1 Three, and perhaps four, of these experiments are considered in an excellent study by Charles Schmitt, B., ‘Experimental Evidence For and Against a Void: the Sixteenth-Century Arguments,’ Isis 58 (1967) 352–366. Discussions of experiments appear also in Duhem, Pierre, Le Système du monde VIII (Paris 1958) 121–168 (chapter 9: ‘L'horreur du vide’) (a nearly identical version of this chapter was published by Duhem in <e>A. Little, G. [ed.], Roger Bacon Essays [Oxford 1914] 241–284 [Chapter X: ‘Roger Bacon et l'horreur du vide’]) and Cornelis de Waard, L'expérience barometrique: ses antécédents et ses explications (Thouars 1936) especially 14–20. The ‘experiments’ were largely observations, or alleged observations, cited for the apparent purpose of supplying additional confirmation of a theory and belief the truth of which was beyond dispute. See also Schmitt, op. cit. 353–354 n. 3.Google Scholar

2 Nicholas of Autrecourt; see my article, ‘The Arguments of Nicholas of Autrecourt for the Existence of Interparticulate Vacua,’ XII ^e Congrès International d'Histoire des Sciences, Paris, 1968, Actes (Paris 1971) IIIA 65–68.Google Scholar

3 A few argued for the existence of a real, infinite void beyond the finite cosmos. See my article, ‘Medieval and Seventeenth-Century Conceptions of an Infinite Void Space Beyond the Finite Cosmos,’ Isis 60 (1969) 39–60. It was also commonplace to allow that God, by His supernatural powers, could, if He wished, create a vacuum anywhere within the world.Google Scholar

4 The source of the medieval Latin dogma that ‘nature abhors a vacuum,’ which was already expressed in the thirteenth century and perhaps earlier (see Duhem, Le Système du monde VIII 158 and also note 9, below, on Adelard of Bath, who may have implied it), is uncertain. It seems not to have been derived directly from the works of Aristotle, who, despite his vigorous arguments against the existence of any kind of vacuum (see especially Physics IV 6–9), did not explicitly declare an equivalent of the medieval principle. A more plausible candidate is Philo of Byzantium's Liber de ingeniis spiritualibus (although various titles exist, the one cited here appears in Wilhelm Schmidt's Latin edition and German translation in Heronis Alexandrini Opera I [Leipzig 1899] 459–489; Schmidt's edition was based upon Valentin Rose's earlier text, which bears the same title, in Anecdota Graeca et Graecolatina II [Berlin 1870] 299–313), a treatise on pneumatics probably translated into Latin no later than the thirteenth century (a judgment based upon the existence of a thirteenth century manuscript version, British Museum, Sloane MS 2030, fols. 110^r-114^r, mistakenly titled Liber Aristotelis de conductibus aquarum) from a much longer extant Arabic text (for the Arabic text with French translation, see Baron Carra de Vaux, ‘Le Livre des appareils pneumatiques et des machines hydrauliques par Philon de Byzance,’ in Notes et Extraits des Manuscrits de la Bibliothèque Nationale et Autres Bibliothèques [Paris 1930]).Google Scholar

Philo argued that air and water (as indeed air and fire) were commingled and continuous and that water would follow air as if glued to it with birdlime (see Schmidt's edition p.464; also 468 and 472). Should air rise, it would draw up the water below it. Philo denied the existence of natural or artificial separate vacua because ‘if air is evacuated, any of the bodies that are mixed with it succeed it immediately because by their very natures they are impelled [to do so]’ (my translation from ibid. 476). Evidence of such behavior and proof that separate void spaces do not exist (he mentions interparticulate vacua without committing himself on their existence [ibid. 462]) are found in some of Philo's experiments. Philo's attribution of a glue-like connection between air and water may have been but an extension of Aristotle's declaration in De caelo IV 5 312^b 4–12 that ‘air will not move upwards into the place of fire if the fire is removed, except by force in the same way as water is drawn up (σπᾶται) when its surface is amalgamated with that of air and the upward suction (σπάσῃ) acts more swiftly than its own downward tendency. Nor will water move into the place of air, except as just described’ (<e>W. K. C. Guthrie, trans. [Loeb Classical Library; London/Cambridge, Mass. 1939] 360–3). For both Aristotle and Philo water rises, contrary to its natural tendency to descend when in air. Perhaps it was from Aristotle's passage that Philo and others inferred what was probably implied by Aristotle, namely that water rises against its nature in order to prevent formation of a vacuum. This same Aristotelian passage elicited from Averroes a lengthy comment in which Averroes argues that, in order to prevent a vacuum, air will descend (when the water below has been removed) and water will rise (when the air above has been removed). See Averroes' Commentary on De caelo IV Comment 39 (<e>ed. Junta V [Venice 1562; repr. under the title Aristotelis opera cum Auerrois commentariis, Frankfurt 1962] fols. 264^v-266^v). In the course of his discussion Averroes had occasion to summarize opinions of the Greek commentators Alexander of Aphrodisias and Themistius whose views on this subject might not otherwise have been known in the Latin West, since the works containing these opinions were not translated during the Middle Ages. Among the ideas cited is one by Alexander that when air contracts and occupies a smaller volume, it will attract water upward to prevent formation of a vacuum. Much of Averroes' Comment 39 is given over to a defense of his contention that water cannot rise as easily as air can descend (see also Duhem, Le Système du monde VIII 124–126).

