'Rivulet' is Latin for 'tiny stream' — diminutive of 'rivus' (stream). The smallest flowing water.
From Italian 'rivoletto,' diminutive of 'rivolo' (small stream), itself from Latin 'rīvulus,' diminutive of 'rīvus' (stream, brook), from PIE *h₁reyH- ('to flow, to stream'). The word entered English in the 16th century during the Renaissance absorption of Italian vocabulary. The double diminutive—Latin 'rīvulus' already small, then Italian 'rivoletto' making it smaller still—reflects a pattern of affectionate minimisation common in Romance languages. The PIE root *h₁reyH- also produced
The word 'rival' comes from Latin 'rīvālis' (one who shares the same stream), from 'rīvus' (stream). The original rivals were neighbors who shared access to the same irrigation stream — and since water rights were the most contentious issue in Roman agriculture, people who shared a stream were, almost by definition, in competition. From a shared stream came the concept of competition itself. 'Rivulet' and 'rival' are