The art historian Heinrich Wölfflin defines a range of formal characteristics – his famous "fundamental concepts" or "principles" of art history – with which he describes the Classical and Baroque styles. Aside from their historical coincidence in these styles, Wölfflin thought that the 'Classical' concepts had some special affinity, or "rational" quality binding them together, as did the 'Baroque' concepts. Equally, he believed, to combine 'Classical' and 'Baroque' concepts would be to combine "contradictory" tendencies. This paper explores what it is that link the concepts into Classical and Baroque groupings, and examines what happens when 'Classical' and 'Baroque' concepts appear together. Wölfflin barely touched on this at all, partly since from his point of view such combinations of his concepts obscures rather than illuminate the grand movement between Classical and Baroque which he saw as central to art history. Indeed, reading his Principles of Art History, one might have the impression that they do not exist; but they do, having a presence throughout post-Renaissance European art. I argue, that applying Wölfflin’s concepts to these works illuminates them in significant and unexpected ways.