It is perhaps worthy of mention that the Greek terms cited above in the quotation from Aristotle were translated by forms of trahere in the Latin translation made from the Greek text of De caelo by William of Moerbeke in the thirteenth century. Hence the important sense of suction or drawing was preserved. In Michael Scot's earlier translation from the Arabic, no counterpart for the Greek terms appears, leaving the impression that water rises to replace the displaced air by means of a violent pushing motion rather than by some kind of suction power. Both translations accompany Averroes' commentary on De caelo cited above (see fol. 264 col. 1 for Moerbeke's version and col. 2 for Michael Scot's).

Some of the ideas described above were given a rather different emphasis by Peter of Abano in the Conciliator differentiarum, written in 1310 (on this, see also Duhem, Le Système du monde VIII 164–165). Peter argues that ‘if air were removed [from above water], water rushes into its [i.e. air's] place by violence; similarly if fire were removed [from above air], air will fill its place by violence, but not conversely. For if water or earth should withdraw [from below air], air tends naturally [to move downward] into its place by the inclination of its heaviness and not by the necessity [of avoiding] a vacuum.’ (‘Si vero removeatur aer violentia in ipsius concurrit locum aqua; similiter si tollatur ignis, aer ipsius locum violentia replebit et non e contra. Si autem secedat aqua vel terra naturaliter aer [text: aere] tendit in ilium locum ex inclinatione gravitatis et non necessitate vacui,’) (Conciliator differentiarum philosophorum et precipue medicorum, Differentia XIV [<e>ed. Mantua 1472, fol. 30^v col. 2]).

In a manner similar to that of Philo and Aristotle, Peter sees in the common surface shared by air and water the cause of the water's motion as it rises to replace the withdrawn air. (‘Rursus quorum [i.e., air and water] est una superficies, unum inclinatur in aliud cum habeant inter se communionem. Sed una extat superficies aeris et aque’ [ibid.]). The upward motion of the water is violent because water is heavier than air. (‘Descendit igitur naturaliter aer ad aquam; non autem ipsa [i. e., the water] cum sit gravior aere ad ipsum sed violenter magis coadiuvante tamen superficie una prefata’ [ibid.]). Peter makes no appeal to nature's abhorrence of a vacuum as an explanatory principle. Indeed, in the case of the air's downward motion, he explicitly denies it as a cause, since the air's downward motion is natural by virtue of its relative heaviness. On the basis of another rejection of an appeal to nature's abhorrence of a vacuum as a physical explanation (ibid.), there is reason to believe that Peter of Abano was one of the few in the Middle Ages who refused to invoke nature's abhorrence of a vacuum to explain the contrary motions of air and water in the absence of readily identifiable external motive forces.

5 The theory is discussed in Roger Bacon's Communia naturalium (Opera hactenus inedita Rogeri Baconi Fasc. III [<e>edited by Robert Steele; Oxford 1911] 219–224). The text of the Summa philosophiae has been published by Baur, Ludwig, Die philosophischen Werke des Robert Grosseteste (BGPMA 9; Münster 1912). For summaries, see Duhem, Pierre, Le Système du monde VIII 146–152 (an almost identifical description also appears in Duhem's above cited article in Roger Bacon Essays at 266–273) and Charles McKeon, K., A Study of the ‘Summa philosophiae’ of the Pseudo-Grosseteste (New York 1948) 177–182. The author of tht Summa, it should be noted, does not explicitly infer the impossibility of vacuum from the existence of a universal nature (discussed below), but from the nature of place and lighe (see McKeon 179).edited by Robert Steele; Oxford 1911] 219–224). The text of the Summa philosophiae has been published by Baur, Ludwig, Die philosophischen Werke des Robert Grosseteste (BGPMA 9; Münster 1912). For summaries, see Duhem, Pierre, Le Système du monde VIII 146–152 (an almost identifical description also appears in Duhem's above cited article in Roger Bacon Essays at 266–273) and Charles McKeon, K., A Study of the ‘Summa philosophiae’ of the Pseudo-Grosseteste (New York 1948) 177–182. The author of tht Summa, it should be noted, does not explicitly infer the impossibility of vacuum from the existence of a universal nature (discussed below), but from the nature of place and lighe (see McKeon 179).' href=https://scholar.google.com/scholar?q=The+theory+is+discussed+in+Roger+Bacon's+Communia+naturalium+(Opera+hactenus+inedita+Rogeri+Baconi+Fasc.+III+[edited+by+Robert+Steele;+Oxford+1911]+219–224).+The+text+of+the+Summa+philosophiae+has+been+published+by+Baur,+Ludwig,+Die+philosophischen+Werke+des+Robert+Grosseteste+(BGPMA+9;+Münster+1912).+For+summaries,+see+Duhem,+Pierre,+Le+Système+du+monde+VIII+146–152+(an+almost+identifical+description+also+appears+in+Duhem's+above+cited+article+in+Roger+Bacon+Essays+at+266–273)+and+Charles+McKeon,+K.,+A+Study+of+the+‘Summa+philosophiae’+of+the+Pseudo-Grosseteste+(New+York+1948)+177–182.+The+author+of+tht+Summa,+it+should+be+noted,+does+not+explicitly+infer+the+impossibility+of+vacuum+from+the+existence+of+a+universal+nature+(discussed+below),+but+from+the+nature+of+place+and+lighe+(see+McKeon+179).>Google Scholar

