For medieval scholars, philosophy was the path to true knowledge about the world, and its proofs consisted of the authority of ancients (as interpreted by Christian theologians) and their techniques of logical argumentation. Questions about the physical nature of the universe and how it functioned belonged to a minor branch of philosophy, called natural philosophy. Natural philosophy was based primarily on the ideas of Aristotle, the great Greek philosopher of the fourth century B.C.E. According to the Christianized version of Aristotle, a motionless earth stood at the center of the universe and was encompassed by ten separate concentric crystal spheres in which were embedded the moon, sun, planets, and stars. Beyond the spheres was Heaven with the throne of God and the souls of the saved. Angels kept the spheres moving in perfect circles.

Aristotle’s views also dominated thinking about physics and motion on earth. Aristotle had distinguished between the world of the celestial spheres and that of the earth — the sublunar world. The sublunar realm was made up of four imperfect, changeable elements: air, fire, water, and earth. Aristotle and his followers also believed that a uniform force moved an object at a constant speed and that the object would stop as soon as that force was removed.

Aristotle’s cosmology made intellectual sense, but it could not account for the observed motions of the stars and planets and, in particular, provided no explanation for the apparent backward motion of the planets (which we now know occurs as planets closer to the sun periodically overtake the earth on their faster orbits). The ancient Greek scholar Ptolemy offered a theory for this phenomenon. According to Ptolemy, the planets moved in small circles, called epicycles, each of which moved in turn along a larger circle, or deferent. Ptolemaic astronomy was less elegant than Aristotle’s neat nested circles and required complex calculations, but it provided a surprisingly accurate model for predicting planetary motion.

The work of Ptolemy also provided the basic foundation of knowledge about the earth. Rediscovered around 1410, his Geography presented crucial advances on medieval cartography by representing a round earth divided into 360 degrees with the major latitude marks. Ptolemy’s work reintroduced the idea of using coordinates of latitude and longitude to plot points on the earth’s surface, a major advantage for long-distance navigation. However, Ptolemy’s map reflected the limits of ancient knowledge, showing only the continents of Europe, Africa, and Asia, with land covering three-quarters of the world. Lacking awareness of the Pacific Ocean and the Americas, Ptolemy vastly underestimated the distance west from Europe to Asia.

These two frameworks reveal the strengths and limitations of European knowledge on the eve of the Scientific Revolution. Overcoming the authority of the ancients to develop a new understanding of the natural world, derived from precise techniques of observation and experimentation, was a monumental achievement. Europeans were not the first to use experimental methods — of which there was a long tradition in the Muslim world and elsewhere — but they were the first to separate scientific knowledge decisively from philosophical and religious beliefs and to accord mathematics a fundamental role in understanding the natural world.