Apud is a Latin preposition that originally meant "by," "with," "near," "at the home of," and so on, with dozens of secondary connotations that you may explore at the online Lewis & Short if you are so inclined.
In English, apud has developed a specialized meaning that you will encounter only in very specific types of academic footnotes.
In many cases (more than you think, much more), an important ancient document does not survive on its own, but only as a quotation within another ancient document. For example, no complete book of Sappho's poetry is extant, despite Sappho's popularity both in antiquity and in modernity. In fact, only one poem survives in its entirety; the rest of her oeuvre is fragmentary.
Sappho was considered such a brilliant poet, however, that many ancient writers quoted her. Sometimes they weren't even talking about the poetry as such; several of her poems are only known through quotations in tedious academic books about grammar or syntax. It would be like if the only reference we had to a Shakespeare sonnet was buried in an old encyclopaedia entry about the comma.
Modern historians who want to cite a text that only survives within another text will use apud to signal that the quotation is indirect. For example, since Fragment 31 survives only in an essay by Longinus, a footnote to this poem might read "Sappho apud Longinus." In this context, apud means something like "according to."
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