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Sorry for the simple question, but I last took Latin in 1987 and I don't remember how to make a first-person plural imperative for "cogitare" (or any "are" verbs), and my Google searches are failing me. I've found many sites that conjugate "cogitare" and/or "are" verbs, but they only include the four "standard" imperatives: active singular (cogita), active plural (cogitate), passive singular (cogitare) and passive plural (cogitamini), but I'm pretty sure they are all second person (you) as far as I can tell.

This all started trying to translate "let's think!" or "let's think together!" into Latin for a motto.

Thanks.

Gabe
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Unlike some other Indo-European languages, Latin has no first-person imperatives! And it only barely has third-person ones: it has third-person "second" (or "future") imperatives, but no third-person "first" (or "present") imperatives.

Instead, the first-person plural subjunctive can be used as a "hortatory" ("let's ___!"), which is probably what you want. For cogitāre, this form is cogitēmus, "let's think!".

Draconis
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    To support this, there's this Latin song that's popular on graduations that begins with "Gaudeamus" which translates to "let us rejoice" in the exact same situation OP wants: https://en.wiktionary.org/wiki/gaudeamus – htmlcoderexe Feb 20 '20 at 12:34
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    It might be worth mentioning that this hortatory construction has survived in the Romance languages and it's the standard way to translate the English "let's think" – Denis Nardin Feb 20 '20 at 16:21
  • Thanks @Draconis and others. I think if I had thought about it more, I would have remembered phrases I had to memorize like "venite, adoremus" or "ergo bibamus". Brain cells are not what they used to be. – Gabe Feb 20 '20 at 22:32