'non-intersecting' originates from the prefix 'non-' meaning 'not' and the verb 'intersect' from Latin 'intersectus', where 'inter-' meant 'between' and 'sectus' meant 'cut'.

'Intersect' changed from the Latin word 'intersectus' and eventually became the modern English word 'intersect'.

Initially, 'intersect' meant 'to cut between', but over time it evolved into its current meaning of 'to cross or meet'.