For us Romanists, I believe the parallel is spiritus (breath) from whence spirit:
1) The vital principle or animating force within living beings.
2) The soul, considered as departing from the body of a person at death.
3) Spirit, The Holy Spirit.
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Which makes me also ponder that literally it would be the Father, Son and Holy Breath.
Correct. We are on the same page. All living things by definition exchange gases (i.e. "breathe"). The ancients knew that intrinsically. That process stops when the living things become dead.