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The words I want to look at are those that come in series: we have primary, secondary, tertiary; we have unary, binary; we have centenary, bicentenary. We're pretty clear about those ones but rapidly fall into doubt about how to continue the series. The reason is not just that they come from Latin, because it would be quite easy to learn the Latin for 'one' to 'ten' if that's all there was to it: but that Latin had several distinct series of numbers for different purposes. Furthermore, these have got mixed up in the course of creating established English words, so we now have false precedents for creating new ones.

English has two complete series: a cardinal series 'one, two, three, four, ...' and an ordinal series 'first, second, third, fourth, ...'. The first two ordinals are wholly different words, the next one 'third' is irregular but clearly related to 'three', then after that we can see a regular ending -th but still with some irregularities as we go through the numbers. We also have a short series of multiplicatives going 'once, twice, thrice'.

The Latin situation is like this but with four complete series rather than two. I'll give them up to ten, then skip the more complicated ones beyond that, and return to hundred and thousand at the end. And I'll ignore the fact that some of them are declined for case and gender: see Latin numbers for those details.

As well as cardinals, ordinals, and a full set of multiplicatives, Latin has distributives meaning 'one each, two each, three each, ...'.

```       CARDINAL    ORDINAL      DISTRIBUTIVE      MULTIPLICATIVE
1      unus        primus       singuli           semel
2      duo         secundus     bini              bis
3      tres        tertius      terni, trini      ter
4      quattuor    quartus      quaterni          quater
5      quinque     quintus      quini             quinquiens
6      sex         sextus       seni              sexiens
7      septem      septimus     septeni           septiens
8      octo        octavus      octoni            octiens
9      novem       nonus        noveni            noviens
10     decem       decimus      deni              deciens
```

You'll recognize lots of these from various English words and contexts, but will soon find that none of the familiar series are based neatly on any of these. Geologists switched from Tertiary to Quaternary. Mathematicians talk about unary but binary functions (though very occasionally I have seen or heard one with a smattering of Latin trying to talk about singulary functions). Modems have specifications including bis and ter.

Actually I've left out a series, because the above are free-standing words. We also have prefixes, which were used in Latin for forming new words, and the same habits have been borrowed into English: thus uni-, bi-, tri, quadri-, quinqui-, sexi-, septi-, .... To further complicate the English, we also very commonly create scientific words using the corresponding Ancient Greek prefixes: mono-, di-, tri-, tetra-, penta-, hexa-, hepta-, .... It's a fairly simple rule of thumb to use Latin prefixes with Latin roots (e.g. bilingual) and Greek prefixes with Greek roots (e.g. monoglot), but occasionally someone coins a hybrid, like monoplane or monolingual.

Now to turn to centenaries and their cousins centennials and millennia. To clear one spelling confusion out of the way: centenary comes from cent- 'hundred' plus some derivational endings, whereas the ones with double N also contain annus 'year' (with A changing to E in Old Latin). So a centenary relates to a hundred, whereas a centennial relates to a hundred years.

The words for hundred and thousand have their own representatives in all the series (I'm omitting some that aren't relevant):

```       CARDINAL    ORDINAL      DISTRIBUTIVE    MULTIPLICATIVE
100    centum      centensimus  centeni         centiens
200    ducenti                  duceni
300    trecenti                 treceni
400    quadringenti             quadringeni
500    quingenti                quingeni
600    sescenti                 sesceni
700    septingenti              septingeni
800    octingenti               octingeni
900    nongenti                 nongeni
1000   mille       millensimus  singula milia   miliens
```
So the plain word centenary looks like it comes from the distributive. But we don't say ducenary, trecenary, or any of the later ones. What we say is bicentenary, tercentenary, quatercentenary, using multiplicatives of the numbers 1, 2, 3, 4..., as if they're 'twice centenary, thrice centenary'. Well, if we were to follow that pattern logically the next ones would go... oh dear, quinquienscentenary, sexienscentenary? Clearly we don't say those, we just use a mixed bag of Latin number words.

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