A short history of finite continued fractions (from antiquity to the 18th century)

Finite continued fractions are used mainly for approximating rational fractions with large numerators and denominators; in particular, because they give the closest approximations. Such is also their role in the first historical examples. To begin with, they were applied to common reckoning, probably already in Greece (Aristarch), certainly in the beginning of the 17th century (D. Schwenter). Next, towards the end of this same century, to technique, for constructing a planetary mechanism using gear wheels (Huygens). Finally, at the end of the 18th century, to astronomy, with the determination of the intercalation for the civil year (Lagrange).