This dissertation draws attention to reciprocal influences linking the arts and sciences, represented respectively here by two seemingly disparate subjects---Rhetoric and Medicine. Both of these disciplines, I argue, share a long and intersecting history with one another still visible in the fifth- and fourth-century BCE Greece, when they began to develop separately and to be thought of as distinct disciplines. Exploring the historical connections between Rhetoric and Medicine in the Classical period offers us food for thought for bridging the gap between the arts and sciences today because it obliges us to recognize the historical intersections between them, the mutual influence each had upon the other, as well as the acknowledgment of these intersections and these influences by the ancient Greeks. The chapters that follow explore links between Rhetoric and Medicine on practical, professional, and theoretical levels. Following the introduction, chapter two investigates the therapeutic functioning of words in ancient Greece and finds that the influence of medicine on rhetoric extends from the usage of healing words in the Homeric epics through the rhetorical practices of healing in Antiphon, to the influence of medicine on the theory of persuasion in Gorgias. Chapter three explores the influence of medicine on rhetoric as it registers in Plato. The chapter shows that the clear-cut division Plato imposed onto Rhetoric and Medicine breaks down in the Phaedrus and that Plato's project to reframe Rhetoric as a true art borrows heavily from Medicine. While chapters two and three deal with the influence of medicine on rhetoric, the next two chapters turn in the opposite direction to explore the influence that rhetoric exerted on medicine. Chapter four demonstrates the prevalence of rhetorical issues about disciplinarity in the Hippocratic Corpus. Chapter five continues to explore this influence, this time arguing that Hippocratic physicians used rhetoric to craft an identity for themselves vis-a-vis other medical healers of the time. Finally, chapter six shows how the mutual and reciprocal influences between rhetoric and medicine, demonstrated through the previous chapters, can be tapped to pave the way for future possibilities in the contemporary study of Rhetoric and Medicine.