Abstract
The Mechanical Problems traditionally attributed to Aristotle is a short problem collection that also contains an ambitious project of reduction, which traces various mechanical devices back to the lever, the balance and the radii of a circle. This work is thus not just a collection of problems, but also the first theoretical mechanical treatise that has come down to us: Basic concepts of technical mechanics such as force, load, fulcrum are abstracted from an analysis of simple technology, and the workings of this technology are explained by arguments cast in syllogistic form. This chapter traces the origins of mechanical theory in this work and analyzes the form and structure of its argument. The key steps in the concept formation of basic mechanics carried out in this treatise are analyzed in detail. We focus on the special role of the balance with unequal arms in the early development of mechanics, on the interaction of various forms of explanatory practice and on their integration into systems of knowledge in the Peripatetic school.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
- 2.
Galilei (1638, 11).
- 3.
There is no accepted critical edition of the Mechanical Problems. We use the Greek text given in Hett 1936, cited, as is customary, according to page and column of the Bekker edition of 1831. All translations from the Greek are our own. They are intended to be as literal and interpretatively open as possible.
- 4.
- 5.
- 6.
There is no consensus on authorship or dating. Based on the way letters are used to locate points and figures, the work predates the Euclidean reform. On such formal questions see Heiberg (1904) and Netz (1999). Euclid’s Elements are generally taken to have been compiled shortly after 300 BCE; Aristotle died in 322 BCE. If we don’t want to resolve the question of Aristotle’s possible authorship by stipulation, we have to date the work at some time between 330 and 270 BCE. Recent commentators tend to favor the later date.
- 7.
- 8.
- 9.
For the manuscript tradition see van Leeuwen (2012, 2013, 2016); for the Arabic translation see Abattouy (2001). On the ancient lists see Flashar (2004, 189–191) and Hein (1985, 304). On Athenaeus, see Whitehead and Blyth (2004, 44) and Bodnár (2011); Vitruvius (1931–1934, Bk. 10,3); Hero of Alexandria (1900 , Bk. 2.8; 2.33, pp. 114, 170).
- 10.
Clagett (1959, 71, n.5 and 75–76, n. 6).
- 11.
- 12.
The reduction program was already noted by Duhem (1905, 8).
- 13.
Problem 4: The oars of a ship are identified as levers.
Problem 6: The mast of a ship is identified as a lever.
Problem 9: The wheels of pulleys are identified as levers.
Problem 13: Handles of spindles and windlasses are identified as levers.
Problem 14: A piece of wood broken over the knee is identified as a lever.
Problem 15: Pebbles at the beach rotated and worn down by water are identified as levers.
Problem 16: Wooden planks raised are identified as levers.
Problem 17: Wedges are identified as consisting of levers.
Problem 18: A pulley is identified as a lever.
Problem 20: An asymmetric balance is identified as a lever.
Problem 21: The forceps of a dentist are identified as a pair of levers.
Problem 22: A nutcracker is identified as a lever.
Problem 26: Wooden planks carried on the shoulder are identified as radii.
Problem 27: Wooden planks raised up to the shoulder are identified as radii.
Problem 29: A plank carried by two men is identified as a lever.
- 14.
- 15.
There has been some disagreement in the literature on the meaning of ischus (force) here, Duhem (1905 and 1913), De Gandt (1982), and Krafft (1970). See the discussion in Schiefsky (2009, 59–61). For our purposes it suffices to note that motion presupposes a force and that wherever the force is applied to the rotating radius or beam: outside points move faster than inside points.
- 16.
Since Krafft’s analysis in Dynamische und statische Betrachtungsweise (1970); this argument about the geometry of a moving point has been the focus of attention of scholars dealing with the Mechanical Problems. See also Mark Schiefsky, (2009) and De Groot (2009, 2014). No convincing argument has so far been advanced as to why the later problems should need this proof.
- 17.
