Abstract
This paper offers a reassesment of Simon Stevin’s mechanics, by focusing on how Stevin tries to anchor his mathematical demonstrations in the behavior of material instruments. It is shown how his views on the relation between spiegheling (speculation) and daet (practice) are crucial to correctly understand his famous proof of the law of the inclined plane and his experimental test of the Aristotelian law of free fall. The distance separating spiegheling and daet is reproduced in that between instruments at rest and instruments in motion, because of Stevin’s claim that impediments to motion are “inseperable accidents” of all moving objects.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
Simon Stevin was born in Flanders in 1548 and died in the Dutch Republic in 1620, which makes him about one generation older than Galileo. The best general treatment (although outdated on a number of points) of Stevin remains Dijksterhuis’ monograph from 1943, which was translated in an abridged version in 1970 (Dijksterhuis 1943; Dijksterhuis 1970).
- 2.
I use “mechanics” here as general name for the subject matter of the whole of Stevin’s treatises. Stevin himself reserves the term “mechanical” for operations involving practical constructions, and stresses that the mathematical theory is rather one of the “free arts”. All three treatises are included with English translation in Volume 1 of the modern edition of Stevin’s Principal Works (Stevin 1955).
- 3.
The English terms that best translate Stevin’s are “reflection” and “speculation”: a spieghel is a mirror, and spiegheling can be both the image reflected in a mirror, and the act of mirroring. I’ll translate it as “speculation”.
- 4.
I altered the translation from the Principal Works at a number of places, as I have also done in further quotations. Page numbers are given to the English translations for ease of reference.
- 5.
It’s interesting to remark that all three ways in which Stevin aligns his theoretical treatment with material practice are also to be found in the slightly earlier work on mechanics of the Italian mathematician Guidobaldo del Monte (see (Van Dyck 2006) for a detailed analysis on all three points – see also (Bertoloni Meli 2006, 26–32)). We’ll come back to a further, related similarity between Stevin and Guidobaldo in Sect. 2.4.
- 6.
As we will see below, Cardano is explicitly cited at two crucial places in Stevin’s Appendix. Apart from a passing reference to Jacques Besson and the curious case of Jean Taisnier (see Sect. 2.5), Cardano and Commandino are the only contemporary authors in mechanics who are cited by Stevin. Whereas the latter provided an exemplar, the former served as a foil. In the same work cited by Stevin in the Appendix, the Opus Novum de Proportionibus… of 1570, Cardano had not only given an incorrect law of the inclined plane, he had also denied indifferent equilibrium and had claimed that one should consider the lines of weight as converging in the centre of the earth (Cardano 1570). In his Appendix, Stevin indicated that he wanted to refrain from explicitly engaging with other authors in his main text, but it is fair to assume that in the passages just referred to in the text he has Cardano in view as one of the authors who “practised many false propositions” (Stevin 1955, 509).
- 7.
Dijksterhuis provides a succinct overview in (Dijksterhuis 1970, 54–57). The explanatory scheme in Guidobaldo del Monte’s Liber Mechanicorum, the only contemporaneous book that can rival Stevin’s in terms of rigor, breaks down exactly with forces that are not applied in the direction of weight (Van Dyck 2006, 394–96; Renn and Damerow 2012).
- 8.
Stevin himself often comments on pedagogical issues, and presents the most important collection of his works (the Mathematical Memoirs) as the set of courses he used with Prince Maurice. Approaching his work from this angle also allows us to place Stevin’s work squarely in its historical context, more specifically that of late humanism at Leiden, which was characterized by an intense pedagogical focus on the proper interrelation of theory and practice (van Bunge 2001, chapter 1).
- 9.
The translation in the Principal Works opts for “automatically” and “absurd” respectively (Stevin 1955, 179). Stevin’s Dutch literarily states that the spheres perform a perpetual motion “out of themselves” (“uyt haer selven”). The 1605 Latin translation by Willebrord Snell has “ex sese” and “falsum” respectively (Stevin 1605, 35). Girard’s 1634 French edition states “ce mouvement n’auroit aucune fin, ce qui est absurde”, leaving out all explicit reference to the qualification that the motion is self-caused (Stevin 1634, 448). As will become clear in Sect. 2.4.3, this qualification is crucial for a good understanding of the grounds of Stevin’s argument. As for “absurd”, in this context that is a perfectly acceptable translation of Stevin’s “valsch”, but we will see in Sect. 2.4 that the distinction between “truthful” and “false” plays a central role in Stevin’s thinking about acceptable idealizations within the science of mechanics. As I will also argue that this distinction is crucially linked to the ambiguity I will uncover in Stevin’s appeal to this “absurdity” or “falsehood”, it is preferable to keep the terminological link explicit. (In his hydrostatics, Stevin calls the possibility of perpetual motion “ongeschickt” (which at other places in his work he uses both to mean “absurd” and to literally mean “irregular”) (Stevin 1955, 400).
