This article analyzes Galileo's mathematization of motion, focusing in particular on his use of geometrical diagrams. It argues that Galileo regarded his diagrams of acceleration not just as a complement to his mathematical demonstrations, but as a powerful heuristic tool. Galileo probably abandoned the wrong assumption of the proportionality between the degree of velocity and the space traversed in accelerated motion when he realized that it was impossible, on the basis of that hypothesis, to build a diagram of the law (...) of fall. The article also shows how Galileo's discussion of the paradoxes of infinity in the First Day of the Two New Sciences is meant to provide a visual solution to problems linked to the theory of acceleration presented in Day Three of the work. Finally, it explores the reasons why Cavalieri and Gassendi, although endorsing Galileo's law of free fall, replaced Galileo's diagrams of acceleration with alternative ones. (shrink)

: In the concluding pages of his Epistolae duae de motu impresso a motore translato (1642), Pierre Gassendi provides a brief summary of the explanation of the tides found in Galileo's Dialogue over the Two Chief World Systems (1632). A comparison between the two texts reveals, however, that Gassendi surreptitiously modifies Galileo's theory in some crucial points in the vain hope of rendering it more compatible with the observed phenomena. But why did Gassendi not acknowledge his departures from the Galilean (...) model? The present article argues that cautiousness was just one of the reasons that stopped the French priest from turning Galileo's theory into his own theory. He was probably also aware of the fact that Kepler's model of planetary motion, which he endorsed in the Epistolae, could not be reconciled with Galileo's explanation of the tides. In the postumously published Syntagma philosophicum (1658), Gassendi tried to mend this major inconsistency by arguing that Galileo's theory of the tides not only remained valid, but became even more coherent, if one attributed to the Earth an elliptic orbit. But given that in the Syntagma Gassendi officially adhered to the Tychonic system, his effort to reconcile Kepler and Galileo, while already unconvincing by itself, appears completely futile. (shrink)

In the ten years following the publication of Galileo Galilei's Discorsi e dimostrazioni matematiche intorno a due nuove scienze , the new science of motion was intensely debated in Italy, France and northern Europe. Although Galileo's theories were interpreted and reworked in a variety of ways, it is possible to identify some crucial issues on which the attention of natural philosophers converged, namely the possibility of complementing Galileo's theory of natural acceleration with a physical explanation of gravity; the legitimacy of (...) Galileo's methods of proof and of his theory of the composition of continuous magnitudes; and the adequacy of the experimental evidence in favor of his theory.Through his published works and his correspondence, Marin Mersenne contributed in a significant way to each of these discussions. In the following, I shall provide a sketch of Mersenne's multiple engagement with the new science of motion, while trying to account for his growing skepticism concerning Galileo's law of free fall. Whereas in the 1630s, Mersenne still firmly believed in the validity of this law and tried to devise experimental and mathematical proofs in its favor, in the 1640s he developed serious doubts regarding the possibility of constructing an exact science of motion. As we shall see, Mersenne's evolving attitude sheds an interesting light on his views concerning the relation between physics and mathematics.---------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ----------------------------------------------------. (shrink)

Numerical tables are important objects of study in a range of fields, yet they have been largely ignored by historians of science. This paper contrasts and compares ways in which numerical tables were used by Galileo and Mersenne, especially in the Dialogo and Harmonie Universelle. I argue that Galileo and Mersenne used tables in radically different ways, though rarely to present experimental data. Galileo relied on tables in his work on error theory in day three of the Dialogo and also (...) used them in a very different setting in the last day of the Discorsi. In Mersenne's case they represent an important but so far unrecognized feature of his notion of universal harmony. I conclude by presenting a classification of different ways in which tables were used within the well-defined disciplinary and temporal boundaries of my research. In doing so, however, I provide a useful tool for extending similar investigations to broader domains. (shrink)

ABSTRACT. In his Letters on the motion impressed by a moving mover, Gassendi offers a theory of the motion of composite bodies that closely follows Galileo’s. Elsewhere, he describes the motion of individual atoms in very different terms: individual atoms are always in motion, even when the body that contains them is at rest; atomic motion is discontinuous although the motion of composite bodies is at least apparently continuous; and atomic motion is grounded in an intrinsic vis motrix, motive power, (...) while composite bodies simply persist in their state of motion or rest in the absence of outside intereference. Gassendi does not make much effort to explain how his accounts of atomic and composite motion fit together, and it’s difficult to see how they could possible be integrated. My goal is to explain, given this difficulty, why he accepted both the Galilean theory of the motion of composite bodies and the Epicurean theory of atomic motion. (shrink)

: This paper investigates the influence of Galileo's natural philosophy on the philosophical and methodological doctrines of Thomas Hobbes. In particular, I argue that what Hobbes took away from his encounter with Galileo was the fundamental idea that the world is a mechanical system in which everything can be understood in terms of mathematically-specifiable laws of motion. After tracing the history of Hobbes's encounters with Galilean science (through the "Welbeck group" connected with William Cavendish, earl of Newcastle and the "Mersenne (...) circle" in Paris), I argue that Hobbes's 1655 treatise De Corpore is deeply indebted to Galileo. More specifically, I show that Hobbes's mechanistic theory of mind owes a significant debt to Galileo while his treatment of the geometry of parabolic figures in chapter 16 of De Corpore was taken almost straight out of the account of accelerated motion Two New Sciences. (shrink)

: Marin Mersenne was central to the new mathematical approach to nature in Paris in the 1630s and 1640s. Intellectually, he was one of the most enthusiastic practitioners of that program, and published a number of influential books in those important decades. But Mersenne started his career in a rather different way. In the early 1620s, Mersenne was known in Paris primarily as a writer on religious topics, and a staunch defender of Aristotle against attacks by those who would replace (...) him by a new philosophy. In this essay, I would like to examine Mersenne's changing attitude toward Galileo. In the early 1620s, Mersenne lists Galileo among the innovators in natural philosophy whose views should be rejected. However, by the early 1630s, less than a decade later, Mersenne has become one of Galileo's most ardent supporters. How, then, did Mersenne learn to love Galileo? (shrink)