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Heaviness, Lightness and Impetus in the Seventeenth Century: A Jesuit Perspective

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Part of the book series: Boston Studies in the Philosophy and History of Science ((BSPS,volume 270))

Abstract

This paper examines the mechanical project of a Jesuit scientist-engineer Paolo Casati (1617–1707), as presented in his Mechanicorum libri octo (1684). The core of the project consists in an attempt to physicalize the mathematical science of machines while using Archimedes’s lever principle and his theory of buoyancy. Casati, however, aimed at enriching this science with principles originating in the Aristotelian science of motion. The fusion of Archimedean and Aristotelian elements—including the concept of impetus as the sole cause of motion—allowed him to deal with the motion of machines in terms of a hydrostatic theory of motion, neutralizing the Aristotelian notion of “positive lightness,” but without erasing it. This he did while engaging himself with experiments on “positive lightness” done at the Academia del Cimento (1657–1667). While this analysis throws light on the transformation of Aristotelian science in Jesuit schools of the seventeenth century, it also frees some Jesuits, at least, from a far too simplistic historiographical category of Galileo’s “nemici” (foes) and inserts them instead into the field of debates relevant for understanding the emergence of “the new science.”

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Notes

  1. 1.

    For a modern translation into English, see Middleton (1971, 92–255); on the Academy, see Beretta et al. (2009); Boschiero (2003, 2007); Galluzzi (1981, 2001).

  2. 2.

    G followed by a number is one of the 347 volumes of the Galilean manuscripts at the Biblioteca Nazionale Centrale in Florence (FBNC). Here G. 283, 35r–36r, cited by Middleton (1971, 225).

  3. 3.

    G. 262, 83r; G. 268, 117r–18r in Middleton (1971, 224, n. 252).

  4. 4.

    For an English translation, see Middleton (1971, 221–225).

  5. 5.

    In proposition xc, we find a version of the first part of this experiment. Borelli refers explicitly to experiments performed in the Accademia, see Borrelli (1670, 128 and 170).

  6. 6.

    For a good account of Casati’s life and work, see Gavagna (1999, 3–15).

  7. 7.

    On the category of engineer-scientists, see Valleriani (2010, 207–211).

  8. 8.

    Pierre Duhem dedicated a chapter to Jesuit treatises in his Les Origines de la Statique Duhem (1905, XVI). Even though Casati’s book was published in the 1680s, in the letter to the reader the author remarked that it was based on materials for the courses he had given at the Collegio Romano during the 1650s. The inclusion of the academicians’ experiment may testify that Casati updated the text later on.

  9. 9.

    The full title of the book reads as follows: “Eight books of Mechanics in which by one and the same principle of the lever, the forces are physically explained & geometrically proven.”

  10. 10.

    On the tradition of writing problems, see Blair (1999, 171–204).

  11. 11.

    Casati (1684, Introduction to Book II, 125). The original reads as follows: “Nunc propius ad ipsam machinalem scientiam accedendum, quam Mechanicam dicimus. Haec Geometriae subjicitur, neque enim, ut illa, puram corporum quantitatem molisque extensionem abstracte considerat, sed quatenus gravitati illigatam aut levitati; […] Quamvis autem ea quoque Statices pars, quam Hydrostaticen indigitamus, se pariter in corporum gravitate consideranda exerceat, aliam tamen sibi contemplationem assumit; motum siquidem corporum singulorum naturae congruentem, pro humorum in quos incurrunt, diversitate, potissimum speculatur. Mechanice vero eatenus solum ingenitam corporibus propensionem in motum aut quietem explorat, ut earum facultati perspectae vim possit opportuna instrumentorum machinatione inferre. Quapropter ut certa methodo machinas oneribus movendis pares construere valeamus, motus machinalis causas ante cognitas habere necesse est quam machinas ipsas aggrediamur” Casati (1684, Introduction to Book II, 125).

  12. 12.

    See Chap. 1, by Renn et al. in this volume.

  13. 13.

    On the physicalisation of the Aristotelian “mixed mathematical sciences,” see Schuster (2013, 24). On the science of motion developed by Jesuits in the second half of the seventeenth century, see Chap. 10 by Feldhay and Elazar in this volume.

  14. 14.

    For the interpretation of Descartes, Galileo and Beeckman in terms of preclassical mechanics, see Damerow et al. (2004).

  15. 15.

    See note 3.

  16. 16.

    “[…] in calling things heavy and light we mean that they have a capacity for a certain natural motion,” Aristotle and Guthrie (1939, 307b32–4).

  17. 17.

    See Mugler (1951, 202, fn. 11).

  18. 18.

    In Galileo’s words: “…it appears to me that Signor Buonamico imposed on Archimedes, deducing from what he said more than he set forth or that can be deduced from his propositions, inasmuch as Archimedes neither denied nor admitted positive lightness …” Drake (1981, 66).

