Meet, meet, and mete

Greetings all,

I'm trying to unravel a bit of a linguistic matter and hope some of
you might have some advice for me.
I was looking at a few terms on the AHDIER website:

Meet (1) = "To come upon by chance or arrangement." and saw it was
derived from Middle English meten; originally from Old English mētan.

Meet (2) = "Fitting; proper" seems to derive from Middle English
mete, from Old English gemāēte. See med- in Appendix I.

Mete = "To distribute by or as if by measure; allot; To measure.
From the Middle English meten, from Old English metan. See med- in
Appendix I.

Does this mean that while mete and meet(2) have the same root, the
two forms of "meet" come from different roots?

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I was told the term mæþel (maethel) "assembly, council," derives from
root of mētan "to meet". It seems to make sense well enough.

It would likewise seem that the term Metod "Measurer", stems from
mete (and thus med-).

I assume that maethel and metod have no shared root?


My thanks for any light you can shine on the situation.
Sincerely,
Aydan