This paper explores the embodied character of mathematical understanding. It supports that the various findings from the fields of psychology, philosophy and pedagogy have enhanced mathematical thinking because mathematics has endorsed the idea that the sensory-motor properties of the human body play a crucial role in mathematical activity. In fact, certain mathematical ideas and axioms are based on sensory-motor experience. More specifically, the research embraces the concept of conceptual metaphor and its role in the formation of mathematical meanings. In this way, the study attempts to link the formal and the intuitive aspects of mathematics. The work of Lakoff & Núñez (2000) is taken into account in order to discuss the Archimedes’ treatise on the quadrature of the parabola (Archimedes' "Method"), within the scope of geometry.