Abstract
In the general context of physics and in the planetary theory, in our specific case, the tendency of a rotating body to recede along the tangent is a fundamental element. We have seen that paracentric motion depends on the two opposite tendencies due to the solicitation of gravity and to the conate to recede. In terms of Newtonian physics the latter is a consequence of the inertia principle. Although Leibniz considered the conate to recede as a pivotal physical feature of curvilinear motions, he never associated it to the word inertia. Leibniz spoke of natural inertia, but this has nothing to do with the tendency to escape along the tangent. More in general: the natural inertia in Leibniz is not Newton’s inertia. Therefore some questions arise:
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Notes
- 1.
It is possible to speak of Galilean inertia or Cartesian inertia or, without referring to the inventor of inertia principle, of rectilinear inertia. I prefer to use the expression Newtonian inertia, as a principle becomes really significant only when it is inserted in a general picture—a theory—where it plays a precise role in the architectonics of the theory and in its deductive structure. This happened with Newton’s Principia. On this problem, I agree with Garber (see Garber 1992, pp. 200–204). Garber, even avoids using the expression “inertia principle” in reference to Descartes and writes: “[…] I have chosen to break the tradition and not to use the term ‘inertia’ in connection with Descartes’ first two laws of motion” (ivi, p. 203).
- 2.
Almost in every research on Leibniz’s physics there is a section concerning inertia. As studies specifically dedicated to the concept of inertia in Leibniz, I mention, without any pretension of being exhaustive: Bernstein (1981), Gabbey (1971), Ghins (1990), Giorgio (2011), Giulini (2002), Lariviere (1987), Look (2011), Ranea (1986), Woolhouse (2000a). Important references to the concept of inertia in Leibniz are also present in: Arthur (1998), Bertoloni Meli (1993), Bouquiaux (2008), Crockett (2008), Duchesneau (1994), Garber (1994, 2006, 2009), Jauernig (2008), Papineau (1977), Puryear (2012), Roberts (2003), Suisky (2009) (in particular Chap. 2).
- 3.
KGW, VII, p. 79, lines 31–34. Original Latin text: “Tertiò iners quidem est terra ad motum, eidemque aliunde illato quadamtenus resistit: at talia sunt omnia corpora, quatenus corpora; non meretur igitur Terra prae alijs corporibus locum centri hac inertia”.
- 4.
Ivi, p. 88, lines 9–13. Original Latin text: “Terra tota, quatenus tota, et respectu suae materiae, motum planè nullum habet naturaliter: materiae enim, qua plurima Terra constat, propria est inertia, repugnans motui, eaque tanto fortior, quanto major est copia materiae in angustum coacta spacium”.
- 5.
Ivi, p. 296, lines 30–33. Original Latin text: “Etsi globus aliquis coelestis non est sic gravis, ut aliquod in Terra saxum grave dicitur, nec sic levis, ut penes nos ignis: habet tamen ratione suae materiae naturalem άδυναμίαν transeundi de loco in locum, habet naturalem inertiam seu quietem, qua quiescit in omni loco, ubi solitarius collocatur”.
- 6.
I mention here some passages from Leibniz’s epistolary and works I consider particularly significant. Many other quotations could have been chosen, since Leibniz expressed these conceptions on several occasions.
- 7.
Leibniz for Sturm, before 5 July 1687, LSB, II, 3, pp. 335–346. Quotation pp. 339–340. Original Latin text: “[…] atque adeo ut resistentia generalem corporis materiam, ita nisus peculiarem cujusque corporis formam vel primam activitatem (ut ἐντελέχειαν τἡν πρώτην ex meo sensu interpreter) constituit; cum ipsa etiam extensi in partes divisio atque adeo figura, ex ipso oriatur. Et resistentia non tantum facit corporum impenetrabilitatem sed et aliud minus vulgo expensum nempe inertiam naturalem, a Keplero sic appellatam, qua fit ut materia non sit ad motum quietemque (ut plurimi arbitrantur) indifferens sed potius novo motui proportione molis suae repugnet, quemadmodum videmus navem magis oneratam, eodem vento tardius ferri”. The concept of Leibniz’s entelechy is developed, among other writings, in the Specimen Dynamicum.
- 8.
Leibniz to De Volder, 24 March (3 April) 1699, in LSB, II, 3, pp. 544–551. Quotation p. 547. Translation drawn from Leibniz (1989, p. 517). Original Latin text: “Cum igitur materia motui per se repugnet vi generali passiva resistentiae; at vi speciali actionis seu entelechiae in motum feratur; sequitur ut etiam inertia durante motu Entelechiae seu vi motrici perpetuo resistat”. The correspondence Leibniz–De Volder has been edited and translated by P. Lodge, see Leibniz (2013).
- 9.
