When did the infinitive of purpose arise?

Question

In Classical Latin, purpose would normally be expressed with ut, or ad with a gerund, or a supine with a verb of motion, or numerous other ways.

However, in later and vulgar Latin (most notably the Vulgate Bible), a bare infinitive could be used instead. The most famous example is probably from the apocryphal Acts of Peter: Saint Peter is fleeing persecution in Rome when he meets Jesus, and asks quō vādis, Domine? ("where are you going, Lord?"). Jesus replies, ad Rōmam eō iterum crucifīgī ("I'm going to Rome to be crucified again").

When did this arise, and when did it catch on? To my understanding, it doesn't appear in the vulgar Latin of Plautus, who prefers the supine.

Answer 1

It actually does appear in vulgar Latin. Here's Palmer, The Latin Language 319:

[Infinitives], as we saw, are formally either old datives or locatives and both these cases could express purpose. This function is apparent in the expression dare bibere ... Such infinitives of purpose are especially common in colloquial and poetical texts after verbs of motion: 'turbare qui huc it' (Plt. Bacch. 354); 'eamus visere' (Ter. Phormio 102); 'venerat aurum petere' (Plt. Bacch. 631). This construction was avoided in classical prose but was affected as an archaism by the poets from Lucretius on and by the archaizing prose writers. It survived in the colloquial language and is preserved in Romance.