  19. 19.

    Many can be added to this list, among them: Clavius’ edition of the Elements (1589), printed by Bartolomeo Grassi, presents Archimedes’ work as the last stage of the work of Euclid thus articulating a purely geometrical interpretation of Archimedes, Dollo (1992, 201). A. F de Gottignies, V. Giordani and D. Quarteroni were also inspired by Archimedes, Baldini (1992a, 273).

  20. 20.

    Although some of those letters have been lost (Clavius–Commandino), others—those written to Guidobaldo del Monte and Bernardino Baldi—have survived and been published, Philips (1939, 193–222). Both are cited in Baldini (1992a, 246).

  21. 21.

    Cited in Gorman (1998, 33).

  22. 22.

    Anon. Praefatio 1591 attributed to C. Grienberger by Michael J. Gorman (2003, 40).

  23. 23.

    “Omissis aliorum solutionibus, respondeo gravitatem et levitatem sumi posse dupliciter. Primum pro actu primo, scilicet pro qualitate ipsa movente sursum aut deorsum. Secundo, pro actu secundo, scilicet pro motu ipso […] In fine ergo motus non augetur gravitas aut levitas primo modo accepta ut supra dixi, augetur tamen gravitas secundo modo, hoc est gravitatio. Haec enim nihil est aliud quam excessus virtutis motivae super resistentiam medii.” Dollo (1992, 215) quoting M. Vitelleschi, Libros de Coelo Disputationes, Tractatiotertia De Elementis, cc. 124v–125r, in Dollo (1990, 184–5).

  24. 24.

    See Baldini (1992a, 1992b, 75–78, 157–8); Dear (1995, Chap. 2); Dollo (1990); Elazar (2011); Feldhay (2006); Palmerino (2003); Wallace (1977, 1981, 1984).

  25. 25.

    Benedetti (1553, 17–18): “I say that if there are two bodies of the same shape and the same material, whether equal [in size] to each other or unequal, they will, in the same medium, move over an equal distance in an equal time.” See also the introduction to Drake and Drabkin (1969, 32–41).

  26. 26.

    On Galileo’s possible reading of Benedetti and his relation to Benedetti’s legacy, see Renn and Damerow (2012, Chap. 3.10).

  27. 27.

    Machinarum vires, quibus innatæ corporum in motum aut quietem propensioni obsistimus” Casati (1684, Liber Primus, 1).

  28. 28.

    His porrò jactis fundamentis operosum non erit in ædificare, & machinarum singularum vires, sivè simplices illæ sint, sivè compositæ, exponere: adeò ut iis ritè intellectis, quæ hoc secundo libro disputabuntur, vix quicquam in reliquo opere supersit difficultatis” Casati (1684, Liber secundus, 125).

  29. 29.

    The original reads: “Cùm enim radij à sphæræ centro ad superficiem ducti longiùs à se invicem recedant, æquum fuit, ut quæ plus habent materiæ atque substantiæ sub minori mole, in angustiore spatio collocarentur; ea verò, quæ sub majoribus dimensionibus continentur, ampliora spatia occuparent, ubi radij magis distant: ut videlicet hac ratione æqua substantiæ distributio fieret in totâ sphærâ” Casati (1684, 2–3).

  30. 30.

    Quare centrum hoc, quod motus, vel quies corporum respicit, dicitur Centrum gravium, & levium; atque idem creditur esse cum centro universi: vel saltem (ne parùm utili nos disputatione torqueamus) centrum eorum, quæ in hac sphærâ elementari gravia, aut levia dicuntur,” Casati (1684, 3): “Therefore this center to which the motion or rest of bodies relates is called the center of heavy and light things, and it is believed to be identical to the center of the universe, or at least (to avoid being dragged into useless disputation) the center of the things called heavy or light in this elemental sphere.”

  31. 31.

    quæ plus habent materiæ atque substantiæ sub minori mole” Casati (1684, 4).

  32. 32.

    See, for example, Borelli (1670, proposition 41, 93ff). The argument is that it is superfluous to assume two principles of motion when one will suffice to explain everything.

  33. 33.

    Nam si ea, quæ levia dicuntur, eatenus dicas ascendere, quatenus à gravioribus in inferiorem locum descendentibus propelluntur; mihi æquè liberum erit tollere omnem positivam gravitatem, solâ levitate admissâ; & omnia pariter solvam dicendo ea gravia censeri, quæ minùs levia sunt, atque ideò tantùm descendere, quòd extrinsecùs à levioribus ascendentibus loco pulsa detrudantur, non quòd ab internâ facultate deorsum impellantur” Casati (1684, 4).

  34. 34.

    Original reads: “… non leviter suadere potest corpora suis nutibus non deorsum tantum sed etiam sursum conari” Casati (1684, 5).

  35. 35.

