This study situates Ptolemy's philosophy within the second-century milieu of Middle Platonism and the nascent Aristotelian commentary tradition. It focuses on Ptolemy's adaptation and application of Aristotle's tripartite division of theoretical philosophy into the physical, mathematical, and theological. In Almagest 1.1, Ptolemy defines these three sciences, describes their relations and objects of study, and addresses their epistemic success. According to Ptolemy, physics and theology are conjectural, and mathematics alone yields knowledge. This claim is unprecedented in the history of ancient Greek philosophy.Ptolemy substantiates this claim by constructing and employing a scientific method consistent with it. In Almagest 1.1, after defining the theoretical sciences, Ptolemy adds that, while theology and physics are conjectural, mathematics can make a good guess at the nature of theological objects and contribute significantly to the study of physics. He puts this claim into practice in the remainder of his corpus by applying mathematics to theology and physics in order to produce results in these fields.After the introductory chapter, I present Ptolemy's philosophy and practice of the three theoretical sciences. In Chapter 2, I examine how and why Ptolemy defines the sciences in Almagest 1.1. In Chapter 3, I further analyze how Ptolemy defines mathematical objects, how he describes the relationships between the tools and branches of mathematics, and whether he demonstrates in the Harmonics and Almagest that he believed mathematics yields sure and incontrovertible knowledge, as he claims in Almagest 1.1. In Chapter 4, I present Ptolemy's natural philosophy. While in Chapter 2 I discuss his element theory, in Chapter 4 I focus on his physics of composite bodies: astrology, psychology, and cosmology as conveyed in the Tetrabiblos, On the Kriterion, Harmonics, and Planetary Hypotheses. I do not devote a chapter to theology, as Ptolemy refers to this science only once in his corpus. Therefore, I limit my analysis of his definition and practice of theology to Chapter 2. In the concluding chapter, I discuss Ptolemy's ethical motivation for studying mathematics. What emerges from this dissertation is a portrait of Ptolemy's philosophy of science and the scientific method he employs consistently in his texts.