To me it looks like a metal type version of Bembo. The 'r' is characteristic and different from Garamond, which is what I first thought this might be. The very low stem above the crossbar of the 't' also seems like Bembo, but I can see from Monotype's digital version, these features are not identical. I don't think it's a digital font, even though it looks similar to Adobe Garamond. I will stay with Bembo, although I recognize that Monotype's digital Bembo has a number of differences.

This is a joke, right? These are taken from books published by Christopher Plantin in the 16th century. These typefaces don't exist anymore, except at the Plantin Museum in Antwerp.

There are some modern interpretations of them. The best known is Matthew Carter's Galliard.