- 10.
- 11.
Dijksterhuis has already been quoted to this effect. Gabbey also states that Stevin assumes that the spheres are “frictionless” (Gabbey 1985, 74).
- 12.
- 13.
See (Festa and Roux 2006) for different examples, both in antiquity (Heron) and in the sixteenth century, and further analysis; surprisingly, Stevin is not mentioned.
- 14.
This also shows in the fact that when he replies to the same anti-Copernican arguments as Galileo, his discussion is not connected to these mechanical considerations at all (Stevin 1961, 125–27).
- 15.
One author who held the very same position as Stevin on this crucial point was, again, Guidobaldo del Monte (see (Van Dyck 2006; Laird 2013)). Stevin almost certainly knew Guidobaldo’s treatise on perspective from 1600 when he published his own in 1605 (see (Andersen 1990)), but there are no indications he was familiar with the Italian’s treatise on mechanics in 1586. It cannot be excluded, but the absence of any attention to pulley systems makes it rather unlikely: pulleys take up a large part of Guidobaldo’s treatise, but Stevin only added an analysis in a supplement in 1605, reportedly after prince Maurice had seen a treatment thereof in Buonaiuto Lorini’s Delle Fortificationi, a work dependent on Guidobaldo for its treatment of the simple machines.
- 16.
This obviously raises the further question what lies behind this change in perspective, a question that cannot be addressed here. Let me just stress that it is easy to state that in the absence of all impediments, a body would have a certain behavior – but quite a bit more challenging to explain why we should think that this statement teaches us anything significant concerning the behavior of bodies in empirical circumstances!
- 17.
This is why I chose not to render Stevin’s “valsch” as “absurd” (see footnote 9); the former more than the latter stresses its basis in physical considerations, as his use of “false” for empirically invalid statements (see the examples in Sect. 2.4.2) makes clear.
- 18.
This author had published a treatise in which he had actually presented the text of Giovanni Battista Benedetti’s Demonstratio proportionum motuum localium contra Aristotilem et omnes philosophes from 1554. Stevin was unaware of this plagiarism and ascribed the ideas to Taisnier.
- 19.
In his Appendix, all references to Aristotle are directly taken over from Taisnier/Benedetti; but in the Dialectike, Stevin’s related treatment of the problem of fall shows that he was indeed familiar with the relevant parts of Aristotle’s Physics (Stevin 1585, 144–48).
- 20.
In Stevin’s work on musical theory, never published during his lifetime, he speaks about the “infinite power” inherent in the Dutch word for proportionality (Stevin 1966, 427).
- 21.
Again, Cardano is one of the authors who believed in the validity of such proof (Cardano 1570, 34). This is not explicitly mentioned by Stevin, although he does refer to Cardano’s erroneous statement of the law of the inclined plane in the same chapter of the Appendix. In the second chapter, in which he disproves the possibility of having laws of motion, he does single out Cardano for his faulty reliance on the “appearance of proportionality” in motion, which led him to errors “in a great many different propositions”, which can be plausibly read as also referring to this proof of the law of the lever (Stevin 1955, 513).
- 22.
Guidobaldo del Monte’s detailed commentary of the slightly different original Archimedean proof is analyzed in (Van Dyck 2013).
References
Andersen, Kirsti. 1990. Stevin’s Theory of Perspective: The Origins of a Dutch Academic Approach to Perspective. Tractrix 2: 25–62.
Aristotle. 2001. The Basic Works, ed. Richard McKeon. New York: The Modern Library.
Bertoloni Meli, Domenico. 1992. Guidobaldo Dal Monte and the Archimedean Revival. Nuncius 7(1): 3–34. doi:10.1163/182539192X00019.
———. 2006. Thinking with Objects: The Transformation of Mechanics in the Seventeenth Century. Baltimore: Johns Hopkins University Press.
Cardano, Hieronymus. 1570. Opus Novum de Proportionibus Numerorum, Motuum, Ponderum, Sonorum …. Basel: Henricus Petri.
Dijksterhuis, E.J. 1943. Simon Stevin. Den Haag: Martinus Nijhoff.
———. 1970. Simon Stevin: Science in the Netherlands around 1600. Den Haag: Martinus Nijhoff.
