Firenze University Press www.fupress.com/substantia Dissecting with Numbers: Mathematics in Nicolaus Steno’s Early Anatomical Writings, Citation: N. Castel-Branco (2021) Dis- secting with Numbers: Mathematics 1661-64 in Nicolaus Steno’s Early Anatomi- cal Writings, 1661-64. Substantia 5(1) Suppl.: 29-42. doi: 10.36253/Substan- tia-1276 Nuno Castel-Branco1 Copyright: © 2021 N. Castel-Branco. This Department of History of Science and Technology, Johns Hopkins University, 3400 N. is an open access, peer-reviewed arti- Charles Street, Gilman Hall 301, Baltimore, MD 21218 cle published by Firenze University Press (http://www.fupress.com/substan- tia) and distributed under the terms Abstract. At the height of his scientific career, the anatomist Nicolaus Steno pub- of the Creative Commons Attribution lished the Elementorum myologiæ specimen (Florence, 1667), a book unlike any other License, which permits unrestricted anatomy book until then. Rather than an anatomy book, it seemed more like a book use, distribution, and reproduction of mathematics, with propositions, lemmas and corollaries. Steno is thought to have in any medium, provided the original developed his mathematical interests in Florence with the school of Galileo. However, author and source are credited. this article challenges this interpretation and argues that Steno’s turn towards math- Data Availability Statement: All rel- ematics was a gradual process that began earlier in Copenhagen and Leiden. By sur- evant data are within the paper and its veying Steno’s early anatomical writings, mathematical methods such as quantification Supporting Information files. measurements, mechanical analogies, and geometrical models come to light. More importantly, these methods are read in their own context, by considering what math- Competing Interests: The Author(s) ematics really meant in the early modern period and how anatomists used it. As such, declare(s) no conflict of interest. this article provides a more complete picture of Steno’s interest in mathematics and it sheds new light on the rise of mathematics in the early modern life sciences. Keywords: Nicolaus Steno, Early Modern Science, History of Anatomy, Mathematiza- tion, Mechanical Philosophy, Mixed Mathematics, Quantification, Dissec- tion Culture. INTRODUCTION1 When the anatomist Nicolaus Steno arrived in Florence and published the Elementorum myologiae specimen (1667), he claimed that the study of the muscles had to become “part of mathematics” and that the cause of “many errors … in the description of the human body” was that “until now anat- omy has disdained the laws of mathematics.”2 The book seemed more like a 1 I would like to thank the editors Stefano Dominici and Gary Rosenberg, as well as the review- ers Peter Dear, Jeremy Gray and François Duchesneau for very helpful comments and sugges- tions. I also benefitted much from discussions with Troels Kardel and John Heng at the work- shop “Galilean Foundations for a Solid Earth” in October 2019, in Florence. Finally, a special thanks to Evan Ragland and María Portuondo who kindly read and commented on an earlier version of this article. 2 Nicolaus Steno, Elementorum myologiae specimen (Florence, 1667), p. iii-iv: “non posse in mus- culo distincte partes eius nominari, nec motum eiusdem considerari feliciter, nisi Matheseos pars Substantia. An International Journal of the History of Chemistry 5(1) Suppl.: 29-42, 2021 ISSN 2532-3997 (online) | DOI: 10.36253/Substantia-1276 30 Nuno Castel-Branco display such an explicit use of mathematics, it may seem that he completely changed his research methods when he arrived in Florence. However, as this article argues, that was not the case. Rather than a sudden shift, Steno’s turn towards mathematics was a gradual process. Early in his anatom- ical career, Steno used methods directly associated with the early modern pure and mixed mathematics. The mixed mathematic disciplines, such as astronomy, mechanics or optics, used the methods of pure mathematics – arithme- tic and geometry – to explain natural phenomena. Such methods included quantification measurements, geomet- rical models, and even the axiomatic structure of mathe- matical treatises.5 Simple uses of quantification like count- ing did not necessarily entail an interest in mathematical methods, unless they were used to make stronger episte- mological claims. Scholars who worked on mixed mathe- matics aimed to achieve higher levels of certainty in their description of the natural world.6 For that reason, seven- teenth-century mixed mathematics, later known as phys- Figure 1. “Lemma IV: The height of a contracted muscle is equal ico-mathematics, used not only mathematical methods to the height of the non-contracted muscle.” Steno, Elementorum but also new experimentation techniques and mechanical myologiæ specimen, p. 21; BOP, p. 667. analogies to explain natural phenomena.7 For example, historian Peter Dear explains that the book Ars magnesia (Würzburg, 1631) by the Jesuit Athanasius Kircher (1602- mathematics than an anatomy book, due to its proposi- 1680) was “a physico-mathematical