Isidore of Seville, Etymologies 1.38: (Full text on Lacus Curtius)
Prose is speech drawn out and free from the restraint of meter. For the ancients used to call prose productum [drawn out] and straight. Thus, Varro says that in Plautus, the phrase prosis* lectis means ‘read straight through.’ Thus, whatever speech is not contorted by number, but stands straight, is said to be prose, from its drawing forth [producendo] into a straight path.
Others say that prose is so called because it is profuse (profusa), or because it pours forth proruat) and runs on at length, with no limit prescribed to it.
Furthermore, among both the Greeks and the Latins, songs were their chief concern long before prose was. For originally, all things were composed in verse; the pursuit of prose flourished late. Among the Greeks, the first to write prose was Pherecydes the Syrian; among the Romans, Appius Caecus first exercised the composition of prose against Pyrrhus. From that point, others contended in the eloquence of their prose.
*Isidore has conflated prosa with prorsus, meaning “straight onward” or “direct”.
Prosa est producta oratio et a lege metri soluta. Prosum enim antiqui productum dicebant et rectum. Vnde ait Varro apud Plautum “prosis lectis’ significari rectis; unde etiam quae non est perflexa numero, sed recta, prosa oratio dicitur, in rectum producendo. Alii prosam aiunt dictam ab eo, quod sit profusa, vel ab eo, quod spatiosius proruat et excurrat, nullo sibi termino praefinito. Praeterea tam apud Graecos quam apud Latinos longe antiquiorem curam fuisse carminum quam prosae. Omnia enim prius versibus condebantur; prosae autem studium sero viguit. Primus apud Graecos Pherecydes Syrus soluta oratione scripsit; apud Romanos autem Appius Caecus adversus Pyrrhum solutam orationem primus exercuit. Iam exhinc et ceteri prosae eloquentia contenderunt.