Abstract
This chapter will describe and comment a treatise on Galileian Mechanics, Exercitationes in Mechanicis Aristotelis by the Jesuit scholar Giovan Battista Zupi, revealing the sources from which the author derived his text. The treatise presents the course of lessons on mechanics that Zupi gave when he first began to teach at the Neapolitan Jesuit College. Although the ideas exposed in this work were not generally original, because the lessons are skillfully compiled using works on mechanics by followers of Archimedes, such as Bernardino Baldi and above all Galileo Galilei, it is interesting to scholars in the history of science for at least three reasons: 1) The lessons result from a skilled compilation, demonstrating Zupi’s wide knowledge of mechanics, including the latest works circulating at that time. He was able to put together and harmonize chapters from the most meaningful works by different authors, thus creating an organic essay containing all the subjects concerning a modern theory of the simple machines. 2. The text is eloquent proof of the contradictions that characterized many aspects of Jesuit educational politics in the scientific field. 3) The treatise is an important documentation of the diffusion within Jesuit schools of the mechanical theories that Galileo exposed in his Le Mecaniche, a work he did not publish during his lifetime but that circulated at the time among the scholars featured in manuscript. This diffusion, in the case of the Neapolitan College, assumes the form of a popularization of Galilean ideas on mechanics since, at that time, the Jesuits had an almost complete monopoly on education in Naples.
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Notes
- 1.
The text of the Exercitationes is published in the appendix to Gatto (2006c). All the bibliographical references relate to this edition.
- 2.
See Galilei (2002).
- 3.
For more than one century, until 1650, there was no chair of mathematics established at the University of Naples.
- 4.
“Ea enim est huius facultatis nobilitas, ea dignitas, ut sapientissimi quoque illam praebaverint et acutissimis lucubrationibus illustraverint, ita Aristotelis, Pappus, Heron, Athenaeus, Archimedes, et ex recentioribus Alexander Piccolomineus, Guidus Baldus ex marchionibus Montis, Maurolicus, Baldus abates et alii” Exercitationes, 73.
- 5.
“sequimur autem tum Aristotelis, tum Archimedes, aliorumque in hac re peritorum doctrinam” Exercitationes, 73.
- 6.
We are referring to the Μηχανικά Προβλήματα (Mechanical Questions), at that time attributed to Aristotle. Today this work is almost unanimously attributed to an unidentified student of Aristotle, referred to as pseudo-Aristotle. Despite this, at that time an author had already expressed doubts about such an attribution, but Zupi was nevertheless persuaded that Aristotle was the author of the Quaestiones mechanicae (for this reason most Renaissance authors translated the title of the above-mentioned work from Greek into Latin).
- 7.
See Clavius (1589). The first edition of this work is Apud Vincentium Accoltum, Rome, 1574. During Clavius’s lifetime, this work was published again in 1589, 1591, 1603, 1607 and 1612. The impossibility of identifying “the difficult places” by Vernalione also led to discussions. I maintain that it is the 1589 edition, see Gatto (1994, 70–73). This is also Ugo Baldini’s and Pier Daniele Napolitani’s opinion, see Clavius (1992). On the contrary, Rosario Moscheo maintains that it must be a later edition, see Moscheo (1993–1994).
- 8.
“molti luoghi difficili, non ben capiti, ricevuti da Giovanni Paolo Vernalione colla promessa, che nello stampare gli suoi ingegnosissimi Commentari su la stessa materia di Euclide, facesse testimonianza al Mondo aver avuto da lui questo lume.” See Arcudi (1719, 160–161). About Giovanni Paolo Vernalione and the matter under discussion here, see Moscheo (1993–1994).
- 9.
See Gatto (2006a).
- 10.
- 11.
- 12.
See Galilei (1890–1909).
- 13.
See Gatto (2006a).
- 14.
See the manuscript at the Biblioteca Nazionale di Napoli (BNN) V H 370. Staserio applied his competence in mechanics to the planning of a mill.
