well, let's go the gasto! sorry, I know Here's the etymology of fart from Merriam-Webster. And, Dr. Bill, there's some Greek roots here, wouldn't'cha know it?
And tsuwm, O Purveyor of Smelly Palindromes, is there anything more on OED?

Main Entry: 1fart
Pronunciation: 'färt
Function: intransitive verb
Etymology: Middle English ferten, farten; akin to Old High German
ferzan to break wind, Old Norse freta, Greek perdesthai, Sanskrit
pardate he breaks wind
Date: 13th century
often vulgar : to expel intestinal gas from the anus