grammar - そういうふうに meaning

At the start of the book (no previous context) the teacher asks this question:

「ではみなさんは、そういうふうに川だといわれたり、乳の流れたあとだといわれたりしていたこのぼんやりと白いものがほんとうはなにかご承知ですか。」
Well everyone, this vague white thing which has been called a river and has been called a trail of flowing milk, do you know what it really is ?

I'm unsure about how the ending of this sentence works (italics) but I'll ask a separate question for that.

For this question, I don't understand the meaning of そういうふうに. Literally I think it means "in that kind of way" but I can't make such a translation work in this sentence.

Answer

"in that kind of way" or "like that/like those" are feasible translations for そういうふうに. We can (if it makes sense to you) understand it as "as in examples mentioned above" in this sentence.

If it's still unclear, let's consider the context. The teacher has apparently been giving some lecture before asking the question. S/he is talking about "ぼんやりと白いもの" and mentions about it having been called a river or a trail of milk. Most likely, s/he has just told their students about how the thing was believed to be milk in certain part of the world and a river in another, and this is what 「そう」いうふうに refers to.

Other examples:

「そういうふうに力を入れるんじゃねえといったら、わからんやつだな。」 (source) -- Don't put too much power like that (as you are doing).

…景色のよいところで食うことが望ましい。叶わぬまでも、なるべくそういうふうにする心がけが必要である。(source) -- to try to meet these conditions (mentioned above)

そういうふうに考えてみると -- thinking that way, or when following these thoughts