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I want to confirm my understanding of the word duco.
According to Wiktionary, it is a third conjugation, irregular short imperative. The examples are:
I understand it is therefore singular, present and first person.
Why is it irregular? The present infinitive is ducere and regular third conjugations have infinitives ending in '-ere'?
Please could someone provide an example of duco being used in a valid sentence?
In Latin a verb has several forms. In Wiktionary you can click the little "More" button to the right of "Conjugation of duco" under the title "Inflection". There you will notice that duco is only one of the many forms.
The word duco means "I lead" (let me choose only one from the list of translations to keep things simple). The word ducere means "to lead". This verb is listed in dictionaries as duco or ducere. There are different forms for different persons, tenses and such.
Here is a simple use example: Te duco si sequi vis. "I lead you if you want to follow."
For a verb like this (third conjugation), you would expect the second person singular present imperative to be duce but it is duc. There is no obvious reason why it is irregular. Only some of the most common verbs have an irregular imperative like this: dicere (to say), ducere (to lead), facere (to do) and ferre (to carry).
Duco is regular in the indicative and subjunctive moods but irregular in the imperative mood.
So you might say, using the indicative,
Dido Æneam in aulam ducit.
Dido leads Æneas into the palace.
If duco took a regular imperative, the singular second-person imperative would be duce. However, since it doesn't, the singular second-person imperative is duc.
So if you were Æneas, you might say
Dido! Me in aulam duc!
Dido! Lead me into the palace!
Good luck with your project!
There isn't much more to add to Joel's and Joonas' posts, but I just wanted to make an additional note about the irregular imperatives. First, ducere, dicere, and facere are only irregular in the imperative singular: duc, dic, fac, but are fully regular in the imperative plural: ducite, dicite, facite.
Ferre, however, is still irregular in the plural, ferte instead of *ferite. It's also irregular in the 2nd/3rd-sing-ind-act (fers/fert), 2nd-pl-ind-act (fertis), and 2nd/3rd-sing-ind-pass (ferris/fertur).
The verbs nolle and esse also have irregular imperatives, which is expected since they're fully irregular verbs: s. noli, s. es, and pl. este. Ire is surprisingly regular in the imperative.