    Original reads: “Quid enim partis immersae ad extantem (si moles spectetur) ea ratio est, quae specificae gravitatis ligni ad differentiam gravitatum ligni, atque mercurij.”

  36. 36.

    “Non ausim tamen in lapide, qui gravitatem in aqua & aere, levitatem in mercurio, aut plumbo liquente obtinet, duplicem statuere virtutem …” (Casati (1684, 11).

  37. 37.

    “…ab uno eodemque principio, pro varia contigui corporis conditione, ascensum, descensumve prodire posse.”

  38. 38.

    Quandoquidem motus, qui in eadem lineâ perficitur, similes planè includit ubicationes successivè acquisitas, sivè ascensus sit, sivè descensus, ordine tantùm in earum adeptione, commutato. Quare cum ascensus à descensu hoc uno differat, quòd quam ubicationem lapis demùm obtineret post alias propè finem motûs, [.. .] ad ordinem hunc permutandum non videtur necessaria virtutis motricis dissimilitudo; nihil quippe producitur dissimile. Sed si quis sufficere dicat conditionum varietatem, nihil absonum fortè loquatur.” Casati 1(684, 11).

  39. 39.

    See also Des Chene (1995, 245): “To ‘ubicate’ something is to change its Ubi, that accident of a thing which consists in its being here or there.

  40. 40.

    “quandiu enim corpus ita simili secundum gravitatem corpore circumfun ditur, ut naturali in loco consistere dicendum sit” Casati (1684, opening of Book II, Chap. 3, 146).

  41. 41.

    “Impetum hunc, qui naturali se movendi facultati respondet, & est ipsa gravitatio, seu naturalis ad descensum propensio” Casati (1684, 146).

  42. 42.

    “Cum enim eadem descendentis lapidis natura perseveret [....] qui fieri possit, ut descendens velocitatem augeat, nisi ei, quem primum produxit, alium atque alium momentis singulis impetum adjiciat” Casati (1684, 136).

  43. 43.

    Cave tamen existimes parem esse lapidis ejusdem, & in aëre, & in aquâ descendentis impetum: natura scilicet ex medio dividendo, in quo perficiendus est motus, metitur impetûs modum” Casati (1684, 138).

  44. 44.

    Perit igitur Acquisitus impetus non totus simul; sed sensim extenuatur; idque non aliâ ratione, quàm quâ proportione impeditur motus, quocumque tandem ex capite impedimenta oriantur. Cum enim impetus contrarium impetum non habeat, si præcisa quidem impetûs natura spectetur [...] reliquum est, ut pereat pro ratione eorum, quæ aut motui corporis obsistunt, aut illud aliò quoquomodo dirigunt.”

  45. 45.

    “Illud certe extra omnem controversiam positum videtur, naturam gravem sponte sua non ascendere; quid ergo illud est., quod eburneum globulum, in subjectam rupem delapsum resilire cogit […] nisi quia conceptus natura procurante impetus pergit motum efficere, ipsa etiam natura quantum potest, obsistente” Casati (1684, 136–137).

  46. 46.

    In 1667 Rinaldini left for Padua, see Middleton (1971, 34–35).

  47. 47.

    Because Casati thinks that a trochlea will solve the problem of a perpendicular ascendance, and that the measuring was not accurate, the position Borelli refers to is that it is not possible to elevate the cylinder in this way, using either the balance or the trochlea.

  48. 48.

    The unpublished Cimento diary can be found amongst the Galilean manuscripts held at the Biblioteca Nazionale Centrale di Firenze (BNCF) in the folio labeled Gal. 262.

  49. 49.

    Although unable to offer a full analysis in this format, we shall try to delineate schematically the main contours of the field.

  50. 50.

    In a letter to Paolo del Buono, October 10, 1657 he wrote of a “rotten and mouldy peripatetic” among the academicians. In Abetti and Paganini (1942, DIS, 20, note 2); Middleton (1971, fn. 83, 34).

  51. 51.

    Here is a quotation from Casati’s Terra machinis mota where he contends that the experiment is incapable of deciding the matter of the weight of air and the connection to the existence or non-existence of void: “Quare nihil est in toto hoc experimento; quod vel leuem inferat Vacui suspicionem; in oculos semper incurrit corpus, tenue illud quidem ac rarum, à quo vasis spatia occupantur. Hoc itaque experimento non satis probari nostri aëris grauitatem absolutè , mihi certissimum est; sed illud vnum ex inæquali recipientis pondere antè ac post aëris extractionem vi antliæ, confici potest, quod non inficior, scilicet communem hunc nostrum aërem in aëre alio magis raro grauitare posse.” Casati (1658, 171).

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Feldhay, R., Even-Ezra, A. (2018). Heaviness, Lightness and Impetus in the Seventeenth Century: A Jesuit Perspective. 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_9

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