Where does “Eairdsidh” come from?

Eairdsidh (Scottish Gaelic) comes from English Archie, from English Archimedes, from Latin Archimēdēs, from Ancient Greek Ἀρχιμήδης, from Ancient Greek μήδεα, from Ancient Greek μέδω, from Proto-Indo-European mēd-, from Proto-Indo-European med- — to measure; to give advice; healing.

Ancestry of “Eairdsidh”, step by step

Step	Language	Word	Meaning
1	English	Archie	also used as a formal given name
2	English	Archimedes	A large lunar impact crater on the eastern edges of the Mare Imbrium
3	Latin	Archimēdēs	Archimedes
4	Ancient Greek	Ἀρχιμήδης	in particular, the 3rd century mathematician Archimedes of Syracuse
5	Ancient Greek	μήδεα	counsel, plan, art, prudence, cunning; male...
6	Ancient Greek	μέδω	to protect, rule over
7	Proto-Indo-European	mēd-	to measure
8	Proto-Indo-European	med-	to measure; to give advice; healing

Every word from Proto-Indo-European med- →Every word from Proto-Indo-European mēd- →Every word from Ancient Greek μέδω →