Reading phalanx (beam) for plastinx (pan). Not only does the sense of this text argue for this reading, but also the next problem, which deals with a material beam balance (without actually calling it a beam), would be much easier to understand if the material beam had already been introduced. No modern translation takes the author to mean ‘pan’. Forster (1995, 1302) and Hett (1936, 347), (both take the author to mean “balance” and not “scale pan.” The Arabic translation (Abbatouy 2001, 114–115) renders whatever was in the original Greek text all three times as beam or pole. We thank Sonja Brentjes for advice on the Arabic.
- 18.
The term spartion (the diminutive of sparton: cord) becomes a technical term meaning suspension point after its identification with the center of a circle here. The two later occurrences of the non-diminutive sparton (in Prob. 3 and 20) may be copying mistakes, since in each case the text refers back to a cord previously mentioned in the diminutive form. In Problem 1, on the other hand, we are dealing with larger balances, where the larger cord might actually be meant.
- 19.
The phrase menei gar touto otherwise occurs only in Problem 27, where it plays exactly the same role as in 1, 3, and 4. The verb ginetai (it becomes) is used to express the identification of a part of a device with the fulcrum or center in Problems 1, 3, 4, 5, 6, 12, 15, 16, 19, 20, 26, 29. In Problems 9, 13, 14, 17, 21, 22, and 27 only the verb to be or no verb at all is used.
- 20.
The author discusses the horizontal motion of a suspended beam balance in Prob. 10.
- 21.
Stevin (1586, 65, 509) condemned Aristotle for this internally contradictory formulation. The strict proportionality of lengths and weights holds only in equilibrium, that is, in that case in which there is neither a moving weight nor a moved weight. When one weight moves the other, they are not in equilibrium. If we assume the author was aware of this fact, we have an explanation for his avoidance of the language of proportions.
- 22.
For instance: Problems 16, 20, 29. As we shall see in Problem 20: With a given lever and a given force, the closer to the load the fulcrum is put, the greater the load that can be moved, but the increase in effect is not proportional to the change in distance from the fulcrum.
- 23.
There are two uses of logos in a different sense in Prob. 19 and 23.
- 24.
- 25.
In this particular case the rower in the middle does not in fact effect more, he just has an easier time of it. Moreover, if the arm-length of the rowers is the same, the rower on the longer lever moves it the same length as the rowers on the shorter levers (oars) and thus actually effects less. Problem 3 asserted: the farther, the more easily; Problem 4 asserts: the farther, the more effective. Whereas Problem 3 held that the same effect is achieved with less force, Problem 4 wants to assert that a greater effect is achieved with the same force.
- 26.
The verb apereidein means to fix or support and is related to the term peisma for the ship’s cable used to tie down the ship to land. This sentence may be a later insertion since the text then continues with a renewed identification of the sea as the load and a repetition of the explanation of why the lever (now of the first kind again) is longer in the middle. There is clearly some corruption in the text. Renaissance authors often pointed out that Aristotle should have used a lever of the second kind in his analysis. See Galileo’s letter to Giacomo Contarini, March 22, 1593, in Galilei (1968, vol. 10, 55–57); Biancani (1615, 159); Baldi (1621, 41).
- 27.
The three sentences quoted make up the entire Problem 6, 851a38–b6. Note that the principle invoked is that the same force moves the same load more easily and thus more swiftly—and thus has a greater effect.
- 28.
hêmizugiou. This is the only occurrence of the term in the classical Greek corpus: it could either be an adjective (hêmizugios) meaning “forming a half-balance,” Liddell et al. (1996) or (as Markus Asper has suggested to us) a diminutive noun (hêmizugion) meaning “small half-balance.”
- 29.
On the history of the balance in general, see Robens et al. (2014).
- 30.
From the end of the Anglo-Hanseatic War (1474) until 1598, Hanseatic merchants (who apparently used such devices) had a compound on the north bank of the Thames near London Bridge called the “Stalhof” (steel yard).
- 31.
Aristophanes (1998, lines 1245–49, pp. 58, 304).
- 32.
See Damerow et al. (2002).