Ivi, pp. 546–547. Translation drawn from Leibniz (1989, p. 516). Original Latin text: “Inertiam in materia alicubi, exemplo Kepleri, et Cartesium in Epistolis agnovisse notavi. Hanc deducis ex vi quam quaevis res habeat permanendi in statu suo, quae ab ipsa ejus natura non differat: ita simplicem extensionis conceptum sufficere etiam ad hoc phaenomenon arbitraris. Sed axioma ipsum de conservando statu, modificatione indiget, neque enim (ex. gr.) quod in linea curva movetur curvedinem per se, sed tantum directionem servat. Sed esto, sit in materia vis tuendi statum suum; ea certe vis ex sola extensione duci nullo modo potest. Fateor unumquodque manere in statu suo, donec ratio sit mutationis, quod est metaphysicae necessitatis principium, sed aliud est statum retinere donec sit quod mutet, quod etiam facit per se indifferens ad utrumque, aliud est multoque plus continet rem non esse indifferentem sed vim habere et velut inclinationem ad statum retinendum atque adeo resistere mutanti”. I do not enter into the problem of Leibniz’s reference to Descartes. It seems that Leibniz—also considering the reference to Descartes’ letters—is not referring to the first law of motion posed by Descartes in his Principia philosophiae, II, 37 (see Oeuvres de Descartes, 8, pp, 62–63), whose formulation is associated with the inertia principle. With regard to Descartes and natural inertia I refer to D.M. Clarke (1982), Appendix 2: The impact rules of Cartesian dynamics, in particular note 12, p. 232.
- 10.
Leibniz expressed several times the idea that the essence of the bodies cannot be reduced to their extension. For example the beginning of the Specimen Dynamicum 1, is quite clear as to this problem. See Leibniz (1695, 1860, 1962, VI, pp. 234–236).
- 11.
Leibniz to Papin 28 February (10 March) 1699, in LSB III, 8, pp. 67–71. Quotation pp. 69–70. Original French text: “Or, selon moy le repos n’estant autre chose qu’une simple privation; il s’ensuit que c’est donc la masse en elle même qui resiste au mouvement, et c’est ce que j’appelle avec Kepler, inertie. Mais quand le corps est en mouvement, et resiste au repos, alors je tiens qu’il a une force ou entelechie, qui le fait tendre à continuer le mouvement. D’où il s’ensuit que la masse resiste continuellement à l’entelechie, et ainsi qu’il y a action et reaction dans le corps même”.
- 12.
- 13.
Leibniz (1885, 1978, 6, pp. 119–120). Original French text : “Le celebre Kepler et apres luy M. des Cartes (dans ses Lettres) ont parlé de l’inertie naturelle des corps; et c’est quelque chose qu’on peut considerer comme une parfaite image et même comme un echantillon de la limitation originale des creatures […] C’est donc que la matiere est portée originairement à la tardivité, ou à la privation de la vitesse; non pas pour la diminuir par soy même, quand elle a déja reçu cette vitesse, car ce saroit agir, mais pour moderer pas sa receptivité l’effect de l’impression, quand elle le doit recevoir”.
- 14.
- 15.
- 16.
Leibniz (1695a, 1875–1890, 1978, IV, pp. 486–487). Original French text: “Et quant au movement absolu, rien ne peut le determiner mathematiquement, puisque tout se termine en rapports: ce qui fait qu’il y a tousjours une parfaite equivalence des Hypotheses, comme dans l’Astronomie, en sorte que quelque nombre de corps qu’on prenne, il est arbitraire d’assigner le repos ou bien un tel degré de vistesse à celuy qu’on en voudra choisir, sans que les phenomenes du mouvement droit, circulaire, ou composé, le puissent refuter. Cependant il est raisonnable d’attribuer aux corps des veritables mouvemens, suivant la supposition qui rend raison des phenomenes, de la maniere la plus intelligible, cette denomination estant conforme à la notion de l’Action, que nous venons d’étabilir”.
- 17.
Bertoloni Meli (1993, pp. 75–84), section 4.2: Mathematical representation of motion.
- 18.
Ivi, p. 83.
- 19.
Jauernig (2008, pp. 20–26), section IV. Proving EH.
- 20.
It is important to point out that the possible origin of curvilinear motions from rectilinear ones does not mean, obviously, to eliminate the physical differences between the two. The curvilinear motions maintain their own properties. Nevertheless their—so to speak—microscopic structure depends on the rectilinear motion. This structure, in Leibniz’s perspectives, allows him to explain, from a physical standpoint, properties as the tendency to recede along the tangent.
- 21.
Bertoloni Meli (1993, p. 31).
- 22.
Garber (2009, p. 115).
- 23.
Duchesneau (1994, p. 121).
- 24.
Leibniz (1671, 1860, 1962, VI, p. 68). Original Latin text: “Nam ubi semel res quieverit, nisi nova motus causa accedat, semper quiescet. Contra, quod semel movetur, quantum in ipso est, semper movetur eadem velocitate et plaga”.
- 25.
Bernstein (1981, p. 101).
- 26.
Suisky (2009, p. 55).
- 27.
Ivi, p. 62.
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Bussotti, P. (2015). An Interlude: Leibniz’s Concept of Inertia. In: The Complex Itinerary of Leibniz’s Planetary Theory. Science Networks. Historical Studies, vol 52. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-21236-4_3
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