- 15.
- 16.
A Tractado breve de Machinas Hydraulicas is included in a codex in the Archivio Nacional-Torre do Tombo of Lisbon (Manuscrito de livraria, 1770). In this codex the manuscripts of the lessons given by Lembo at the Jesuit college of Santo Antão in Lisbon between 1615 and 1617 are joined together. See Leitão (2001).
- 17.
In the school year 1631–1632 Camassa taught mathematics at the Neapolitan College. At the end of that year, at explicit request of King Philippe IV, he was sent to teach mathematics at the Estudio Reale de Santo Isidro in Madrid. Regarding his teaching, see Astrain (1916, 106).
- 18.
Sgambati taught mathematics at the Neapolitan College in the school year 1626–1627. The Disputationes are in the cc. 27–44 of his Compendiosa tractatio aliquarum rerum mathematicarum, ms V H 388 of the BNN which, besides the aforesaid text of mechanics, also includes De optica partition dicendorum, and Sphaera. The Disputationes are three in total: I De auctoribus ac definitionibus Mechanicae; II De motu circulari; III De instrumentis Mechanicis. About Sgambati and his Compendiosa tractatio, see Gatto (1994, 130–150).
- 19.
See Gatto (1996).
- 20.
About Colantonio Stigliola, see Ricci (1996, f. I), which contains an extensive bibliography about Stigliola’s life and work. Stigliola wrote a very interesting treatise on mechanics (1597), which soon became very rare. An anastatic copy of this treatise was published in Gatto (1996). About the analysis of this opera, see Gatto (2006b).
- 21.
- 22.
See Gatto (1994, 185–208, 211–221).
- 23.
For a wider and complete description of this treatise, see Gatto (1994).
- 24.
“et constet ex purissimo, et liquidissimo aere in quo planetae omnes tamquam avies ab intelligentiis sustentati, semper regulari girentur, huius crassities sit a firmamento usque ad terram et consequenter totum includat aera” Compendiariae adnotationes, cit., c. 105v. Zupi introduces this subject writing: “Quum in materia de coelo satis probavimus,” that is, “as about the sky we have already much proved.” Let us suppose that he explained his theory shortly before, probably in 1624 during his second year of teaching philosophy in the course of physics. This date would be justified by the fact that Bartolomeo Amico quotes Zupi’s theory in Amico (1626, 274).
- 25.
More details can be found in Gatto (1994).
- 26.
This manuscript is held at the BNN, XII D 75, cc. 1r–17r, see Gatto (1991). Imperiali himself wrote a treatise on mechanics, clearly following the Galilean style and subsequently datable to 1644. This treatise remained in manuscript form and is published in Gatto (1996). As regards Imperiali, see Gatto (1988).
- 27.
“quod insita propensione in centro mundi fertur” Exercitationes, 73. This definition is taken verbatim from Baldi (1621, 1).
- 28.
“quod per vim extrinsecam impressam pellitur” Exercitationes, 74. Baldi writes: “quod impressio extrinsecus pondere ab impellente pellitur,” Baldi (1621, 1).
- 29.
“Illum punctum in corpore gravi, quod corpore undecumque suspenso semper deorsum, id est directe versus centrum universi, pellet” Baldi (1621, 1).
- 30.
Sunt qui putent mechanicis instruentis naturae institutum fallere se posse, atque quavis minima vi seu potentia posse se quodlibet pondus superare, qua spe concepta, multa et mira se facturos praedicant. Sed tantum inani spe decepti, operam, et oleum, ut aiunt se perdidisse animadvertunt. Statuimus igitur fieri non posse, quibuscumque machinis ut potentia pondere minor, eodem tempore ac velocitate pondus per idem spatium moveat quo potentia ponderi aequalis ut eo minor.
- 31.
