In his Ten Books on Architecture, Vitruvius provides the earliest surviving account of the origins of what we have called, since the Renaissance, the orders of Greek architecture. Vitruvius, however, wrote during the early years of the Roman Empire—some six hundred years after the orders first developed—and his first-hand experience of early Greek architecture must have been limited at best. The numerous Greek treatises on architecture that he had at his disposal and to which he routinely refers in his writings were for the most part relatively late, dating by and large to the Hellenistic period, again, long after the orders began to exist. As a result of archaeological exploration and study undertaken during the last two centuries in Greece, Turkey, and Italy, we find ourselves today in the paradoxical situation that, even after an additional two millennia, we are better positioned than Vitruvius to study and understand the origins of the orders. This is the premise of Barbara Barletta’s interesting book on this subject. The Origins of the Greek Architectural Orders has a straightforward arrangement: six chapters, each of which closes with a succinct summary of its main points and arguments, are organized in relevant pairs. Numerous photographs, line...