This is a pretty elementary concerning the terminology commonly used in Desargues' Theorem from plane geometry (or really, projective geometry).
At least in some representative cases, I totally buy the terminology of two triangles being "perspective from a point," at least in the sense that if I visualize the triangle furthest from the perspective point as the base of a tetrahedron (with the perspective point as a vertex), then the closer of the two triangles is a cross-section of that tetrahedron. Alternatively, I can make it mesh reasonably well in my head with the point of view of taking a triangle in an "object plane" and projecting it on to a "target plane" (or in the language of art, to see a triangle in the distance and to correctly paint a picture of it on my canvas.)
I have no similar picture for the notion of two triangles being "perspective from a line" used in the theorem. Can someone clue me in here? Is there any link to the "painting on a canvas" point of view, or is it just something like the formal dual notion to being perspective from a point?
Thanks for your help.