'inadvertently' originates from Latin, specifically the word 'inadvertentem,' where 'in-' meant 'not' and 'advertentem' meant 'turning the mind to.' 'Establish' originates from Old French, specifically the word 'establir,' where 'es-' meant 'out' and 'stabilire' meant 'to make stable.'

'inadvertently' changed from the Latin word 'inadvertentem' and eventually became the modern English word 'inadvertently.' 'Establish' transformed from the Old French word 'establir' and eventually became the modern English word 'establish.'

Initially, 'inadvertently' meant 'not turning the mind to,' but over time it evolved into its current meaning of 'unintentionally.' 'Establish' initially meant 'to make stable,' and this meaning has largely remained the same in modern usage.