The first appearance of the set of rational numbers of which I am speaking was in James Bernoulli's Ars Conjectandi. This work was published in 1713, eight years after the death of its author. In the 2nd chapter, Bernoulli deals with permutations and combinations.
Proceedings of the Iowa Academy of Science
©1950 Iowa Academy of Science, Inc.
McClenon, R. B.
Proceedings of the Iowa Academy of Science, 57(1), 315-319.
Available at: https://scholarworks.uni.edu/pias/vol57/iss1/39