Thanks for the information on Pieri which I did not know. Concerning
von Staudt, he has a synthetic proof of the dual of Desargues' triangle
theorem in his "Geometrie der Lage" of 1847, Nr. 87 and Nr. 90 on pages
39 and 41. He projects one of the coplanar triangles to a plane through
the axis of perspectivity different from the given plane, and so on.
No surprise. The dual of Desargues' theorem is, of course, equivalent
to the "primal" one.
Heinz Lueneburg