The Mathematics of Isochronism in Galileo: From his Manuscript Notes on Motion to the Discorsi
Mohammed Abattouy
Abstract. This article surveys Galileo’s contribution to the conceptualisation of the problem of isochronism, as his most important input in the study of the oscillation of heavy bodies. We will deal essentially with the mathematical aspects of his various attempts to discover mathematical proofs for his theorems of isochronism, in his early manuscripts (1600-1609), bound in Volume 72 of the Galilean Manuscripts, and in his later two major publications, the Dialogo and the Discorsi. The experimental procedures he implemented in his research will be dealt with as far as they shed light on different aspects of properly mathematical issues of the Galilean analysis of iscohronism. Alternating between the analysis of Galileo’s private manuscripts and the relevant passages in his mature works, we follow the emergence and evolution of Galileo’s theory of the pendulum within his physics of motion, and we witness how his investigation was faced with serious challenges, mathematical and experimental, that he could never overcome completely.
Keywords: Isochronism, Galileo Galilei, theory of the pendulum, law of isochronism, law of length, experiments with pendulum, modern physics, chronometry.