I remember my Latin teacher told us Romans numbered their children. Tertius (third), Sextus (sixth) and Octavianus (eighth) are some well known examples. What did those numbers refer to? Was there ever a time when it was common to number all your kids in order, like the oldest kid being called Primus, the second Secundus, the third Tertius and so forth? And when did that stop?
Remarkably, no, and I'll admit I was very startled when I first found out the real reasons. I had always assumed, like you and your teacher, that number-names were nice and systematic. But then one day I started wondering why there are no Romans named Quartus, and so I started looking for some scholarship on the subject. What I found was this:
They're named after months.
First, notice that this only applies to men's names. Women's names show a fuller set of number-names, including Tertia. It's possible that women could be named for the order of birth; we don't know (as far as I know).
Second, notice that in male praenomina, only a few number-names are represented: Quintus, Sextus, and Decimus are the common ones. Septimus exists but is rare and archaic. There are no people with praenomina corresponding to the numbers 1 to 4 until late into the Principate, and mainly in the provinces, especially Celtic areas: that points to a non-Roman origin for those names. The old Roman ones are Quintus, Sextus, and Decimus (and Septimus).
Tertius, which you mention, doesn't appear as a praenomen (first name), only as a cognomen (official nickname). Octavianus does appear, but it's late and it's clearly modelled on the family name Octavius -- an 'eight' number name following the pattern of Quintus et al. would have been Octavus. So these are exceptions.
The general pattern, it turns out, is: there are masculine praenomina and gentiliican (family) names modelled on the months March, and May to December. The praenomina take a plain -us ending, and the gentilician names take an -ius ending. Here's the set:
| Month | Praenomen | Gentilician name |
|---|---|---|
| Martius (March) | Marcus | Marcius |
| Aprilis (April) | -- | -- |
| Maius (May) | Maius | Maius |
| Iunius (June) | Iunius (very rare) | Iunius |
| Quintilis (July) | Quintus | Quinctius |
| Sextilis (August) | Sextus | Sextius |
| September | Septimus (rare, archaic) | Septimius |
| October | -- | Octavius |
| November | -- | Nonius |
| December | Decimus | Decius (Roman), Decimius (Samnite) |
A few notes:
(1) There's reason to infer a very ancient context for the origins of these names. Note that January and February aren't represented, and that some of the names are rare/archaic. It's been suspected since antiquity that an early form of the Roman calendar had just ten months, running March to December (hence Decem-ber = '10th month'), and that January and February were added at some point (very early on). If this is true, it would have to have been in the regal period, centuries before any written records. So the idea of naming people after months -- presumably the month in which they were born -- would have to be at least as early as that. As far as surviving Roman authors are concerned, naming people after months hadn't been a thing for many centuries.
(2) April: the etymology of April is unknown. We don't even know whether it comes from Etruscan or somewhere else. As a result it's not all that surprising that there are no names corresponding to it: it may be a relatively late (but still very old) name. It could well be that in the regal period it had another name, and that another well-known praenomen is based on that lost name. That's speculation, but the point is, the situation around April is completely obscure.
(3) July and August: as you may already be aware, Quintilis and Sextilis -- the basis for the names Quintus and Sextus -- were renamed in the 1st century BCE to their modern names, July and August. This is many centuries after when the practice of naming people after months would have been in use, so there's no expectation of anyone being named after 'July' and 'August' -- of course, with those, it's the other way round: the months were named after people.
(4) The basic idea that number-names are actually month-names is an ancient one. It was proposed by Varro in the 1st century BCE, and it appears he was dead right. The standard modern treatment is Hans Petersen's 1962 article 'The numeral praenomina of the Romans', Transactions and Proceedings of the American Philological Association 93: 347-354 [JSTOR link].
(5) As I mentioned above, Octavus doesn't appear (though Octavianus does); neither does Nonus. We don't have good enough data to explain why.
(6) Not all number-names are month-names: as I mentioned above, we do find names like Tertius and Quartus in Celtic contexts, and Tertia in women's names. As well as these, we get various numbers used in cognomina; and a couple of gentilician names, Petronius and Pomponius, are derived from Oscan forms of the numbers 'four' (pettiur, pitora) and 'five' (pompe).