The Classical World and the Middle Ages wrestled with the cause of the tides for centuries. Although one early scholar (Alpetragius, who flourished in the late 1100s) felt it was caused by some general motion of the world/celestial spheres that ran from east to west, most others (such as Bede and Gerald of Wales) felt it had a stronger connection to the movement of the Moon.
Alpetragius died in 1204, and his theory on the motion that caused the tides was translated into Latin by Michael Scot. This brought it to the attention of Robert Grosseteste (c.1175-1235), who had an explanation for the tides that relied on his theories of light. (The following is from the Questio de fluxu et refluxu maris, attributed to Grosseteste, although that attribution is disputed.)
Remember that there was no working theory of gravity yet; just a feeling that substances could be heavier or lighter depending upon their composition and gravitate (see? in this enlightened age, the concept of gravity pervades even our language) toward like substances: solids fall to earth; liquid (containing more of the element of water) flows to a lower spot to find its kind; fire yearns upward through air, because fire is even "lighter" than air.
For Grosseteste, light imparted force. Rays of light could carry with them the power to generate heat, for instance (see his theory on the sun). He postulated that, when the Moon rose above the horizon, its rays impressed against the waters and pushed them ahead of it, toward the west. This was not as simple and direct as a physical object pushing against water, and so water didn't rush to the shore as soon as the Moon rose. The rays of the Moon started pushing against the sea closest to it, pushing that water toward the observer. When the Moon was overhead, its rays had pushed as much water as it could at that time. Once the Moon passed the zenith and was over land, then the waters started to recede. The Moon then passes west and under the earth, at that point causing (somehow) the tides again.
Grosseteste admits that we don't know everything about this process, and my summary is a radical simplification of his detailed analysis. He notes the changes in tides as the Moon changes its declination, and theorizes that the Sun also "helps" the Moon in some manner.
For more detail, find the Question on the flow and re-flow of the sea (available in Isis, Vol. 57, No. 4 (Winter, 1966), pp. 455-474 in an article by Richard C. Dales) and enjoy.