Q:

Should the "L" in the term latin/Latin square be capitalized?

In Denes and Keedwell's book the word "latin" is not capitalized, and there seems to be some precedent in the literature 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 Miriam 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. 

A:

English adjectives that derive from proper nouns are usually capitalised. However, over time, such an adjective can lose its capitalisation provided that it sufficiently departs from its origins in the speaker's mind. 
The word 'latin' derives from the central western Italian region of Latium but its mathematical meaning has little to do with Latium, so it seems sensible to de-capitalise it, much like the term 'roman' in 'roman numerals'.

