I. No, I haven't heard of this problem, and can give no other source, sorry.
II. According to page 2, the Desargues theorem used in the document is the projective version in the wiki page. (The author of the interesting document employs of the theorem to prove that the point $C$ in the construction actually lies on the line $AB,$ so as to reduce the distance from $\overline{AB}$ to one of $\overline{AC}$ and $\overline{BC}.$)
P.S. Have you read the references in the document? Especially the Reelle projektive Geometrie der Ebene of Coxeter might be quite interesting.
Hope this answers the doubt, at least partially.