Swinging and Rolling: Unveiling Galileo’s Unorthodox Path From a Challenging Problem to a New Science

Dordrecht: Springer Verlag (2019)
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Abstract

This volume explores the reorganisation of knowledge taking place in the course of Galileo's research process extending over a period of more than thirty years, pursued within a network of exchanges with his contemporaries, and documented by a vast collection of research notes. It has revealed the challenging objects that motivated and shaped Galileo's thinking and closely followed the knowledge reorganization engendered by theses challenges. It has thus turned out, for example, that the problem of reducing the properties of pendulum motion to the laws governing naturally accelerated motion on inclined planes was the mainspring for the formation of Galileo's comprehensive theory of naturally accelerated motion.

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9789402415926   9402415920   9789402415940

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10.1007/978-94-024-1594-0
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Appendix: Documents

Il nostro auttore molto raggionevolmente dice, quella non essere una attrattione, ma conversione più tosto, nascendo dalla virtù d’una et dell’altra, che vogliono essere situate in un certo muodo insieme, perilchè il più desiderato muodo di situarsi è quello quando per li poli: imperochè fa l’asse u... see more

Appendix: Folio Pages

The content of those folios upon which the interpretation presented in this book substantially rests is presented in full and discussed exhaustively in this appendix.

Conclusion: The Emergence and Early Evolution of Galileo’s New Science of Motion

The chapter summarizes the clear-cut, firmly source-based account of how Galileo’s new science of naturally accelerated motion emerged. In 1602, a challenging similarity Galileo perceived between what he held to be true concerning pendulum motion on the one hand and accelerated motion on inclined pl... see more

Toward a New Science: Axiomatization and a New Foundation

The chapter discusses Galileo’s attempt to provide his new results concerning the pheno-kinematics of naturally accelerated motion—his new propositions concerning the regular relations between spaces traversed and the corresponding times elapsed in motions of this type—with a foundation. Providing h... see more

Toward a New Science: Gathering Results and the Rise and Demise of a Dynamical Foundation

The chapter discusses how around 1602, and in any case before 1604, Galileo started to collect and systematize the results he had obtained while pursuing his challenging research program on swinging and rolling. The folios he used for this work all share the same watermark showing a small star with ... see more

Whatever Happened to Swinging and Rolling: Faint Echoes and a Late Insight

Confronted with overwhelming problems, in or shortly after 1602, Galileo abandoned his ardent investigation into the relation of swinging and rolling without, however, entirely giving up on his approach. The fundamental idea of his early research, namely, to approximate motion along an arc by motion... see more

Toward a Foundation: The Ex Mechanicis Proof of the Law of Chords

In a letter to Guidobaldo del Monte written in November 1602, Galileo mentioned having found a proof for the so-called law of chords, i.e. the statement that fall along any chord inscribed in the same circle and sharing either its apex or nadir is completed in equal time. The proof alluded to in the... see more

Accumulating Insights: The Problem of Motion Along Broken Chords Driving Conceptual Development

The chapter discusses how Galileo’s attempt to approximate motion along an arc by naturally accelerated motion along paths composed of a series of inclined planes, in or around 1602—and thus, as he believed, in due course pendulum motion—bestowed him with a number of new results. These results were ... see more

Swinging and Rolling Revisited: Motion Along Broken Chords and the Pendulum Plane Experiment

Galileo’s early investigations into the relation of swinging and rolling had led him to the understanding that the time to fall along a polygonal path should ever the closer approach the time to fall along the arc, which he believed was the same as the time to swing along the same arc, the closer th... see more

Squaring the Pendulum’s Arc: Motion Along Broken Chords

The chapter deals with Galileo’s considerations regarding motion along polygonal paths inscribed into an arc that have been preserved in the Notes on Motion. Galileo’s approach was motivated by the assumption that fall of a heavy body along a concave surface supported from below was kinematically eq... see more

Sparking the Investigation of Naturally Accelerated Motion: The Pendulum Plane Experiment

Based on the experimental record preserved in the Notes on Motion, the chapter reconstructs and discusses an experiment which, thus far, has been almost completely overlooked. Galileo timed the swinging of a pendulum as well as the rolling of a ball down along a long, gently inclined plane. From the... see more

A Glimpse at a Challenging Research Agenda: Galileo to Guidobaldo del Monte in 1602

In November 1602, Galileo wrote a letter to his friend and patron Guidobaldo del Monte in which he outlined his current work. This letter has received particular attention as it provides the first explicit evidence that Galileo had returned to the question of the fall of heavy bodies along inclined ... see more

Before Natural Acceleration

By way of introduction, the chapter considers aspects of Galileo’s considerations regarding motion and mechanics prior to his conceptual shift toward the assumption that motion of fall is naturally accelerated. The aspects discussed have been selected for the relevance they assumed when, from 1602 o... see more

Introduction

This book sets out to demonstrate how around 1602, the exploration of a challenging similarity that Galileo perceived to hold on a phenomenological level between the swinging of pendulums and the rolling of heavy bodies down along inclined planes, led him to new insights, which he successively trans... see more

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