Ho visto ingannarsi l’universale de mecanici, nel volere a molte operazioni, di sua natura impossibili, applicare machine dalla riuscita delle quali, ed essi sono restati ingannati, ed altri parimente sono rimasti defraudati della speranza, che sopra le promesse di quelli avevano conceputa. Dei quali inganni parmi di aver compreso essere principalmente cagione la credenza, che i detti artefici hanno avuta ed hanno continuamente, di potere con poca forza muovere ed alzare grandissimi pesi, ingannando, in un certo modo, con le loro machine la natura; instinto della quale, anzi fermissima constituzione, è che niuna resistenza possa essere superata da forza, che di quella non sia più potente.
- 32.
Quod ut clarius illigitur, quattuor sunt considerando: primo pondus movendum ut ex uno loco in altrum transferendum, 2° vis, seu potentia quam tale pondus debet movere, 3° intervallum seu distantia ad teminum a quo et ad quem talis motus fieri debet seu velocitas et tarditas motus.
- 33.
Ci si fanno avanti quattro cose da considerarsi: la prima è il peso da trasferirsi di luogo a luogo; la seconda è la forza o potenza, che deve muoverlo; terza è la distanza tra l’uno e l’altro termine del moto; quarta è il tempo, nel quale tal mutazione deve esser fatta; il qual tempo, torna nell’istessa cosa con la prestezza e velocità del moto, determinandosi, quel moto essere di un altro più veloce che in minor tempo passa eguale distanza.
- 34.
All of these examples are also taken from Galilei (2002).
- 35.
On the contrary, Galileo introduces this example only after having demonstrated the principle of the lever.
- 36.
“sunt etiam qui in mensuranda distantia, quam intercedit inter fulcimentum vectis, seu centrum librae et pondus, seu potentia, maxime errant, unde in fabricandis machinis falluntur” Exercitationes, 76.
- 37.
“tunc certum est, haec pondera habere suum moment et centrum gravitatis in medio C a quo puncto suspense, aequiponderabunt” Exercitationes, 76.
- 38.
“descendet pondus A, neque momentum erit in B sed in F” Exercitationes, 76.
- 39.
“Primo: aequalia pondera ab aequalibus radiis, seu brachiis suspensa, aequiponderarent et potentia aequali sustineri; 2° pondus sive sublimius, sive humilius suspensum aequiponderare; 3° aequalium ponderum, quod maiori brachio suspensum est, magis ponderare; 4° unius corporis, unum tantum esse centrum gravitatis; 5° hoc centrum gravitatis respectu sui corporis semper in eodem esse situ; 6° suum hoc gravitates centrum pondera deorsum ferri; 7° aliud esse in re quanta corpus gravitatem et momentum. Saepe enim aliqua sunt aequalia in ratione corporis, et inaequalia sunt gravitatem, etc.” Exercitationes, 79.
- 40.
“Momentum est gravitas corporis compositum ex naturali propensione rei gravis ad motum deorsum, et ex positione, et collocatione eiusdem rei; qua re, corpus, a longiore librae brachio pendet, maius habere moment dicitur.” Galileo’s definition is: “Moment is the propensity of descending, caused not so much by the gravity of the mobile body, as by the disposure which divers grave bodies have in relation to one another; by means of such a moment, we often see a body less grave to balance another of greater gravity: as in a steelyard, a great weight is raised by a very small counterpoise, not through the excess of gravity, but through the remoteness from the point hereby the beam is upheld, which conjoined to the gravity of the lesser weight adds there unto moment, and impetus of descending, wherewith the moment of the other greater gravity may be exceeded. Moment then is that impetus of descending, compounded of gravity, position, and the like, whereby that a propensity may be occasioned” Exercitationes, 79.
- 41.
“Dico primo potentia sustinens pondus vecti appensum eandem ad ipsum proportionem habet quam habet pars vecti inter fulcimentum et pondus ad partem vectis inter fulcimentum et potentiam” Exercitationes, 79.
- 42.
