'curvilinearity' originates from Latin, specifically the words 'curvus' and 'linea', where 'curvus' meant 'bent, curved' and 'linea' meant 'line'.

'curvilinear' was formed in English by combining the combining form 'curvi-' (from Latin 'curvus') with 'linear' (from Latin 'linea'); the noun-forming suffix '-ity' was later added to create 'curvilinearity'.

Initially it meant 'the state or quality of being composed of curved lines'; over time this technical/ descriptive sense has remained largely the same in modern usage.