'accidentally-demonstrated' originates from the combination of 'accidentally' and 'demonstrated', where 'accidentally' comes from Latin 'accidentalis', meaning 'happening by chance', and 'demonstrated' from Latin 'demonstratus', meaning 'pointed out'.

'accidentalis' transformed into the Old French 'accidental', and 'demonstratus' into the Old French 'demonstrer', eventually forming the modern English 'accidentally-demonstrated'.

Initially, 'accidentally' meant 'by chance', and 'demonstrated' meant 'shown or proven'. The combined term retains these meanings, indicating something shown by chance.