This being clearly understood (participle clause)

[GeneD]

This being clearly understood, Harris gave in his adhesion; and our start was fixed for early Wednesday morning. (from "Three men on the bummel" by Jerome K. Jerome)

I understand, of course, the meaning of the sentence, but what confuses me (from the grammar view point) is this participal clause. Would I be mistaken saying that this clause could be changed into "Having understood this clearly..."? I've looked for some explanation and found the following: "[FONT=british_council]We can use participle clauses when the participle and the verb in the main clause have the same subject" ([/FONT]https://learnenglish.britishcouncil.org/en/quick-grammar/participle-clauses[FONT=british_council]). But is it true for the clause I'm asking about? The clause seems to be passive, but the meaning isn't.

Or wait... It's just come to mind that the clause possibly is passive. It obviously means "The thing we talked over being clearly understood". And at the same time it has its own subject.

Is it somewhat old-fashioned or is it used in modern-day English? And if used, how common is the use of such participle clauses? [/FONT]

 

[Raymott]

It's quite correct. Yes, your two clauses mean the same. It's not old-fashioned, it's not common; it's literary.

"My friend asked me to take care of her pet over the holidays. Imagining it to be a cat or a dog, I consented. However, she then explained, after much evasion, that it was an orangutan. Having understood this clearly [This being clearly understood], I felt I had to decline."

In your version, it's not clear whether it was Harris or someone else who understood something clearly.
"I explained to the students in detail the requirements of the test. These requirements being understood by all the students, I left the room." You couldn't replace this clause with "Having understood these requirements." You could say, "The students having understood these requirements, I left the room." That's grammatical but awkward.