Abstract
The content of Stevin’s hydrostatics was original and became a cornerstone of the advances in hydrostatics that were to follow it. Stevin grasped the fact that the force on a solid surface in contact with water is independent of the orientation of that surface and depends only on its depth beneath the uppermost surface of the water. Some of Stevin’s proofs were highly ingenious. However, his postulates, the most significant of which acknowledged that the depth to which a vessel sinks is proportional to the weight it carries, were insufficient to yield the content of his theory as deductive consequences. In a way that he did not make explicit, Stevin inserted into his theory features of the behavior of water with which he was familiar as a hydraulic engineer but which were not licensed by his postulates. For instance, he assumed, rather than proved or explained, that water presses horizontally against a vertical surface, a phenomenon with which Stevin was familiar through his dealings with lock gates. It was only during the course of the seventeenth century that the facts about hydrostatics identified by Stevin were explained and adequately theorized. Those developments required the recognition that experiment needs to be read as supplying evidence for hydrostatics rather than as being mere applications of it, as Stevin had assumed.
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
Notes
- 1.
For more detail on Stevin’s life see Dijksterhuis (1970).
- 2.
Original versions of those two works in Dutch are reproduced, together with an English translation in Dijksterhuis (1955), pp. 35–295 for The Art of Weighing and pp. 375–483 for The Elements of Hydrostatics. To each work is appended a section dealing with practical applications, The Practice of Weighing (pp. 297–373) and Preamble of the Practice of Hydrostatics (pp. 485–501). Also included in this source is Stevin’s Appendix to the Art of Weighing (pp. 503–521) and Supplement to the Art of Weighing (pp. 523–607).
- 3.
Peter Dear (1995) has studied in detail scholastic attempts, especially by Jesuit scholars, to accommodate the developing mathematical sciences into their philosophy during the Scientific Revolution, noting in particular the modifications that were made in the scholastic understanding of ‘mixed mathematics’ . Stephen Gaukroger and John Schuster (2002, pp. 335–338) discuss similar issues in the context of Descartes’ hydrostatics.
- 4.
According to Jürgen Renn (in Schemmel 2008, p. viii) these are ‘knowledge representation structures’ which can have longevity as resources to be exploited by scientists and survive changes from one theory or conceptual framework to another. Examples include the notion of a center of gravity or a model of a balance that abstracts from its physical features other than weight and the presumed rigidity of the balance arm. I would prefer the term ‘theoretical model’ rather than ‘mental model’ to avoid the impression that these models exist only in the mind. Stevin’s ‘surface vessels’ are capable of holding water!
- 5.
Stevin introduced his Art of Weighing with a Discourse on the Worth of the Dutch Language (Dijksterhuis 1955, pp. 59–65).
- 6.
When Stevin identified definitions in addition to postulates as forming the basis from which he would derive the propositions constituting his theory he was following the example of Euclid rather than Archimedes. The latter listed only postulates, taking for granted the kinds of matters Euclid and Stevin made explicit with their definitions.
- 7.
Pierre Duhem (1905, p. 603), one of the few historians to have paid detailed attention to Stevin’s hydrostatics, may well have been justified in acclaiming the latter for its novelty, but, as we shall see, his extension of that acclaim to include rigor cannot be allowed. Dijksterhuis (1955, p. 377), another historian to have given serious attention to Stevin’s hydrostatics, also failed to pick up on all of the shortcomings that I will identify. The attribution of rigor to the deductions in Stevin’s hydrostatics seems to have remained unchallenged in more recent literature. For example, in their otherwise excellent historical analysis of early work of Descartes on hydrostatics, Gaukoger and Schuster (2002, pp. 539–540) impute to him a firm belief in Stevin’s rigor and seem to endorse this judgment themselves, even though doing so is not material to their historical case.
- 8.
My use of the term ‘surface element’ serves to make explicit in a modern way what is only implicit in Stevin’s own words. The notion of a surface element is necessary because the extent to which a liquid presses on a solid surface is a continuous function of the depth of that solid surface beneath the uppermost surface of the liquid. This much is implicit in Stevin’s hydrostatics and is handled by him through the use of limits, an example of which we will shortly be discussing.