“eadem erit proportio potentiae ad pondus quam est. inter distantiam ponderis a fulcimento, ad totum vectem” Exercitationes, 81.
- 43.
In reality he wants only to show that (1) and (2) allow the various problems of the two different classes of lever to be solved: to determine the position of the fulcrum such that a given power can lift a given resistance; to determine the power or the resistance once assigned the place of the fulcrum and the resistance or the power and so on. Zupi does not solve these problems arithmetically, that is, by determining the unknown term of the proportion (1) or (2), but practically, dividing materially the lever in a convenient number of parts and placing, according to the cases, fulcrum, power and resistance in such a way as to satisfy (1) or (2).
- 44.
“quantum ponderis substineant duae potentiae si loco fulcimenti statuatur alia potentia” Exercitationes, 81.
- 45.
“Ex quo aperte colligitur quantum medio vecte facilitates acquiritur tantum derogari de velocitate,” that is, the same as what Galileo himself affirms in Galileo (2002, 61, ll. 601–602): “comprendesi, come negli altri strumenti, in questo ancora, quanto si guadagna in forza, tanto perdersi di velocità,” that is: “we understand that, as in the other instruments, also in this one, the more it acquires in strength, the more it loses in velocity” Exercitationes, 82.
- 46.
See Dal Monte (1577).
- 47.
“cum scilicet vectis horizonti est inclinatus ut in vecte IBG etiam FBH, tunc enim adhuc mensuranda est distantia inter fulcimentum et punctum vectis in quod cadit perpendicularis ad horizonte ducta, ut in vecte FBH est punctum O et in vecte IBG est punctum E in quae puncta perpendiculares, DO, et DE cadunt” Exercitationes, 83. This is what Galileo also maintained in the chapter Alcune considerazioni sopra le cose dette in Galileo (2002, 53–54).
- 48.
“cum deprimitur pondus linea directionis magis recedit a fulcimento, maiusque momentum habet et consequenter maiorem proportionem habet linea OB ad BA, quam CB ad BA, igitur et maiori indigebit potentia” Exercitationes, 83–84.
- 49.
“sive elevetur vectis, sive deprimatur, semper pondus ab eadem potentia sustinebatur” Exercitationes, 85.
- 50.
“cur maiores librae esactiores sint minoribus” Exercitationes, 85.
- 51.
“In hac questione fere omnes in schemate lineando errant ita ut difficile admodum sit authoris sensum assequi” (Exercitationes, 87) where Baldi writes “Pessime omnes schema hoc linearunt, ita ut difficillimum sit autoris inde sensum assequi,” see Baldi (1621, 19).
- 52.
“si perfectae sint, in eodem situ manere, sive deprimantur, sive elevantur” Exercitationes, 88.
- 53.
“Verum hoc non esplicat quo modo fieri posse ut parvo existente motu gubernaculi tam magnus in ipsa prora oritur motus” Exercitationes, 89.
- 54.
“Ratio est, quia malus, sive navis arbor, est veluti vectis cuius fulcimentum est in fundo navis, pondus vero est in ea parte ex qua malus e carina, exit potentia movens est ventus in velum inpingens. Igitur quo sublimior est antenda eo longior evadit vectis, atque facilius movetur navis ab eodem vento. Hic notat quod si navis rexisteret a vento deberet puppies illius elevari, et prora in aquas demergi, quia vero propter maris liquiditatem, navis non resistit semper a vento impellitur ad partes anteriores” Exercitationes, 89.
- 55.
To confirm the aforesaid theory, Zupi adds an argument drawn by Baldi, that is, because the sails are more aloft they are more exposed to the wind “such as the towers, that the higher they are, the more they are hit from the winds” “sicut turres, quo sublimiores sunt eo magis a ventis infestantur,” see Exercitationes, 90.
- 56.
