'nonintersection' originates from English, combining the prefix 'non-' (from Latin 'non' meaning 'not') and the noun 'intersection' (from Latin 'intersectio'), where 'inter-' meant 'between' and 'secare' meant 'to cut'.

'intersection' entered English via Latin 'intersectio' (from 'inter-' + 'secare'); the negative prefix 'non-' was available in English, and in modern English these elements were compounded to form 'nonintersection' to denote the absence of intersection.

Initially, 'intersection' referred to the act of cutting between or a point/line of crossing; over time it shifted to the general sense of a crossing or overlap, and 'nonintersection' came to mean simply the absence of such crossing or overlap.