'ligate' originates from Latin, specifically the word 'ligare', where 'ligare' meant 'to bind'.

'ligate' passed into Late Latin/Medieval Latin (e.g. 'ligatus'/'ligare') and was adopted into English via scientific and medical Latin, eventually becoming modern English 'ligate'.

Initially it meant 'to bind' in a general sense; over time it acquired a more specialized medical/biological sense of 'to tie off (a vessel or duct)', while retaining the core idea of binding.