'non-algogenic' originates from English, specifically the construction 'non-' + 'algogenic', where 'algogenic' ultimately stems from Greek 'algos' meaning 'pain' and the suffix '-genic' meaning 'producing'.

'algogenic' was formed from Greek 'algos' (pain) via New Latin/Modern formation with the suffix '-genic' (producing), and in Modern English the negative prefix 'non-' was attached to form 'non-algogenic'.

The root concept originally meant 'producing pain' (algogenic); 'non-algogenic' therefore developed to denote the opposite — 'not producing pain'.