Festa, Egidio, and Sophie Roux. 2006. La Moindre Petite Force Suffit À Mouvoir Un Corps Sur L’horizontal. L’émergence D’un Principe Mécanique et Son Devenir Cosmologique. Galilaeana 3: 123–147.
Gabbey, Alan. 1985. The Mechanical Philosophy and Its Problems: Mechanical Explanations, Impenetrability, and Perpetual Motion. In Change and Progress in Modern Science, ed. Joseph C. Pitt, 9–84. Dordrecht: Reidel. http://link.springer.com/chapter/10.1007/978-94-009-6525-6_2.
Hoyrup, Jens. 1992. Archimedism, Not Platonism: On a Malleable Ideology of Renaissance Mathematicians. In Archimede: Mito Tradizione Scienza, ed. Corrado Dollo, 81–110. Firenze: Leo S. Olschki.
Laird, Walter Roy. 1991. Archimedes Among the Humanists. Isis 82(314): 629–638.
———. 2013. Guidobaldo Del Monte and Renaissance Mechanics. In Guidobaldo Del Monte (1545–1607). Theory and Practice of the Mathematical Disciplines from Urbino to Europe, ed. Antonio Becchi, Domenico Bertoloni Meli, and Enrico Gamba, 35–51. Berlin: Edition Open Access. http://edition-open-access.de/proceedings/4/3/.
Mach, Ernst. 1919. The Science of Mechanics: A Critical and Historical Account of Its Development. Translated by Thomas J. McCormack. 4th ed. Chicago/London: Open Court.
Machamer, Peter. 1998. Galileo’s Machines, His Mathematics, and His Experiments. In The Cambridge Companion to Galileo, ed. Peter Machamer, 53–79. Cambridge: Cambridge University Press.
Renn, Jürgen, and Peter Damerow. 2012. The Equilibrium Controversy Guidobaldo Del Monte’s Critical Notes on the Mechanics of Jordanus and Benedetti and Their Historical and Conceptual Backgrounds. Berlin: Edition Open Access.
Stevin, Simon. 1585. Dialectike ofte Bewysconst. Leyden: Christoffel Plantijn.
———. 1605. Mathematicorum Hypomnematum … : Tomus Quartus: De Statica. Leiden: Ioannis Patius.
———. 1634. Les Oeuvres Mathematiques de Simon Stevin de Bruges, ed. Albert Girard. Leiden: Bonaventure & Abraham Elsevier.
———. 1955. The Principal Works of Simon Stevin. Vol 1: General Introduction. Mechanics, ed. E. J. Dijksterhuis. Trans. C. Dikshoorn. Amsterdam: Swets & Zeitlinger.
———. 1961. The Principal Works of Simon Stevin. Vol 3: Astronomy. Navigation, ed. A. Pannekoek and Ernst Crone. Trans. C. Dikshoorn. Amsterdam: Swets & Zeitlinger.
———. 1964. The Principal Works of Simon Stevin. Vol 4: The Art of War, ed. W.H. Schukking. Amsterdam: Swets & Zeitlinger.
———. 1966. The Principal Works of Simon Stevin. Vol. 5: Engineering. Music. Civic Life, ed. R.J. Forbes, A.D. Fokker, and A. Romein-Verschoor. Amsterdam: Swets & Zeitlinger.
van Bunge, Wiep. 2001. From Stevin to Spinoza: An Essay on Philosophy in the Seventeenth-Century Dutch Republic. Leiden: Brill.
Van Dyck, Maarten. 2006. Gravitating towards Stability: Guidobaldo’s Aristotelian-Archimedean Synthesis. History of Science 44(4): 373–407.
———. 2013. Argumentandi Modus Huius Scientiae Maxime Proprius.’ Guidobaldo’s Mechanics and the Question of Mathematical Principles. In Guidobaldo Del Monte (1545–1607). Theory and Practice of the Mathematical Disciplines from Urbino to Europe, ed. Antonio Becchi, Domenico Bertoloni Meli, and Enrico Gamba, 9–34. Berlin: Edition Open Access. http://www.edition-open-access.de/proceedings/4/2/.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Van Dyck, M. (2017). Motion and Proportion in Simon Stevin’s Mechanics. In: Adams, M., Biener, Z., Feest, U., Sullivan, J. (eds) Eppur si muove: Doing History and Philosophy of Science with Peter Machamer. The Western Ontario Series in Philosophy of Science, vol 81. Springer, Cham. https://doi.org/10.1007/978-3-319-52768-0_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-52768-0_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-52766-6
Online ISBN: 978-3-319-52768-0
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)