Caramuel's arithmetics of any base (Mathesis biceps, 1670): a printed binary table, and a Guarani counting system defended against its own missionary

A Spanish mathematician printed, on an episcopal press in 1670, a table of the numbers 0 to 32 written with two characters, alongside articles on arithmetic by threes, fours, fives, nines and sixties. His argument was that the base is arbitrary - chosen by the inventor, not by nature. He then applied it to a missionary's report that the Guarani could not count past four, and answered that having a different arithmetic is not the same as having none.