6 It is probable that bodies were thought to possess their particular natures as inherent properties. What is unclear and vague in medieval discussions is the status of the universal nature. Is it also an intrinsic property of all matter? Or is it a separately existing agent acting on bodies from outside? As we shall see, Bacon, and especially Walter Burley, who speaks of a ‘universal celestial agent,’ seem to have conceived it as an independent entity acting on bodies externally. Another author (see below n. 13), who identified the ‘universal agent’ with God, believed that God endowed bodies with the power to prevent separation of their parts when disruption threatened. Because of this ambiguity, however, I speak here not only as if matter possessed a dual nature, but also suggest that the universal nature might be external.Google Scholar

The source of the distinction between universal and particular nature is perhaps the Liber de causis, a work falsely ascribed to Aristotle, which was translated from Arabic to Latin by Gerard of Cremona in the twelfth century (both Arabic and Latin versions were edited by Otto Bardenhewer, Die pseudo-aristotelische Schrift Ueber das reine Gute bekannt unter dem Namen ‘Liber de causis’ [Freiburg i. Br. 1882]; a recent Latin edition based on 90 manuscripts has been published by Adriaan Pattin, Le Liber de causis [Louvain 1966]). The Arabic version was probably an ‘original’ treatise (or perhaps a translation from an ‘original’ Syriac version) based on Proems' στoιχείωσις θεoλoγιϰή (it was Thomas Aquinas who made this discovery after a comparison of the Liber de causis with William of Moerbeke's recently completed Latin translation of the Greek text of Proclus' work, which Moerbeke titled Elemeniatio theologica; see Bardenhewer 270–271 and Pattin 4).

In the first chapter of the Liber de causis, a remote first cause (causa prima longinqua) is distinguished from a proximate cause (causa propinqua). To exemplify the relationship of these causes, the interconnections of ‘existence,’ ‘life’ and ‘man’ are considered. Existence is the cause of life and life is the cause of man. Therefore, existence is the remote cause of man and life the proximate cause. If man is deprived of life, he nevertheless remains as an existence because removal of the effect — i.e., life as the effect of existence — does not remove the cause. Consequently, ‘it is obvious and plain that a primary remote cause is more comprehensive and intense than a proximate cause and for this reason, the operation of the primary remote cause is more intense in a thing than the operation of a proximate cause. And this happens only because a thing is effected first by a remote power and then, secondly, by a power subordinate to the first power; and the first cause aids the second cause in its operation because every operation which the second cause effects, the first cause also effects. But the first cause effects it in a higher and more sublime mode. Now when the second cause is removed from the thing it caused, the first cause is not removed from it because the first cause is of greater intensity in inhering in a thing than the proximate cause. The effect of a second cause is not determined [or established] (figitur) except by the power of the first cause. This is so because when a second cause makes something, the first cause, which is above it, flows into this thing with its power and therefore clings to it intensely and serves it (My translation from Bardenhewer 162 and Pattin 48–49; the two editions are in virtual agreement for the passage summarized and translated here).

