Modern historical linguists often make use of reconstructions: that is, they posit a form of a word that – at least in theory – actually existed at some point in history, even though no language actually preserves exactly that form. Thus, for example, behind the Latin word frāter ‘brother’ lies a form *bhrātēr (an asterisk is used to mark forms which are posited in this way). We can get back to these forms by means of a process called the comparative method, essentially drawing, in a principled way, on comparisons between forms within individual languages (‘internal reconstruction’) and across related languages (‘external reconstruction’).
The scientific approach to reconstructions properly started in the 19th century, but the idea that words were descended from other words was already well established in ancient times. I’ve only recently discovered that the idea of a reconstruction also existed then. Quite a bit of work has been done on Varro in particular, who was a first century BC Roman antiquarian and grammarian: he says things like “‘pallia’ … ‘parilia’ primo dicta”, “pallia (cloaks) were previously called parilia“. But other grammarians did it too, so, for example, Marius Victorinus, in the 4th century AD, says “‘cluaca’, quasi ‘conluaca’”, ‘‘cluaca (sewer), as if conluaca”. Although they weren’t consistent, the grammarians often used quasi, ut or uelut ‘as if’ rather as we would use an asterisk, to mark the reconstructed forms.
They also discovered external reconstruction, so Marius Victorinus notices that d and l in Latin and Greek seem to correspond: “est et communio cum Graecis: nos ‘lacrimae’, illi δάκρυα, ‘olere’ ὀδωδέναι, ‘meditari’ μελετᾶν”, “And there is a relationship with Greek words: we say lacrimae (tears), they say δάκρυα, we say olere (smell), they say ὀδωδέναι, we say meditari (consider), they say μελετᾶν”.
Latin grammarians are often rather looked down on for their outlandish etymologies, and if you read through Varro or other authors, you will certainly find some things that will make you raise your eyebrows. But I think it’s pretty impressive that they had come up with the idea of reconstructing earlier stages of the language, and had noticed consistent relationships between Latin and Greek. It’s also important for classicists nowadays to be aware that this kind of thing is going on in these authors, because they often preserve old forms which aren’t found in any of our extant literature – but we need to be aware that some of these may be (sometimes considerably wonky) ‘reconstructions’ rather than words which definitely existed.