- 33.
sphairôma: literally “round thing”
- 34.
The term weight can be used in two quite different senses: Like length it names an abstract physical quantity, but it also can name a concrete material thing such as a measuring weight. If a piece of silver weighs three talents, the silver has a weight, the talent is a weight. Greek of Aristotle’s time sometimes distinguished the two senses by the gender of the noun: ho stathmos (masculine) could refer to the abstract quantity measured and to stathmon (neuter) to the standardized measuring weight placed in the pan [see Liddell et al. (1996)]. The author of the Constitution of Athens (presumably Aristotle) uses the terms in this manner (Aristotle 1995, pp. 2346, 2373; ch. 10.1–2 and 51.3). However, Aristotle at one prominent place (Metaphysics N, 1087b37) uses the masculine form for the measuring unit. The standard published versions of Problem 20 use both forms of the word: masculine twice and neuter once. Of the relevant manuscripts, all but the one on which the first print edition was based have only the masculine form. We thank Joyce Van Leeuwen for checking the manuscripts for us.
- 35.
Reading (with Cappelle) phalanx (beam) for plastinx (pan).
- 36.
In the text just quoted, the appeal to the lever principle of Problem 3 “the greater the length … the more easily (rhaon) it moves” is marked by the tantum-quantum formula hosô … tosoutô. On the other hand, the state of affairs that this principle is supposed to explain “the nearer the cord … the greater the load it draws” is not so marked.
- 37.
Biancani (1615, 183); cf. Piccolomini (1547, 42v); de Monantheuil (1599, 147): “… aequipondium, Graecis dictum sphairôma, nostris Marcum vel Romanum….” Even Baldi (1621, 134), who mentions that “we could use the steelyard in a different manner” and then describes a bismar, does not suggest that this might have been intended by Aristotle himself.
- 38.
On the possibility of comparable developments in China in the same period, see Renn and Schemmel (2006).
- 39.
See the already cited passage from the Constitution of Athens, ch. 10, in Aristotle 1995, p. 2346.
References
Abattouy, Mohammed. 2001. Nutaf min Al-Hiyal: A partial Arabic version of pseudo-Aristotle’s ‘Problemata mechanica. Early Science and Medicine 6: 96–122.
Aristophanes. 1998. Peace, ed. S. Douglas Olson. Oxford: Clarendon Press.
Aristotle. 1995. The complete works of Aristotle, ed. Jonathan Barnes. Princeton: Princeton University Press.
Asper, Markus. 2008. The two cultures of mathematics in ancient Greece. In The Oxford handbook of the history of mathematics, ed. E. Robson and J. Stedall, 107–112. Oxford: Oxford University Press.
Bacon, Francis. 1858. Novum organum. In The works of Francis Bacon, ed. J. Spedding, R. Ellis, and D.D. Heath, vol. 4. London: Longmans.
Baldi, Bernardino. 1621. In mechanica Aristotelis problemata exercitationes: adiecta succinta narratione de autoris vita et scripti. Mainz: Albinus.
Bechio, Philippo. 1560. Georgii Pachymerii Hieromnemonis in universam fere Aristotelis philosophiam epitome. Basel: Froben.
Bekker, Immanuel, ed. 1831. Aristotelis opera, 2 vols. Berlin: Reimer.
Berryman, Sylvia. 2009. The mechanical hypothesis in ancient Greek natural philosophy. Cambridge: Cambridge University Press.
Biancani, Giuseppe (Blancanus). 1615. Aristotelis loca mathematica. Bologna: Coch.
Bodnár, István. 2011. The pseudo-Aristotelian mechanics: The attribution to Strato. In Strato of Lampsacus: Text, translation and discussion, ed. M.-L. Desclos and W.W. Fortenbaugh, 443–455. New Brunswick: Transaction Publishers.
Clagett, Marshall. 1959. The science of mechanics in the Middle Ages. Madison: University of Wisconsin Press.
Crombie, Alistair C. 1961. Augustine to Galileo. Vol. 2. London: Mercury Books.