One of the most important subjects Zupi treated in this correspondence is how, in a lever, in computing the moments the arms of the power and of the resistance have to be considered. And this especially in consideration of the angular lever, a matter that Zupi explains in detail to his scholars. This correspondence is published in an appendix to Gatto (1996).
- 57.
“Ed ancorché nel muoversi a basso la forza F si venga a girare intorno la girella ABC, non però si muta l’abitudine e rispetto, che il peso e la forza hanno alle due distanze AD, DC; anzi la girella circondotta doventa una libra simile alla AC, ma perpetuata” Galilei (2002, 62, ll. 630–633).
- 58.
This is the same example given by Galileo (2002).
- 59.
“Ex dictis collige primum usum trocleae hoc 2° modo maxime iuvare ad ponderis elevationem, 2° colligitur clavum, quod funis religatur dimidium ponderis sustinere. Ponitur enim potential dimidium eius ponderis substinere, igitur clavus reliquam partem sibstinebit. 3° si duo erunt potentiae beneficio huius trocleae pondus aliquod substinentes, quod utraque simul esse deberet ponderi aequalis. Ratio est quia singulae dimidium ponderis substinent, atque utraque simul totum pondus substinet; et consequenter utraque esset illius aequalis” Exercitations, 92.
- 60.
“non posse haberi potentiae diminutionem remanente eadem velocitate” Exercitations, 92.
- 61.
“Et ratio est quia, ut pondus ascendat per spatium palmare, debet ex duobus funibus secundae figurae, quibus pondus substinetur detrahi duo palmi quod fit cum potentia duos palmos funi trahit” Exercitations, 93.
- 62.
“trocleam superiorem esse inutilem ad diminutionem virium et solum maxime iuvare ad applicandam potentiam, quod quidem et superiori troclea detracta eadem vis requiritur ad pondus A substinendum” Exercitations, 94.
- 63.
“duae diametri KF, ON se habent ut vectes AB CD decimae figurae [here Figure 14] et funes FS, NC IL ut tres potentiae aequales, et funae OB, KD ut duo fulcimenta” Exercitations, 99.
- 64.
“si velis potentiam augere secundum numerum parem scilicet ut sex, ut octo, ut centum, etc., in inferiori troclea tot urbiculos adde, quot dimidium numeri assumpti conflant. Exempli gratia, si sit augenda potenti aut sex, colloca tres urbiculos in inferiori troclea, et alterum funis extremum in superiori troclea, sit relegatum; in superiori vero troclea tot multiplicentur orbiculi quot ad funem per tres inferiores circumducendum necessarii videbuntur” Exercitations, 101.
- 65.
See Pappus Alexandrinus (1588).
- 66.
“quod sine illo per plures et replicatas operationes facere deberemus, eo mediante unica operatione perficimus” Exercitationes, 104.
- 67.
“spatium ponderi moti ad spatium potentiae moventis, sicut se habet potentia ad pondus” Exercitationes, 104.
- 68.
“Bernardinus Baldi docet hoc provenire quia cunei maxime ad superficiei naturam accedunt: clavi, vero subulae pugiones accedunt ad naturam lineae superficiei vero et lineae penetrandi vim conceditur et iis corporibus quam ad illos accedunt. Haec sententia mihi placet quare eam explico et rationibus etiam physicis hoc modo confirmo” Exercitationes, 105.
- 69.
This is the object of pseudo-Aristotle’s Problem XVIII: “Why if a heavy axe is put on a wooden stump and a great weight is on it, the axe does not chop the wood appreciably, but if the axe is lifted up and then the wood is struck, this is broken in half even if the weight of the striking axe is very small with respect to a weight that sets on [the stump] exerts exerting pressure on it.”
- 70.
“quantum virium acquirimus, tantundem amicti temporis, et velocitatis” Exercitationes, 106.
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Gatto, R. (2018). A Treatise on Galileian Mechanics: Exercitationes in Mechanicis Aristotelis by the Jesuit Giovan Battista Zupi. 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_8
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