In every period, Byzantine education was essentially based on the study of the trivium and quadrivium, a program inherited from late antiquity. Educated Byzantines clearly distinguished between astronomy and astrology, the former being concerned with the theoretical study of celestial events, whereas the latter functioned as a practical art. Byzantine treatises were extremely influential in the musical theory of the Renaissance. The sources of Byzantine geography were also of ancient vintage, authors such as Strabo, Pausanias, Ptolemy, and the so-called minor geographers collected in manuscripts of the ninth and tenth centuries. Byzantine scholars made a few contributions to optics and mechanics, both regarded as mathematical sciences. Byzantine alchemy is represented by three main tendencies: to preserve the heritage of Alexandrine alchemy and its commentators; a concern for combining this traditional culture with contemporary elements; and the integration of alchemical chapters. Botany and zoology were less systematically cultivated in Byzantium than the exact sciences.