The Onstelde-Zee seems to be the source of "Prins te Paard" in the Van de Velde paintings book

Michael Robinson, in his Van de Velde paintings book had called Corstiaen Corstiaenszoon's ship Prins te Paard, and attributed that to Dr. Ballhausen, as I recall. The page in the Onstelde-Zee book from 1654 that I mentioned seems to be about that same ship, which it describes in the old Dutch equivalent of Prins Willem te Paard (Prince William on Horseback). The Prins Willem referred to in this case would seem to be Prins Willem II, husband of Mary Stuart, sister of Charles II and James II. Willem II and Mary were the parents of the "the young prince" Willem III, future husband of James's daughter Mary. Without having access to a good reproduction of the entire drawing of the battle thought to be Dungeness, we really can't be sure what annotation there might be about that ship. I had tentatively accepted the Prins te Paard name, but was somewhat skeptical about it. Witte de With's journal definitely calls that ship simply the Prins, not Prins te Paard. Other documents from 1652 and 1653 also seem to just call the ship Prins. That does not mean that the ship's "real name" might not have been Prins te Paard, or even Prins Willem te Paard, but simply that the usual usage was just "Prins". Sources:

1. Dr. Carl Ballhausen, Der Erste Englisch-Hoellandische Seekrieg 1652-1654, 1923
2. Johan E. Elias, Schetsen uit de geschiedenis van ons zeewezen, Vol.V
3. Jodocus Hondius, Onstelde-Zee, Oft Zee-Daden, 1654
4. Michael S. Robinson, Van de Velde Paintings, Vol.I, 1990
5. Witte de With, journals from 1652 to 1658, Archive E8812 from the Riksarkivet, Stockholm