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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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    Oh, you might be thinking of "scholium," I'm sure I've seen that somewhere. But it's nowhere near universal.2012-11-05

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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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    "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.2012-11-05
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You are looking for "porism".