Where does “Gaeilge” come from?

Gaeilge (Irish) comes from Irish Gaedhilge, from Irish Gaedhealg, from Old Irish Goídelc, from Old Irish Goídel, from Old Welsh Guoidel, from Proto-Brythonic guɨðel, from Proto-Celtic wēdus, from Proto-Indo-European widʰu- — forest, wood; tree, beam.

Gaeilge (Irish): the Irish language

Definitions

the Irish language

Ancestry of “Gaeilge”, step by step

Step	Language	Word	Meaning
1	Irish	Gaedhilge	Obsolete spelling of Gaeilge
2	Irish	Gaedhealg	—
3	Old Irish	Goídelc	the Old Irish language
4	Old Irish	Goídel	Gael
5	Old Welsh	Guoidel	wild man, warrior
6	Proto-Brythonic	guɨðel	savage, woodsman
7	Proto-Celtic	wēdus	wild
8	Proto-Indo-European	widʰu-	forest, wood; tree, beam

Every word from Proto-Indo-European widʰu- →Every word from Proto-Celtic wēdus →Every word from Proto-Brythonic guɨðel →