A water drop hollows a stone…

Gutta cavat lapidem non vi, sed saepe cadendo.
A water drop hollows a stone, [not by force, but by falling often]

The main phrase (first part) is from Ovidius (or Ovid, as the English say), Epistulae ex Ponto IV, 10, 5. The second part dates from the Middle Ages. This is what one reads on the internet database ‘List of Latin phrases’. But there is more….

1. Ovidius was not original. He apparently translated an already existing Greek proverb by Choirilos of Samos, an epic poet 5th C B.C.:
πέτρην κοιλαίνει ῥανις ὕδατος ἐνδελεχείῃ.
(Choerilus Epic. Samius, Fragmenta dubia. 330. in: H. Lloyd-Jones and P. Parsons, Supplementum Hellenisticum. Berlin: De Gruyter, 1983: 152)

2. Ovid himsel also expanded on the original, i.e., he added a similis.
Gutta cavat lapidem, consumitur anulus usu.
(… and a ring wears down by wearing it.)

3. And one of the many medieval Anonymous added another example:
Gutta cavat lapidem non vi, sed saepe cadendo. Sic addiscit homo non vi, sed saepe legendo.
(… and so a man learns new things, not by force but by reading a lot)

4. Lucretius (De rerum natura I, 313) once saw the devastating effect of a leaky gutter and wrote:
Stillicidii casus lapidem cavat.
A ‘stilla’ is a drop; ‘‑cidium’ comes from ‘cadere, cecidi, casurus sum’ (to fall); same root as ‘casus’

5. Ovidius returns to the saying once more, in his Ars amatoria (I, 475‑476). He wonders:
Quid magis est saxo durum, quid mollius unda?
Dura tamen molli saxa cavantur aqua
(What is harder than a rock, what softer than water? Nevertheless hard rocks are hollowed out by the the soft water).

Based on a column in Dutch by Bart Mesotten (De Standaard, 28 juni 2002)