disquisition” on mag- tions, lemmas and corollaries, and strong epistemolog- netism where experimental accounts were presented in ical claims about the role of mathematics in the study the form of theorems.8 Steno carefully studied the second of nature (fig. 1).3 This mathematical approach was seen edition of this book as a university student in Copenhagen, likewise in Steno’s most famous work, also published in including the chapters where Kircher illustrated magnetic Florence, the De solido intra solidum naturaliter contento attraction by means of hydrostatic devices.9 (1669), where he laid down the principles of superposi- Besides outlining Steno’s early uses of mathemat- tion of the Earth’s strata and in which he described the ics and mechanical analogies, this article shows that formation of crystals and of the Tuscan mountains by such uses derived in large part from his interest in means of geometry.4 Since Steno’s earlier works did not mixed mathematics and not so much from the mechan- ical philosophies of his time.10 Although Steno may be Myologia fieret,” and “innumerabilium errorum, quibus humani corpo- ris historia fœdè inquinatur, quàm quod Matheseos leges Anatome hac- tenus indignata fuerit.” For a full English translation see Troels Kardel 5 Kirsti Andersen and Henk Bos, “Pure Mathematics,” in Katharine Park and Paul Maquet, Nicolaus Steno: Biography and Original Papers of a and Lorraine Daston (eds.), Cambridge History of Science, vol. 3: Early 17th Century Scientist, 2nd ed. (Berlin: Springer, 2018) (hereafter BOP), Modern Science, pp. 696-723, esp. 702. p. 651. All translations are from BOP unless the Latin is provided in the 6 Peter Dear, Discipline and Experience: The Mathematical Way in the footnote, in which case they are mine. Scientific Revolution (Chicago: Chicago Press, 1995), pp. 32-44; Rivka 3 For in-depth studies of the Elementorum myologiæ specimen see Tro- Feldhay, “The use and abuse of mathematical entities: Galileo and the els Kardel, Steno on Muscles: Introduction, Texts, Translations, (Philadel- Jesuits revisited,” in Peter Machamer (ed.), The Cambridge Companion phia: The American Philosophical Society, 1994); Raphaële Andrault, to Galileo (Cambridge: Cambridge Univ. Press, 1998), pp. 80-145, esp. “Mathématiser l’anatomie: la myologie de Stensen (1667),” Early Science 83-100. and Medicine, 15 (2010), pp. 505-536; Domenico Bertoloni Meli, “The 7 Dear, Discipline and Experience, pp. 32-62, 151-79. Collaboration between Anatomists and Mathematicians in the mid-Sev- 8 Peter Dear, “Mixed Mathematics,” in P. Harrison, R. Numbers and M. enteenth Century with a Study of Images as Experiments and Galileo’s Shank (eds.), Wrestling with Nature: From Omens to Science (Chicago: Chica- Role in Steno’s Myology,” Early Science and Medicine, 13:6 (2008), pp. go Press, 2011), p. 156; Dear, Discipline and Experience, 172-9. 665-709. 9 August Ziggelaar (ed.), Chaos: Niels Stensen’s Chaos-manuscript with 4 Nicolaus Steno, De solido intra solidum naturaliter contento dissertatio- Introduction, Notes and Commentary (Copenhagen: Danish Library of nis prodromus (Florence, 1669), 78-80; BOP, pp. 822-825. See also Alan Science and Medicine, 1997), p. 122; Athanasius Kircher, Magnes sive de Cutler, The Seashell on the Mountaintop: A Story of Science, Sainthood, arte magnetica (Cologne, 1643), pp. 527-9. and the Humble Genius Who Discovered a New History of the Earth 10 This was also the case for the anatomist Fabricius d’Acquapenden- (New York: Dutton, 2003), pp. 105-118. te (1533-1619), see Peter Distelzweig, “Fabricius’s Galeno-Aristotelian Dissecting with Numbers: Mathematics in Nicolaus Steno’s Early Anatomical Writings, 1661-64 31 described as a mechanical philosopher, this does not Galileo’s last disciple, that Steno published the Elemen- mean that he followed strictly the mechanical philoso- torum myologiæ specimen, as historian Domenico Ber- phies of René Descartes (1596-1650) and Pierre Gassen- toloni Meli explains.16 Thus, it would seem reasonable to di (1592-1655).11 Many non-mechanical, early-modern assume that Steno travelled to Tuscany to learn mathe- scholars also used quantification methods and mechan- matics in the Italian school of “the great Galileo,” as Ste- ical analogies in medicine and anatomy, as seen in the no later referred to him.17 case of the vitalist Johannes Baptista Van Helmont (1580- However, a letter recently acquired by the Royal 1644) and the Aristotelian William Harvey (1578-1657).12 Danish Library suggests that Steno’s interests in math- Steno’s early interests in mathematics have two ematics were more developed than previously thought important historical implications. First, they provide before his arrival in Italy. In the same year of Steno’s a more complete picture of Steno’s personal interest in arrival, Prince Leopoldo de’ Medici (1617-75) mentioned mathematics. Steno never wrote about what made him to a friend the arrival of “Mr. Steno, a Danish anatomist turn towards a geometrical explanation of the mus- of young age but remarkable in his work… and a great cles or when he decided to do it.