The relationship between remote and proximate causes described in the Liber de causis may have served as a model for Bacon and Pseudo-Grosseteste in relating universal and particular causes. This conjecture gains a measure of plausibility from Bacon's statement that ‘what a universal cause is is given in the Treatise on Causes’ (‘Quid vero sit causa universalis, expositum est superius in Tractatu de causis’; see the Communia naturalium [ed. cit. 220]). In addition to Roger Bacon and Walter Burley, who will be discussed below, others who explicitly applied the theory of matter's dual nature to explain nature's abhorrence of a vacuum were Aegidius Romanus (Giles of Rome), John of Jandun, Franciscus Mayronis, Graziadei d'Ascoli, Johannes Canonicus, Henry of Hesse (for references see Pseudo-Siger Duhem, Le Système du monde VIII 152–158, 160–161, and 166–168; Burley is not included in Duhem's discussion), and the author of the much later treatise titled Commentationes in octo libros Physicorum Aristotelis wrongly attributed to Aegidius Romanus (Commentationes Physicae et Metaphysicae, Physicorum libros octo, De coelo libros quatuor … traditae a … Fratre Aegidio Romano [Ursellis 1604] Physicorum Aristotelis liber quartus p. 182). By the latter part of the fourteenth century, when the theory of a particular and universal nature was widely accepted, it was sometimes encapsulated, without further elaboration, in one version or another of the expression ‘nature abhors a vacuum’ (see W. K. C. Duhem, ibid. 158–160).

7 In his Summa logicae et philosophicae naturalis, pars sexta, cap. III. See Duhem, , Le Système VIII 162–163, where the source of Dumbleton's passage is erroneously given as Bibliothèque Nationale, fonds latin 16621 fols. 60^c-61^a; for the manuscript probably intended see below n.22. According to Peter of Abano in his commentary on Aristotle's Problemata (completed at Padua in 1310) Avicenna held nature's abhorrence of a vacuum to be so powerful that he believed the heavens themselves would, if necessary, descend to fill a potentially void space (Duhem, ibid. 164).Google Scholar

Not all scholastics were of the opinion that the sides of the heaven would meet to prevent a vacuum. In Bk. IV Question 26 of the Quaestiones super libros Physicorum falsely ascribed to Siger of Brabant, the author argued that the existence of a vacuum in the concavity of the heavens is less impossible than a contactual meeting of the sides of the heaven to prevent that vacuum. Thus although both are impossible, the existence of an actual vacuum in the heavens is more likely than a collapse of the sides of the celestial spheres. (‘Maius autem impossibile esset latera caeli concurrere, et ideo magis ponendum esset vacuum quam latera caeli concurrere’ [K. C. de Brabant, Questions sur la Physique d'Aristote [edited by Philippe Delhaye in Les Philosophes Beiges XV; Louvain 1941] 184).

8 As Duhem observed (Le système du monde VIII 136), the clepsydra was an instrument embracing a variety of decanting vessels, including spigot, funnel, pipette, and chantepleure. Alexander Neckam, who wrote around 1220, defined a number of these, which he calls by the generic title clessedra, in his De utensilibus (see Duhem, , ibid; in his De naturis rerum, cap. XIX [Quod nullus locus sit vacuum, vel diu vacuus], Neckam describes the clepsydra, without naming it, as an ‘urceus habens fundum multis foraminibus distinctum et orificium superius.’ See <e>Thomas Wright [ed.], Alexandri Neckam De naturis rerum libri duo; with the poem of the same author, De laudibus divinae sapientiae [London 1863; reprinted 1967] 64). The instrument which I have described above was sometimes called cantaplora (chantepleure in French).Thomas+Wright+[ed.],+Alexandri+Neckam+De+naturis+rerum+libri+duo;+with+the+poem+of+the+same+author,+De+laudibus+divinae+sapientiae+[London+1863;+reprinted+1967]+64).+The+instrument+which+I+have+described+above+was+sometimes+called+cantaplora+(chantepleure+in+French).>Google Scholar

9 The interpretation of the clepsydra's behavior as a refutation of the formation of a vacuum could have reached the Latin West from a number of possible sources among the earlier of which must be reckoned Philo of Byzantium's Liber de ingeniis spiritualibus, Ch. XI (ed. Schmidt 480, 482) and Averroes' Physics Commentary, IV Comment. 51 (Junta edition, IV fol. 148^r col. 1), which offers a meager account. Although Aristotle mentions the clepsydra in Physics IV 6 213a 22 ff., De caelo II 13 294b 21, De respiratione 473a 15–473b 10, and Problems XVI 8 (the last two works are not by Aristotle himself but derive from his school), he does not interpret the clepsydra's behavior as a demonstration of the non-existence of vacuum but refers to an experiment in which the corporeality of air is demonstrated (Philo in Ch. II [ed. Schmidt 460, 462] also demonstrates the corporeality of air by means of a vessel with only one hole at the bottom). A later thirteenth-century source is Simplicius' commentary on De caelo translated from Greek into Latin in 1271 by William of Moerbeke. Simplicius provides a substantial description of the clepsydra and also explains that it is to prevent a vacuum that the water does not fall when the upper orifice is closed (see Simplicii… commentaria in quatuor libros De celo Aristotelis, Guillermo Morbeto interprete [Venice 1540] fol. 184r col.1; for an English translation of the passage from the Greek text see W. Guthrie, A History of Greek Philosophy II [Cambridge University Press 1965] 221). By the latter part of the thirteenth century mention of the clepsydra and the behavior of the liquid contained within it to prevent formation of a vacuum became commonplace.Google Scholar

