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The declension of the number "duo" (two) looks like the first and the second declension in the nominative ("duo", "du-ae"), genitive ("du-arum", "du-orum") and accusative ("du-os", "du-as", "duo"). However, for dative and ablative, it looks like the third declension ("duo-bus", "dua-bus"). Why this discrepancy?

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The use of the ending -ōbus is exceptional, although not quite unique: we also find ambōbus in place of ambīs (except for in Late Latin). Ambō and duo are clearly closely connected in sense.

As for -ābus, aside from duābus and ambābus, it is found occasionally in cases where it is useful to distinguish a feminine first-declension word from a masculine second-declension word built on the same root: examples in Classical Latin are mainly restricted to deābus and filiābus.

Unlike in those cases, there seems to be no reason why it would be especially useful to distinguish the masculine and feminine genders in the case forms of duo and ambō: other numbers get by fine without making such a distinction. So the use of -bus in the forms of ambō and duo seems to be an unnecessary quirk of declension. I don't have a definite answer for how it came to be.

The derivation of dative and ablative plural forms seems to be one of the more complicated parts of Indo-European historical linguistics, and there's the added complication of dual forms in the case of these words. The different suffixes in Latin virīs vs. duōbus do not seem to be paralleled in Sanskrit, where the cognate words apparently have dative/ablative plural vīrébhyaḥ, dual vīrā́bhyām alongside dative/ablative dual dvā́bhyām. It seems the -īs ending of Latin forms like virīs is sometimes explained as coming from a Proto-Indo-European instrumental or locative plural (Development of nominal endings from PIE to Latin), but this doesn't provide a diachronic explanation for the contrast in Latin between -īs and -ōbus, unless there is some reason this case ending would have been less likely to be generalized for ambō and duo than for other thematic/o-stem/second declension nouns and adjectives. I can't think of such a reason, but someone else who knows more might be able to give a better answer based on comparative data.

Looking at the situation synchronically, I can point out that ambō and duo do not in fact show regular second-declension endings in the nominative, nor, originally, in the accusative: as plural words, the nominative masculine form should end in , and the nominative/accusative neuter form should end in -a, but instead they end in -ō̆. (Duo is also found in the masculine accusative, alongside the regularized form duōs.)

If there was any kind of analogical pressure between the nominative and dative plural forms, it could make some sense to make a paradigmatic comparison between e.g. virī, virīs and duo, duōbus. The first has ī in both the nominative plural and the dative/ablative plural, whereas the second has o~ō in both the nominative plural and the dative/ablative plural. This is nothing more than speculation on my part, though.

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