What is the meaning and grammar of "as with" in the following sentence:
Symbolic logic is a mathematical model of deductive thought; as with other branches of mathematics it has grown beyond the circumstances of its birth.
From Oxford English Dictionary
Your sentence -
Symbolic logic is a mathematical model of deductive thought; as with other branches of mathematics it has grown beyond the circumstances of its birth.
From what we learned from OED note above we can re-write it as the following -
As far as it (Symbolic logic) is with other branches of mathematics, it has grown beyond the circumstances of its birth.
Or simply -
With other branches of mathematics it has grown beyond the circumstances of its birth.
You can also substitute as with with like in your original sentence.
Is that clear to you now?
[The "as with"] was probably located after a different sentence in a paragraph. For example the sentence before would be something like:
Algebra is a very complex and complicated form of math. As with other branches of mathematics it has grown beyond the circumstances of its birth.
Then in this case the "as with" means "the same thing applies to ......".