Already in the first half of the twelfth century, long before any of the sources mentioned above had become available (with the possible exception of Philo's treatise), Adelard of Bath gave a description of the clepsydra without naming it. In Chapter 58 of his Quaestiones naturales, Adelard's nephew recalls a visit to a witch in whose house

But Adelard rejects all appeal to magic and explains that

A considerable literature now exists on the meaning and significance of ancient Greek discussions of the clepsydra; for a recent article, which also includes additional bibliography, see D. Thomas Worthen, ‘Pneumatic Action in the Klepsydra and Empedocles’ Account of Breathing,’ Isis 61 (1970) 520–530. A useful brief account is given by Roger Guthrie in a note to his translation of Aristotle On the Heavens (Loeb Classical Library; London/Cambridge, Mass. 1960) 226–229.

10 While conceding that water remained suspended in the clepsydra under the usual conditions, Bernardino Telesio, in the sixteenth century, argued that the conditions might be varied sufficiently so that the clepsydra could actually be used to demonstrate the existence of a vacuum. For ‘if you would make only one opening of the clepsydra a little wider and you would somehow open the lower part of it, you would see that the fluid within would immediately flow down out of the [enlarged] opening and from the lower part. Furthermore, honey and any other fluids, which are a little heavier, as well as very fine but dense and heavy powder, flow out of the openings of the clepsydra’ and thus leave behind a vacuum. The translation is Schmitt's, art. cit. (above n. 1) at 360.Google Scholar

11 Bacon, Communia naturalium I pars 3 (ed. cit. 219 lines 28–29); Walter Burley, Questiones circa libros Physicorum IV. q. 6 (Thomson 39) (Utrum vacuum possit esse) in MS Basel Universitätsbibliothek F. V. 12 fol. 65^r col. 2. This manuscript of Burley's Questiones (there is no printed edition) dates perhaps from the late fourteenth century and contains only the first 43 of 108 questions listed in a table of questiones on folios 108^r-108^v. Harrison Thomson, S., who discovered the manuscript, describes it in ‘Unnoticed Questiones of Walter Burley on the Physics,’ Mitteilungen des Instituts für österreichische Geschichtsforschung 62 (1954) 390–405. Another manuscript containing Burley's questions on Books I, V, VI, and VII, but not our question from Book IV, has been discovered by Vladimir Richter of Innsbruck in Cambridge, Gonville and Caius 512 fols. 109^r-126^v (I), 220^r-234^v (V-VII). Cf. Zimmermann, A., Verzeichnis ungedruckter Kommentare zur Metaphysik und Physik des Aristoteles I (Leiden-Cologne 1971) 226–8.Google Scholar

12 ‘But a negation is not the cause of an affirmative [action]; “that a vacuum not occur” is a negation.’ (‘Set negacio non est causa affirmacionis: “ne fiat vacuum” est negacio’ — Bacon, Communia naturalium I pars 3 [ed. cit. 219 lines 28–29]). ‘Similarly, this question seeks a positive cause preventing the descent of the water. Therefore it does not suffice to say that the water is prevented from descending “that a vacuum not occur,” for this is not a cause.” (‘Similiter ista questio querit causam positivam prohibentem descensum aque. Non sufficit ergo dicere quod prohibetur descendere “ne fiat vacuum,” hec enim non est causa’ — Burley, Questiones fol. 65^v col. 2; for more on the ‘positive cause,’ see below note 19).Google Scholar

13 Although Bacon consistently uses the expression natura universalis, Burley uses (op. cit. fol. 65^v col. 2, quoted below note 16) indifferently agens superceleste (‘supercelestial agent’), agens celeste (‘celestial agent’), virtus regitiva universi (‘regulative power of the universe’), and agens universale (‘universal agent’), thus indicating a power or force emanating from the heavens. In the Commentationes in octo libros Physicorum Aristotelis, falsely ascribed to Aegidius Romanus (see note 6 above), the author actually identifies the universal agent as God when he says: ‘although every particular agent confers particular tendencies on [each] generated thing — for example, lightness or heaviness so that it can be moved to its place — God, nevertheless, as universal agent, not only confers on the parts of each thing a universal tendency to be joined and united when its better preservation demands it, but He also confers on things, insofar as they are parts of the universe, a tendency to be joined [or connected] when necessity demands it.’ (‘Unde quamvis quodlibet agens particulare tribuat rei genitae particulares appetitus, verbi gratia, levitatem aut gravitatem ut ad suum locum moveatur [text: moventur], Deus, tamen, tanquam agens universale, sicut tribuit partibus cuiuslibet rei appetitum universalem se coniungendi atque copulandi quando melior sui conservatio id postulat, ita etiam tribuit rebus, quatenus sunt partes universi, appetitum sese coniungendi quando id postulat necessitas’) (p. 182).Google Scholar

