Closely Related. With few exceptions, mathematics and astronomy were closely related in the ancient writings on science. From the first century B.C.E. and throughout the Roman Empire, learning, teaching, and practical application was exegetical, that is, dispersed through the interpretation of texts, often through easily understood handbooks. Mathematics was not an isolated pursuit but was considered a part of what a learned person should know. Cicero (On the Orator 1.10, 3.127), for example, claimed that mathematics was an exact, abstruse, and obscure field, but one that an educated person could master, many scholars having obtained perfection in its study. Far from mastering mathematics, the Romans did not indulge in its study in depth, and their contributions to it were more superficial than profound.

Three Distinct Categories. Early Romans knew well the celestial signs—those that told the best times to...