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I know there's a particular word but can not think of it and have been unsuccessful finding it by googling. I want to say "porium" but that doesn't come up when I google.

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I’m not aware of one; I simply call it a corollary to the proof. And in writing it up, I’d simply label it Corollary, assuming that it directly followed the theorem to whose proof it was a corollary. – Brian M. Scott Nov 5 '12 at 21:03
I'd write Corollary (of the proof). – Sigur Nov 5 '12 at 21:06
Oh, you might be thinking of "scholium," I'm sure I've seen that somewhere. But it's nowhere near universal. – Kevin Carlson Nov 5 '12 at 21:07

You are looking for "porism".

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Thanks!!!!!!!!! – Asdf Nov 5 '12 at 21:08

You’re thinking of porism. I’ve never seen it used in normal mathematical writing, though it comes up in works on the history of mathematics.

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IIRC Charles Weibel uses the word in his book on homological algebra. – Mariano Suárez-Alvarez Nov 5 '12 at 21:09
Thanks!!!!!!!!! – Asdf Nov 5 '12 at 21:09
@Mariano: That’s even worse than my using lemmata in my dissertation $-$ just because I could. :-) – Brian M. Scott Nov 5 '12 at 21:10
"Porism" is used in Heath's translation of Euclid - at a quick glance to represent a consequence of a "proposition" or of its demonstration. The best known use of the term "porism" in Mathematics known to me is "Steiner's Porism" - but it has never been obvious to me what the original proposition was of which this might be an obvious consequence. – Mark Bennet Nov 5 '12 at 21:16

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