14 Questiones supra libros octo Physicorum Aristotelis IV Quaestio: Utrum sit ponere vacuum infra celum, in Opera hactenus inedita Rogeri Baconi XIII <e>edd. Delorme, F. M. and Steele, R.; (Oxford 1935) 230.edd.+Delorme,+F.+M.+and+Steele,+R.;+(Oxford+1935)+230.>Google Scholar

15 The collapse of the sides of a vessel in the manner described is called by Bacon ‘essentially unnatural’ (innaturale essentialiter), whereas water at rest above and outside of its natural place is merely ‘accidentally unnatural’ (accidens unnaturale) (ibid.). The greater disruption of nature following the collapse of a vessel is obviously the basis for this terminological distinction.Google Scholar

16 Since I have already summarized the argument, only the Latin text will be cited: ‘Ymmo videtur quod oportet dicere quod virtus regitiva universi vel aliquod agens superceleste regens ordinem universi faciat [text: faciens] aquam moveri sursum ne fiat vacuum; et similiter impediat aliquando aquam moveri deorsum ne fiat vacuum. Contra probo quod agens universale non prohibeat aquam descendere in cantaplora quia si orificium cantaplori obturetur, tunc non descendet; si non obturetur, tunc descendet. Sed agens celeste eiusdem virtutis est et uniformiter agit sive orificium illius vasi [text: vasis] obturetur sive non. Si ergo agens celeste impediret descensum aque quando orificium obturatur, ipsum similiter impediret descensum aque quando orificium non obturatur. Similiter ex quo tale agens est agens universale indifferens est ad hunc effectum et ad eius oppositum. Ergo oportet ibi ponere aliam causam particularem determinantem illud agens celeste ut nunc prohibeat descensum huius aque et alias faciat aliam aquam ascendere. Et tunc redit difficultas de illa causa particulari ibi ponenda’ Questiones super Libros Physicorum IV q. 6 (39) [fols. 65^v col.2–66^r col. 1]).Google Scholar

17 ‘Moreover, in the seventh [book] of the Metaphysics, Comment 32, the Commentator shows that the celestial agent has control over the lower [i.e. sublunar] things where he says that it is impossible that a corporeal agent should move through [or across] matter except with supercelestial bodies mediating. Similarly, in the first [book] of the De celo, Comment 24, the Commentator says that the celestial bodies conserve the elements.’ (‘Quod autem agens celeste habet regere hec inferiora paret Commentatorem [sic] septimo Metaphysice, commento 32, ubi dicit quod impossibile est ut agens corporeum transmuttet materiam nisi mediantibus corporibus supercelestibus. Similiter primo De celo, commento 24, dicit quod corpora celestia conservant elementa’ [ibid. fol. 66^v col. 2]).Google Scholar

18 Whether the downward motion of the air was to be understood as a natural or a violent motion as it replaced the departing water is left unspecified by Burley. Perhaps his silence implies that only the air's particular nature is operative, thus signifying that its motion was conceived as natural. One might justify such an interpretation by the fact that the clepsydra is in the natural place of air, so that the air's descent could be construed as an expansion or rarefaction to fill the place vacated by the water's natural downward movement. Otherwise, the air's descent would be characterized as unnatural and its cause could only be explained as an intervention of the universal agent. Cf. Peter of Abano's interpretation of the air's descent in n.4, above.Google Scholar

19 Excluding the quotation in the preceding note, Burley's text in support of ideas summarized in this paragraph is as follows: ‘Ad rationes. Ad primam dico, sicud ultimo dicebatur, quod aliquod agens celeste prohibet aquam in cantaplora ne descendat et idem agens facit aliquando aquam ascendere ne sit vacuum, natura enim abhorret vacuum. Ideo illud agens quod regit naturam et ordinem naturalem in universo, illud idem salvat plenitudinem in universo, quia si est vacuum in aliqua parte universi, tunc deficeret aliqua pars requisita ad perfectionem universi et tunc universum non esset perfectum. Ideo illud agens celeste quod regit ordinem universi et salvat perfectionem eius, illud prohibet aquam descendere ne fiat vacuum ibi et deficiat aliqua pars requisita ad perfectionem universi. Unde quando arguitur quod oportet ibi ponere causam positivam, iam posita est causa positiva, scilicet agens celeste salvans ordinem universi et ei correspondens effectus positivus, scilicet salvare perfectionem et plenitudinem universi. Unde iste effectus privatus “ne sit vacuum” non est proprius effectus, sed effectus suus est positus, scilicet ut universum sit plenum et perfectum; Universum autem non esset perfectum si esset vacuum quia tunc in aliqua parte universi, vel ‘unum nichil’ esset pars universi. … Ad primum, in contrarium, quando accipitur quod agens celeste uniformiter agit super orificium cantaplore sive obturetur sive [non], dicendum quod uniformiter agit quantum ad effectum primum. Semper enim uniformiter intendit hunc effectum, scilicet salvare plenitudinem et perfectionem universi. Tamen realis effectus secundarii intenti difformiter agit. Aliquando enim facit aquam moved, aliquando quiescere et semper propter effectum eundem, primo, [sic] scilicet propter plenitudinem et perfectionem universi. Nec est inconveniens agens celeste habere contraries effectus in istis inferioribus quia sol aliquando est causa generationis aliquando causa corruptionis’ (ibid).Google Scholar

