This view of the Baths of Trajan (not, as Piranesi and historians since the 16th century thought, the Baths of Titus) offers a rare elevated perspective on its particular subject as well as time and space.
When we know "better" now, that's always a red flag to me.
Edit: So here's the wiki "explanation", it's somehow even more convoluted than I thought:
Although they were correctly known as the Thermae Traiani throughout the Middle Ages and much of the Renaissance, in the late sixteenth century the ruins of the Baths of Trajan were confused with the nearby Baths of Titus and became known as the Thermae Titiani. Doubt arose as to whether the Baths of Trajan had ever existed at all as an independent structure. Supporters of this theory argued that only the Baths of Titus stood on the Oppian, with the name of Trajan applied to them later because he undertook a restoration. Only in the late 19th century did the archaeologist Rodolfo Lanciani untangle the separate identities of the baths, establishing the Baths of Trajan as a separate, much larger structure than the Baths of Titus.
So, the story is... people knew this was the Baths of Trajan until they suddenly didn't but since they were basically built on top of each other (with the Titus baths being a smaller prototype of sorts) the confusion is understandable? There's a drawing of the plan of the supposed two baths in the link above (which doesn't really match Piranesi's floorplan).
Not sure what's going on here, but something seems off.
