In Denes and Keedwell's [book][1] the word "latin" is *not* capitalized, and there seems to be some [precedent][2] [in][3] [the literature][4] for this usage. However, the vast majority of work on the subject capitalizes the term "Latin square."

Indeed, most English dictionaries and computer spell checkers treat the word Latin as a proper noun. To me, this doesn't seem a particularly compelling argument for its usage in mathematics as, for example, neither Merriam Webster nor Dictionary.com contain an entry for the word "quasigroup." 

Perhaps this is a pedantic question, but I have encountered it in personal correspondence several times in the past couple of months. Nonetheless, it may also be worth asking if there is any value to having a consistent convention within the mathematical community. 


  [1]: https://books.google.ca/books/about/Latin_squares_and_their_applications.html?id=W2IPAQAAMAAJ&redir_esc=y
  [2]: https://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i2p45/pdf
  [3]: https://arxiv.org/pdf/1907.08548.pdf
  [4]: https://ajc.maths.uq.edu.au/pdf/71/ajc_v71_p501.pdf