Damerow, Peter, Jürgen Renn, and Simone Rieger. 2002. Mechanical knowledge and Pompeian balances. In Homo Faber: Studies on nature, technology, and science at the time of Pompeii, ed. G. Castagnetti and J. Renn, 93–108. Rome: L’Erma di Bretschneider.
De Gandt, François. 1982. Force et science des machines. In Science and speculation: Studies in Hellenistic theory and practice, ed. J. Barnes et al., 96–127. Cambridge: Cambridge University Press.
De Groot, Jean. 2009. Modes of explanation in the Aristotelian mechanical problems. Early Science and Medicine 14: 22–42.
———. 2014. Aristotle’s empricism: Experience and mechanics in the fourth century BC. Las Vegas: Parmenides.
Dictionary of Scientific Biography. 1970–1980. Ed. Charles Coulston Gillispie. New York: Scribner.
Duhem, Pierre. 1905. Les origines de la statique. Vol. 1. Paris: Hermann.
———. 1913–1959. Le system du monde: Histoire des doctrines cosmologiques de Platon à Copernic. Vol. 10. Paris: Hermann.
Fausto, Vittore. 1517. Aristotelis mechanica ... ac latinitate donata. Paris: Badii.
Flashar, Hellmut, ed. 1961. Problemata physica. Berlin: Akademie-Verlag.
———, ed. 2004. Grundriss der Geschichte der Philosophie. Die Philosophie der Antike. Bd. 3. - Ältere Akademie, Aristoteles, Peripatos. 2nd ed. Basel: Schwabe.
Forster, E.S. 1995. Mechanics. In The complete works of Aristotle, ed. Jonathan Barnes. Princeton: Princeton University Press.
Galilei, Galileo. 1638. Discorsi e dimostrazioni matematiche: intorno à due nuoue scienze attenenti alla mecanica i movimenti locali. Leiden: Elsevir.
———. 1968. Le opera: Nuova ristampa della edizione nazionale 1890–1909. Vol. 21. Florence: Barbera.
———. 1974. Two new sciences, including centers of gravity and force of percussion (trans: Stillman Drake). Madison: University of Wisconsin Press.
Heiberg, Johann Ludwig. 1904. Mathematisches zu Aristoteles. Abhandlungen zur Geschichte der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen 18: 3–49.
Hein, Christel, ed. 1985. Definition und Einteilung in der Philosophie: Von der spätantiken Einleitungsliteratur zur arabischen Enzyklopädie. Frankfurt/Main: Peter Lang.
Hero of Alexandria. 1900. Heronis Alexandrini opera quae supersunt omnia, vol. 2, Mechanica et catoprica. Leipzig: Teubner. (Reprint 1976. Stuttgart: Teubner).
Hett, W.S., ed. 1936. Aristotle: Minor works. Cambridge, MA: Harvard University Press. Loeb Classical Library.
Koyré, Alexandre. 1943. Galileo and Plato. Journal of the History of Ideas 4: 400–428.
———. 1961. Les philosophes et la machine. [Critique 1948]. In Études de la pensée philosophique, 279–309. Paris: Armand Colin.
Krafft, Fritz. 1970. Dynamische und statische Betrachtungsweise in der antiken Mechanik. Wiesbaden: Steiner.
Laird, Walter Roy. 1986. The scope of renaissance mechanics. In Osiris, 2nd Series, vol. 2, 43–68. Philadelphia: University of Pennsylvania.
———. 2013. The text of the Aristotelian Mechanics. The Classical Quarterly 63: 183–198.
———. 2016. The Aristotelian mechanics: Text and diagrams. Boston Studies in the Philosophy and History of Science. Vol. 316. Cham: Springer International Publishing.
Liddell, Henry G., Robert Scott, and Henry S. Jones. 1996. A Greek-English lexicon: With a revised supplement. Compiled by Henry George Liddell and Robert Scott. Revised and augmented throughout by Henry Stuart Jones with the assistance of Roderick McKenzie and with the cooperation of many scholars. 9th ed. Oxford: Clarendon Press.
