'appropinquate' originates from Latin, specifically the word 'appropinquare', where the element 'ad-/ap-' meant 'to, toward' and 'propinquus' meant 'near'.

'appropinquate' passed into Medieval/Late Latin and occasionally into Early Modern English in forms close to 'appropinquare'/'appropinquate' before becoming a rare/archaic verb in modern English.

Initially it meant 'to draw near or come close'; over time this basic sense has been retained but the word itself became rare or archaic in modern usage.