This paper arose out of a much shorter version presented at a seminar in the Department of History and Philosophy of Science, University of Melbourne, during my time spent there as a Visiting Research Fellow. I am grateful to the participants in the seminar for their comments and particularly to Rod Home for his comments on a draft of the paper. The final version of the paper has benefited from the comments of two anonymous referees.

¹ For a general discussion of these issues, see Dugas, R., Histoire de la méchanique, Neuchatel, 1950Google Scholar, and Truesdell, C., Essays in the history of mechanics, Berlin, 1968CrossRefGoogle Scholar. For more detailed treatments, see the contributions of Truesdell to Leonhardi Euleri opera omnia: ‘The rational mechanics of flexible or elastic bodies, 1638–1788’, series 2, vol. xi, section 2, Zurich, 1960Google Scholar; ‘Rational fluid mechanics, 1687–1765’, series 2, vol. xii, Zurich, 1954Google Scholar; ‘Editor's introduction [to Euler's treatise on fluid mechanics]’, series 2, vol. xiii, Zurich, 1955.Google Scholar

² This ‘Cartesian' view is not Descartes’ own. Descartes himself did not attempt to reduce dynamics to kinematics, although in the eighteenth century he was generally taken to have done so. Part of the reason for this must surely lie in the fact that his system, particularly in its more programmatic aspects, lent itself so easily to mechanism. On Descartes' conception of force, see Gueroult, M., ‘The metaphysics and physics of force in Descartes’Google Scholar, and Gabbey, A., ‘Force and inertia in the seventeenth century: Descartes and Newton’, in Gaukroger, S. (ed.), Descartes: philosophy, mathematics and physics, Brighton, 1980.Google Scholar

³ A reasonably thorough discussion of the problems in Newton's view is to be found in Westfall, R. S., Force in Newton's physics London, 1971, chapters VII, VIII.Google Scholar

⁴ I say that force was effectively primitive for Boscovich and Kant because Boscovich, at least, although he in fact took force to be primitive as far as mechanics was concerned, did consider that some further explanation of force might be conceivable: ‘This propensity is the origin of what we call “force of inertia”; whether this is dependent upon some arbitrary law of the Supreme Architect, or on the nature of points itself, or on some attribute of them, whatever it may be, I do not seek to know; even if I did wish to do so, I see no hope of finding the answer; and truly I think that this also applies to the law of forces…’; A theory of natural philosophy, tr. by Child, J. M., Cambridge, Mass., 1966.Google Scholar

⁵ Leonhardi Euleri opera omnia, series 2, vols, i, ii, Leipzig & Berlin, 1912.Google Scholar

⁶ Ibid., series 2, vol. v, Lausanne, 1957.

⁷ Ibid., series 2, vols, iii, iv, Bern, 1948.

⁸ I shall use modern notation and shall modernize symbols from here on.

⁹ That is to say, in the absence of external forces, d²sl(dt²) = 0. Euler did not mention the converse of this principle i.e., that in the presence of external forces d²sl(dt²) ≠0, but his argument strongly suggested that it is implied. The converse in fact holds so long as we specifiy net forces. This is to get round counterexamples where there are forces acting but where the net force is zero, for example the case of a falling body being acted upon by gravity and by air resistance which, as a result, undergoes a uniform rectilinear motion.

¹⁰ Cf. my ‘Descartes' project for a mathematical physics’, in Gaukroger, S. (ed.), op. cit. (2).Google Scholar

¹¹ For sketches of the major schools of thought on this issue in the period, see Jammer, M., Concepts of force, Cambridge, Mass., 1957, chapters VII–XI.Google Scholar

¹² What Euler is referring to when he claims that ‘if mobility be assumed, then inertia is assumed’ is what he earlier defined as that property by which a body persists in a state of rest or uniform rectilinear motion unless acted upon by an external force. He is not referring to inertial mass, a concept which has not yet been introduced.

¹³ Cf., for example, §56 of the Medianica, and §3 of the ‘Recherches sur l'origine des forces’.

¹⁴ One gets the strong impression that Euler's ‘very small’ particles are spherical, and in fact it helps to avoid misunderstanding to assume that they are. In particular, since the extent to which bodies are impenetrable is not a function of the areas of the parts of the surfaces that are in contact in impact, then bodies with flattened surfaces do not offer more impenetrability, or suffer more risk of penetration, than spheres, whose point of contact is infinitely small. The advantage of imagining spherical bodies lies in the fact that we are not tempted to think in terms of the impenetrability of a body as being determined by the extent of its impenetrable surface area: since the surface area of the point of contact does not matter we may just as well make it infinitely small, to avoid possible confusion.

¹⁵ Cf. also letters 52 to 57 of the Lettres à une Princesse d'Allemagne, opera omnia, series 3, vol. xi, Zurich, 1969.Google Scholar

¹⁶ The terms did originally designate forces for Newton. They do so in the De motti (1684) and in the revisions to this treatise; cf. in particular definition 12 of the third version (the manuscript De motu sphaericorum in fluidorum). But by the immediately subsequent drafts of the definitions and the laws of motion, in the De motu corporum in medijs regulariter (Law 1), and the second draft of the definitions, in the De motu corporum (definition 3), vis insita could no longer be regarded as a force maintaining a body in its motion, and this is true of all Newton's subsequent works. For the texts see Herivel, J. W., The background to Newton's Principia, Oxford, 1965.Google Scholar

¹⁷ See Home, R. W. and Connor, P. J., Aepinus' essay on the theory of electricity and magnetism, Princeton, 1979Google Scholar, for the relevant section of the Tentamen(p. 243), a general discussion of the issues (pp. 68 f), and a statement of Euler's reaction (p. 15).

¹⁸ Westfall, R. S., op. cit. (3), chapter I.Google Scholar

¹⁹ Cf. Cohen, I. B., Newton and Franklin, Philadelphia, 1956Google Scholar, and Home's introductory monograph in Home, and Connor, , op. cit. (18)Google Scholar, as well as his ‘Out of the Newtonian straightjacket: alternative approaches to eighteenth century physical science’, in Brissenden, R. F. and Eade, J. C. (eds.), Studies in the eighteenth century, vol. iv, Canberra, 1979.Google Scholar

²⁰ Ellis, B. D., ‘Universal and differential forces’, British journal for the philosophy of science, 1963, 14, 177–94CrossRefGoogle Scholar; ‘The origin and nature of Newton's laws of motion’, in Colodny, R. G. (ed.), Beyond the edge of certainty, Englewood Cliffs, NJ, 1965Google Scholar; ‘The existence of forces’, Studies in history and philosophy of science, 1976, 7, 171–85Google Scholar. Related reformulations are discussed in Sklar, L., ‘Inertia, gravitation and metaphysics’, Philosophy of science, 1976, 43, 1–23CrossRefGoogle Scholar. I have discussed some of the philosophical problems arising from the choice of different laws of inertia in my Explanatory structures, Brighton, 1978, pp. 22–9.Google Scholar