# Mathematics in Galileo's mechanics

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Nature 'is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it.' So wrote Galileo Galilei in his book *The Assayer *(1623). Galileo spoke for many seventeenth-century naturalists who believed that the natural world was fundamentally mathematical and hence that mathematics was essential to understanding the natural world. This conviction was reflected in the growing use of equations to express theories in natural philosophy, the development of new types of mathematics such as the differential calculus, and the use of measuring instruments such as the thermometer and barometer. These changes did not happen suddenly or easily--they were hotly debated even by proponents of mathematics, and they relied on wider changes in the way people conceptualized space and in the institutions that supported natural inquiry. This seminar focuses on one instance of mathematization--Galileo's mechanics--that became a symbol of a new type of science for contemporaries and historians alike.

### Tasks

Read the Dear chapter for an overview of the rising status of mathematics in early modern natural philosophy. Then read **one** of the two other essential readings, ie. either Koyré or Drake. Think about this question, in general and for Galileo's mechanics: what are the preconditions for the mathematical treatment of nature? In other words, what needs to be in place before one can go about studying the world mathematically?

## Essential reading

Chapter 4: "Mathematics Challenges Philosophy," in Dear, Peter. *Revolutionizing the Sciences*.

Koyré, Alexandre. "Galileo and Plato." *Journal of the History of Ideas *4:4 (1943), pp. 400-428.

Drake, Stillman. "Galileo's Experimental Confirmation of Horizontal Inertia: Unpublished Manuscripts (Galileo Gleanings XXII)." *Isis* 64:3 (1973), pp. 291-305 -- **don't worry too much about the numerical details, just read enough to get the gist of Drake's argument**

## Further reading

#### Mathematics in general

Dear, Peter. *Discipline and Experience: The Mathematical Way in the Scientific Revolution*. Chicago: University of Chicago Press, 1995.

Feingold, Mordechai. *The Mathematicians’ Apprenticeship: Science, Universities and Society in England 1560-1640*. Cambridge: Cambridge University Press, 1984.

Wootton, David. *The Invention of Science*, chapter 5 (The Mathematization of the World)

#### Galileo's mechanics

Baldini, Ugo, "The Academy of Mathematics of the Collegio Romano from 1553 to 1623," in Mordechai Feingold, *Jesuit Science and the Republic of Letters*, 2003

Heilbron, John. *Galileo*. Oxford University Press, 2010 - sections 2.4 and 8.2

Wallace, William. "Galileo's Jesuit Connections and Their Influence on his Science," in Mordechai Feingold, *Jesuit Science and the Republic of Letters*, 2003

Westfall, Richard. *The Construction of Modern Science*, pp. 16-24 - a short introduction to Galileo's mechanics

#### Mechanics - theory

Lindberg, David. *The Beginnings of Western Science* (University of Chicago Press, 1992), pp. 290-316 - on Medieval mechanics and optics

Meil, Domenico Bertoloni. "Mechanics," in CHS3.

Gabbey, Alan. "New Doctrines of Motion," in *The Cambridge History of Seventeeth-Century Philososphy*, vol. 1.

#### Mechanics - practice

Bennett, Jim. "The Mechanical Arts," in CHS3.

Bennett, Jim. “The Mechanics’ Philosophy and the Mechanical Philosophy.” *History of Science* 24: 1 (1986): 1–28.

Johnston, Stephen. “Mathematical Practitioners and Instruments in Elizabethan England.” *Annals of Science* 48.4 (1991): 319.

Henninger-Voss, Mary J. “How the ‘New Science’ of Cannons Shook up the Aristotelian Cosmos.” *Journal of the History of Ideas* 63.3 (2002): 371–397.

#### Optics

Mancosu, Poalo. "Acoustics and Optics," in CH3.

Darrigol, Olivier. *A History of Optics: From Greek Antiquity to the Nineteenth Century*. Oxford: Oxford University Press, 2012.

Lindberg, David C. *Theories of Vision from Al-Kindi to Kepler*. Chicago: University of Chicago Press, 1981.

*New Science*(1537)