20 Burley argues as follows: ‘To the second [principal argument], it should be said that the universal agent is adequately determined to this effect, namely to make the water rest in the clepsydra, for the reason that if in this effect the plenitude and perfection of the whole could not be saved [or preserved], then, since an end [or goal] imposes the necessity [for achieving that end] and determines those things that are [necessary] for achieving it, it is necessary that the celestial agent seeking this end, namely to preserve the plenitude [or fullness] of the universe, be necessitated to make the water rest there. Therefore, when you seek what determines this agent to this effect, I say that it is determined by the end [or goal] of the universe and is necessitated by that end. It is unnecessary to assume another determinant than the end [or goal], for [it is] the end [or goal] that determines the agent to make those things that exist for the sake of producing the end [or goal].’ (‘Ad secundum, dicendum quod agens universale satis determinatur ad hunc effectum, scilicet ad faciendum aquam quiescere in canthaplora, propter hoc quod si in isto effectu non posset salvari plenitudo et perfectio universi, (cum ergo finis imponat necessitatem et determinet ad ea que sunt ad finem), oportet quod agens celeste intendens istum finem, scilicet salvare plenitudinem universi, necessitetur ad faciendum ibi aquam quiescere. Unde quando tu queris quid determinat illud agens ad hunc effectum, dico quod determinatur a fine universi et necessitatur a fine. Nec oportet ibi ponere aliud determinans quam finem, finis enim determinat agens ad faciendum ea que sunt propter finem’ [ibid. fols.66^v col.2–67^r col.1]).Google Scholar

21 ‘… quoniam nisi totum universum inferius coniunctum non poterit gubernari a mundo superiori, ut docet Aristoteles, I Meteorologicorum, cap. 2. Ergo natura ipsa abhorret vacuum ratione cuius tribuit singulis rebus appetitum universalem sese coniungendi atque copulandi’ (Pseudo-Aegidius Romanus, Commentationes physicae et metaphysicae, Physicorum libros octo p. 182 [see above n.6]). A similar judgment was expressed by Themon Judaeus, who insisted that the heavens, or celestial region, could not act on the inferior terrestrial world through a vacuum ‘because an agent must be immediate to the patient; the heavens are an agent and inferior things are under its action, …’ (‘… quia agens debet esse immediatum passo et celum est agens et illa inferiora patiuntur ab illo, ….’ [Questiones super quatuor libros Meteororum I questio 1, in Questiones et decisiones physicales insignium virorum: Alberti de Saxonia in octo libros Physicorum, … Thimonis in quatuor libros Meteororum … Buridani in Aristotelis … recognitae rursus et emendatae summa accuratione et iudicio Magistri Georgii Lokert Scotia quo sunt Tractatus proportionum additi (Paris 1518) fol. 156^r col.1]).Google Scholar

22 My translation is from Duhem's French translation of John Dumbleton's Summa (he omits the Latin text) in Le Système du monde VIII 162. As the manuscript source for this passage, Duhem erroneously cites (ibid. 161 n.2) MS Bibliothèque Nationale, fonds latin 16621 fols. 60^c-61^a. Not only are there no double-columned folios in BN lat. 16621, but the folios cited constitute part of Roger Swineshead's De motibus naturalibus (see <e>M. Clagett [ed. and tr.], Nicole Oresme and the Medieval Geometry of Qualities and Motions (Madison, Wis. 1968] 649). Fortunately, Duhem mentions a further discussion of Dumbleton's Summa in his Études sur Léonard de Vinci III (Paris 1913; reprinted 1955) 411–412 and 460–464, where we learn that the passage in question is probably to be found at the same folios in MS Bibliothèque Nationale, fonds latin 16146.M. Clagett [ed. and tr.], Nicole Oresme and the Medieval Geometry of Qualities and Motions (Madison, Wis. 1968] 649). Fortunately, Duhem mentions a further discussion of Dumbleton's Summa in his Études sur Léonard de Vinci III (Paris 1913; reprinted 1955) 411–412 and 460–464, where we learn that the passage in question is probably to be found at the same folios in MS Bibliothèque Nationale, fonds latin 16146.' href=https://scholar.google.com/scholar?q=My+translation+is+from+Duhem's+French+translation+of+John+Dumbleton's+Summa+(he+omits+the+Latin+text)+in+Le+Système+du+monde+VIII+162.+As+the+manuscript+source+for+this+passage,+Duhem+erroneously+cites+(ibid.+161+n.2)+MS+Bibliothèque+Nationale,+fonds+latin+16621+fols.+60c-61a.+Not+only+are+there+no+double-columned+folios+in+BN+lat.+16621,+but+the+folios+cited+constitute+part+of+Roger+Swineshead's+De+motibus+naturalibus+(see+M.+Clagett+[ed.+and+tr.],+Nicole+Oresme+and+the+Medieval+Geometry+of+Qualities+and+Motions+(Madison,+Wis.+1968]+649).+Fortunately,+Duhem+mentions+a+further+discussion+of+Dumbleton's+Summa+in+his+Études+sur+Léonard+de+Vinci+III+(Paris+1913;+reprinted+1955)+411–412+and+460–464,+where+we+learn+that+the+passage+in+question+is+probably+to+be+found+at+the+same+folios+in+MS+Bibliothèque+Nationale,+fonds+latin+16146.>Google Scholar

