If you were a student of physics of let's say between 14-20 years old, what textbook would you be using to learn physics from ?
19s century was long. In the second half of it, if I were an English speaking person, I would study Treatise on Natural Philosophy by Willian Thomson and Peter Tait published in 1867. Before that, I would probably study mechanics from some primary source, rather than a textbook. An excellent source is Laplace, Mécanique céleste, 4 vols (translated into English by Bowditch in 1829-39). Or from the works of Lagrange or Hamilton, depending on my preferred language.
George Green (of the Green formula and the Green Function) grew up in Nottingham and had no formal education at the time he made his principal discoveries. Apparently he had access to only one book on mathematics/physics (this was determined by historians who studied the collection of the only library to which he had access). This was Laplace's book, mentioned above.
Here is an interesting morsel about 19th century Cambridge:"Mechanics was an important part of the curriculum. Newton’s version, despite its relaunching by William Whewell against French competitors in the late 1810s, was not necessarily adopted at Cambridge. In the 1840s Whewell also advocated inclusion of engineering mechanics in the curriculum, which is largely ignored in this book". Whewell's own text came out in 1819, and was apparently quite popular since it went through 5 editions by 1836, here is a link to the 5th edition.
"French competitors" no doubt refers to (popularizations of) Lagrange's Analytical Mechanics (1788), "admired for its clarity and structure, this book has been described as a great mathematical classic and a “scientific poem”", according to MAA. A somewhat later entry is Duhamel's Cours de Mécanique, which also went through multiple editions (1845, 1853, 1862). Some of the late 19th and early 20th century texts, including Rankine's and Wright's, are listed here. And here are some from the 18th century, just in case.