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

Question

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?

Answer 1

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 ... _.