The term "porism" is an archaic type of mathematical proposition whose historical purpose is not entirely known. It is used instead of "theorem" by some authors for a small number of results for historical reasons.
However, two meanings predominate in nonhistorical usage. The first is "corollary," a usage now mostly superseded by that term itself. The second (which may now be considered the "modern" usage) is, "A proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate, or capable of innumerable solutions" (Playfair 1792). Unfortunately, this definition is slightly inaccurate, because the proposition actually states the conditions, rather than affirming the possibility of finding them.