One of the entertaining and disturbing things about learning languages is finding out how badly people have misrepresented the world to you. Translations of Latin mottos are particularly prone to mishandling, in these sad days when few people learn Latin. Heck, you can make up anything and people will swallow it.
The University of Cincinnati’s motto has long been “Juncta juvant.” It’s also New College in Toronto’s motto. Both universities’ official materials say it means “Strength in Unity.” But where on earth do they get that?
Obviously, there are plenty of noble Latin words for strength: virtus, robor, vis, potestas, fortitudo. And unity is unitas. “Virtus in unitate” would be a perfectly cromulent motto. (Although it does sound very Nazi or Communist or collectivist.) But that’s not it.
“Juncta” means yoked. Hence, joined, joint, together. “Juvant” means “They help”, with connotations of support, service, and pleasing each other. None of this is about strength, and it’s a unity of separate things being joined together. “Those joined together support each other.”
So Washington and Jefferson College (which also uses the motto) is giving a lot better information with its official translation, “Together We Thrive.” (Although that we would make it “Juncta Juvamus.”)
Sometimes, you can understand a translator’s liberties. The University of Wisconsin, Madison, has the unexpectedly religious motto “Numen Lumen”. First of all, it’s two rhyming nouns. In Latin, this usually implies an “is” (though three is usually a list). Second, while “lumen” is easy — it’s just “light, lamp” — “numen” is one of those weird Latin words with a lot of meaning. If you were an ancient Roman, and you went up a hill or down into a hollow, and you felt something holy or scary or beautiful, you would say that you were sensing the “numen” of the place. So “numen” means some sort of indwelling of God. “Numen lumen” is saying that the Divine is the guiding Light. There’s no good way to say this as succinctly as Latin does.
Latin mottoes often include some kind of joke. For example, the older motto of the University of Cincinnati was “Alta petit”, which means “She seeks the heights.” The idealistic reason was that they meant students to strive for high standards. But the joke was that UC was built on some very tall hills.