|A sketch of a retaining wall holding a liquid surface back, which shows that the lateral pressure in the water increases with depth.|
In In c.1545, Niccolo Tartaglia, in his booklet on Jordanus Nemorarius, stated the following:
“The deeper the liquid is, the more it will compress the deeper parts; for they are compressed both by the upper parts [vertical pressure] and by those next to them [lateral pressure].”— Niccolo Tartaglia (c.1545), Jordanus: a Small Treatise
This, supposedly, according to William Middleton (1964), was the first clear statement of the idea of both “vertical pressure” and “lateral pressure” (see: mean girls model) in a liquid, e.g. at different depths.
The following are related quotes:
“Tartaglia was the first to have a clear idea of the ‘vertical’ and ‘lateral’ pressure in a liquid.”— William Middleton (1964), The History of the Barometer (pg. 5) 
1. (a) Tartaglia, Niccolo. (c.1545). Jordanus: a Small Treatise: Correction Study with New Growth Figures (Iordani: Opusculum de ponderositate, Nicolai Tartaleae studio correctum novisque figuris auctum) (abs). Publisher, 1565.
(b) Middleton, William E. (1964). The History of the Barometer (pg. 5). Publisher.
2. (a) Middleton, William E. (1964). The History of the Barometer (pg. 5). Publisher.
(b) Jordanus de Nemore – Wikipedia.
● Niccolo Tartaglia (1565), Mean Girls (2004), and lateral pressure (2019) – Reddit.
● Lateral pressure theory – Wikipedia.