I had asked this question
7 months ago and it was never fully answered (in particular the "how and why [the principle of permanence] has two different definitions" part wasn't answered).
There is a new SE site, History of Science and Math, where I might be more likely to get a full answer. I flagged my question for migration but was told that since my question is more than 60 days old, it can't be migrated. The only way left is to cross-post the question.
Please advise me about what I should do now.