Did "quartilis" exist?

Question

In statistics, a point that separates out (a multiple of) 25% of the data set is called a "quartile". Similarly, if it separates out 20% of the data, it's a "quintile", 1% a "percentile", and in general a "quantile".

The first of these seems to come transparently from quartus + -ilis, and the "-ile" ending in English usually comes through French. However, I've never seen such a formation in Latin.

I would normally have attributed this to a later development—except that in the early calendar, the fifth and sixth months were called quintilis and sextilis. This makes me wonder whether there were other adjectives like *quartilis, which were just obscure and/or regularly-formed enough not to appear in L&S.

So: Are adjectives from ordinal + -ilis attested? If so, what did they mean?

Answer 1

There doesn't seem to be any attestation of *quartilis being used in ancient times. I'd imagine you've already checked the PHI Latin Texts corpus and seen that it gives no results.

Logeion, a Latin dictionary and resource lookup tool, has results for tertilis and quartilis, but only from the DMLBS: The Dictionary of Medieval Latin from British Sources. The entry for each word has a single citation in an astronomical context in a postclassical British source.

I found female names ending in -illa, like Quartilla and Secundilla, but I don't think these are related to adjectives ending in -ilis.

This is a bit of an aside, but I found an interesting blog post that says that the praenomina Quintus and Sextus may have originally been related to the month-names Quintilis and Sextilis. It seems that Varro suggested this hypothesis, but it was not an actual custom in his time to name children based on their month of birth, so it's hard for me to evaluate the plausibility of this idea. ("Why are there no Romans named ‘Quartus’?", by Peter Gainsford, 2018 April 16, Kiwi Hellenist)