Merton, Robert K. 1939. Science and the economy of seventeenth-century England. Science and Society 3: 3–27.
Monantheuil, Henri de. 1599. Aristotelis mechanica graeca, emendata, latina facta, et commentariis illustrate. Paris: Perier.
Netz, Reviel. 1999. The shaping of deduction in Greek mathematics : A study in cognitive history. Cambridge: Cambridge University Press.
Piccolomini, Alessandro. 1547. In mechanicas quaestiones Aristotelis, paraphrasis, paulo quidem plenior. Rome.
Plato. 1962. Laws. In Platonis opera, ed. John Burnet, vol. 5. Oxford: Clarendon Press.
Renn, Jürgen, and Matthias Schemmel. 2006. Mechanics in the Mohist canon and its European counterparts. In Studies on ancient Chinese scientific and technical texts: Proceedings of the 3rd ISACBRS. International symposium on ancient Chinese books and records of science and technology. March 31–April 3, Tübingen, Germany, ed. Hans Ulrich Vogel, Christine Moll-Murata, and Xuan Gao, 24–31. Zhengzhou: Elephant Press.
Rhodius, Apollonius. 1967. In Apollonius Rhodius, the Argonautica, ed. Seaton Robert Cooper. Cambridge, MA: Harvard University Press. Loeb Classical Library.
Robens, Erich, Shanath Amarasiri A. Jayaweera, and Susanne Kiefer. 2014. Balances: Instruments, manufacturers, history. Heidelberg: Springer.
Rose, Valentine. 1854. De Aristotelis librorum ordine et auctoritate commentatio. Berlin: Reimer.
Rose, Paul L., and Stillman Drake. 1971. The pseudo-Aristotelian Questions of mechanics in renaissance culture. Studies in the Renaissance 18: 65–104.
Schiefsky, Mark. 2009. Structures of argument and concepts of force in the Aristotelian mechanical problems. Early Science and Medicine 14: 43–67.
Shapin, Steve. 1996. The Scientific Revolution. Chicago: University of Chicago Press.
Stevin, Simon. 1586. De beghinselen der weeghconst. Leiden: Plantijn. (reprint 1955. The principal works of Simon Stevin, vol.1. Amsterdam: Swets & Zeitlinger).
Tannery, Paul. 1915. Sur les problèmes mécaniques attribués à Aristote. In Memoires scientifiques, vol. 3. Paris: privately published.
Tomeo, Niccolò Leonico. 1525. Aristotelis quaestiones mechanicae: Opuscula nuper in lucem aedita. Venice.
van Cappelle, J.P., ed. 1812. Aristotelis quaestiones mechanicae. Amsterdam: den Hengst.
van Leeuwen, Joyce. 2012. The tradition of the Aristotelian mechanics: Text and diagrams. Berlin: Diss. Humboldt University.
Vitruvius. 1931–1934. On architecture. Vol. 2. Cambridge, MA: Harvard University Press. Loeb Classical Library.
Westfall, Richard S. 1993. Science and technology during the Scientific Revolution: An empirical approach. In Renaissance & revolution, ed. J.V. Field and Frank James, 63–72. Cambridge: Cambridge University Press.
Whitehead, David, and Philip H. Blyth. 2004. Athenaeus Mechanicus. On machines (Peri mechanêmatôn). Wiesbaden: Steiner.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Renn, J., McLaughlin, P. (2018). The Balance, the Lever and the Aristotelian Origins of Mechanics. In: Feldhay, R., Renn, J., Schemmel, M., Valleriani, M. (eds) Emergence and Expansion of Preclassical Mechanics. Boston Studies in the Philosophy and History of Science, vol 270. Springer, Cham. https://doi.org/10.1007/978-3-319-90345-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-90345-3_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-90343-9
Online ISBN: 978-3-319-90345-3
eBook Packages: HistoryHistory (R0)