'sate' originates from Latin, specifically the word 'satiāre', where 'satis' meant 'enough' and the verb root meant 'to fill or satisfy'.

'sate' changed from Old French (e.g. 'sacier') and Middle English forms (such as 'saten'/'saten') and eventually became the modern English word 'sate'.

Initially it meant 'to make or become full/enough', and over time it has come to mean more generally 'to satisfy fully' (of appetite, desire, curiosity, etc.).