- 9.
The relevant passage in The Art of Weighing is in Dijksterhuis (1955, p. 179).
- 10.
- 11.
The height of MI above EF is more for the left hand configuration than in the two to its right in Stevin’s figure as it is presented, but it is clear from the text that the depth of EF below the water surface should be the same in all three cases.
- 12.
The significance of this point has been missed by commentators. This is illustrated by the way Stevin’s theory is treated by Spiers and Spiers in Pascal (1937, p. 150). They included a translation of part of the Elements of Hydrostatics as an Appendix to The Physical Treatises of Pascal that breaks off immediately before the treatment of the force on a vertical plane that I am arguing to be of great significance. They justify this on the ground that the rest of the work ‘consists of interesting geometrical demonstrations whereby Stevin determines the centers of pressure on surfaces variously disposed obliquely to the horizon; its content, not directly relevant to the present discussion’. Since what is referred to as the ‘present discussion’ is Pascal’s introduction of pressure into hydrostatics, Stevin’s treatment of the force on non-horizontal surfaces is of crucial importance, as I am endeavoring to show.
- 13.
Here I exploit Stevin’s own articulation of what I have referred to as the Euclidean ideal , illustrated in the passages from The Art of Weighing cited on p. xx.
- 14.
Stevin’s version of this diagram appears in Dijksterhuis (1955, p. 492).
- 15.
Stevin’s discussion is in Dijksterhuis (1955, pp. 495–497).
- 16.
The quotation is taken from a dedication of Stevin’s Practice of Weighing to the burgomasters and rulers of the city of Nuremburg and so should be interpreted while bearing in mind his intent to present his book as serving their interests.
- 17.
Stevin’s work on sluice gates, published in 1617, is discussed in Dijksterhuis (1970, pp. 98–100).
- 18.
I use ‘mechanistic’ in the context of simple machines and reserve the term ‘mechanical’ to refer to explanations that appeal to the ultimate particles involved in the mechanical philosophy, thereby hoping to avoid the confusions that can arise from ignoring this distinction.
References
Boyle, R. 1999. The works of Robert Boyle. 14 volumes, ed. M. Hunter and E. Davis. London: Pickering and Chatto.
Dear, P. 1995. Discipline and experience: The mathematical way in the scientific revolution. Chicago: University of Chicago Press.
Descartes R. 1964–1976. Ouevres de Descartes. 12 volumes, ed. C. Adams and P. Tannery. Paris: Vrin.
Dijksterhuis, E.J. 1955. The principal works of Simon Stevin, Volume 1, Mechanics. Amsterdam: Swets and Zeitlinger.
———. 1970. Simon Stevin in the Netherlands around 1600. The Hague: Matinus Nijhoff.
Duhem, P. 1905. Le Principe de Pascal. Revue Générale des Sciences Pures et Applique. 16: 599–610.
Gaukroger, S., and J. Schuster. 2002. The hydrostatic paradox and the origins of Cartesian dynamics. Studies in History and Philosophy of Science. 33: 535–572.
Pascal, B. 1937. The physical treatises of Pascal: The equilibrium of liquids and the weight of the mass of the air. Trans. A.G.H. Spiers and I.H.B. Spiers. New York: Columbia University Press.
Schemmel, M. 2008. The English Galileo: Thomas Harriot’s work on motion as an example of pre-classical mechanics. Dordrecht: Springer.
Shapiro, A. 1974. Light, pressure and rectilinear propagation: Descartes’ celestial optics and Newton’s hydrostatics. Studies in History and Philosophy of Science. 5: 239–296.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Chalmers, A.F. (2017). Beyond Archimedes: Stevin’s Elements of Hydrostatics . In: One Hundred Years of Pressure. Archimedes, vol 51. Springer, Cham. https://doi.org/10.1007/978-3-319-56529-3_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-56529-3_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-56528-6
Online ISBN: 978-3-319-56529-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)