How do I use the word “obtain” together with mathematical formulas?

Until now, I thought that one can use the word "obtain" together with "that", as in

By ... we obtain that a²+b²=c².

(Many mathematicians who like me are not native speakers are doing this!) Now I found two documents saying that "that" doesn't belong here: This Polish site, and the guide of the London Mathematical Society to writing mathematics, which says that "obtain" should usually not be followed by "that".

Now my question: if instead of the above I write

By ... we obtain a²+b²=c².

how do I read that sentence? "We obtain a square plus b square equals c square"? Then it appears that I use "obtain" with the verb "equals", which sounds a bit strange to me.

What would be the correct version?

Obtain cannot take a that clause, so we obtain that is ungrammatical.

You second example is common in technical papers, and treats the equation as a sort of quotation. What you are saying is something like

We obtain "a squared plus b squared equals c squared"

where the grammar inside the quoted string is irrelevant to the main sentence. (Note that the subscript 2 is read squared, not square).

You could achieve a similar effect by saying we obtain the result a squared... or _we obtain the equation a squared ... _.

• Thanks a lot for this explanation! (And also thanks for pointing out the "squared".) Just to make sure I got it right: are you saying the version "we obtain a²+b²=c²" is alright for a technical paper and I don't need to add the phrase "the result" or "the equation"? – Hendrik Vogt Nov 23 '12 at 12:44
• In mathematics, physics, and computer science, at least, "we obtain a²+b²=c²" is fine for a technical paper. (I suspect you are putting "that" in by analogy with expressions such as "we find that a²+b²=c².") Mathematics, physics, and computer science treat equations as part of the sentence, and use grammar and punctuation accordingly. Some disciplines didn't use to treat equations this way—I don't know whether this is still the case. If it is, you might have to put a noun such as "the result" before "a²+b²=c²." – Peter Shor Nov 23 '12 at 13:45
• @Peter: Thank you very much! I'm talking about math here, so it appears I'm on the safe side. (By the way, my analogy was "we infer that a²+b²=c²", and I thought I could use "obtain" as somewhat of a synonym.) – Hendrik Vogt Nov 23 '12 at 14:06
• @HendrikVogt Though drawing or deducing an inference from a series of calculations is essentially the same as getting a result, the two words infer and get behave differently. We infer that ..., but We obtain ... . In case it helps, obtain simply means get, not infer. – Kris Nov 23 '12 at 14:13
• @Kris: Yeah, that helps, thanks. Now I have a German analogy: "get" means "bekommen", and "wir bekommen, dass" is also ungrammatical. – Hendrik Vogt Nov 23 '12 at 15:35