23 Lucretius On the Nature of the Universe (<e>R. Latham, E., trans.; Penguin Books [Harmondsworth 1951]) 38–39.R.+Latham,+E.,+trans.;+Penguin+Books+[Harmondsworth+1951])+38–39.>Google Scholar

24 The De rerum natura of Lucretius was known to Lactantius, but otherwise he is scarcely mentioned by either pagan or Christian writers of the early centuries of the Christian era. Curiously, two excellent manuscripts — the Leyden Oblongus and Quadratus — were produced in the ninth century and are the basis of the current textus receptus. The manuscript Poggio discovered in 1417 (see Clark, A. C., “The Literary Discoveries of Poggio,” Classical Review 13 [1899] 119–130) is thought to have been of Carolingian times; from it have come the 35 Italian MSS of the fifteenth century. Marullus and Lambinus edited the text in the sixteenth century and, in the nineteenth, Lachmann and Munro, H. A. J.: all of them were primarily interested in Lucretius as a poet and as an example of the best of Roman literature. Concern for the scientific ideas of Lucretius had to await the edition of Giussani (Turin 1896–1898) and Bailey's text, translation and commentary, 3 vols. (Oxford 1947). Hence, in the period of this study, Lucretius was of no influence.Google Scholar

25 My conjecture is based on a statement by Blasius of Parma, who, after describing the experiment and noting the possibility that a vacuum might be left in the center before air rushed in to fill it, declares that the Commentator [i.e. Averroes] gives this as a reason why many philosophers tend to believe that two hard bodies could not mutually touch. (‘Et hec ratio Commentator [is] facit multos philosophos inclinare ad credendum duo corpora dura non posse [text: possint] se tangere’ [Questio Blasij de Parma De tactu corporum durorum, which, though omitted from mention in the title page, appears as the last treatise in Questio de modalibus Bassani Politi] Tractatus proportionum introductorius ad calculationes Suisset/ Tractatus proportionum Thoma Bradwardini/ Tractatus proportionum Nicholai Oren/ Tractatus De Latitudinibus formarum Blasij de Parma/ Auctor sex inconvenientium (Venice 1505); the folios are unnumbered but the quotation above appears in the first column of the second page of Blasius' brief work]). The location of Averroes' discussion is not given.Google Scholar

26 Among those who adopted this position, we mention here only Pseudo Siger of Brabant (Questiones super libros Physicorum IV Questio 24 [op. cit. 178, 180]), Bacon, Roger (Questiones supra libros octo Physicorum Aristotelis IV [in Opera hactenus inedita Rogeri Baconi Fasc. XIII 225–226]), John of Jandun, (Questions on the Physics IV Question 10 [in Aristotelis Phisicorum libros preclarissimi philosophi Johannis de Ganduno Questiones … incipiunt … (Venice 1488) fols.68^v, 69^v]) and the Jesuits, Coimbra (Commentariorum Collegii Conimbricensis Societatis Iesu In octo libros Physicorum Aristotelis Stagiritae Prima Pars [Cologne 1602] cols.77, 83–84).Google Scholar

27 Translated from Questiones supra libros Physicorum Aristotelis, IV (in Opera hactenus inedita Fasc. XIII 226). John of Jandun also adopted this position: ‘Indeed if they [i.e. two plane bodies] were to be separated, it would be necessary that first one part then another be separated successively. And as much space as there is between those parts, just so much air would enter so that the air would enter successively as the planes are successively separated. It is impossible, however, that all parts [of the planes] be separated simultaneously and uniformey because of the avoidance of a vacuum.’ (‘Immo si disiungere<n>tur oportet quod prius separaretur una pars quam alia successive et quantum esset spatium inter illas partes tantum de aere ingrederetur et sic successive subintraret aer sicut successive disiungere<n>tur. Impossible autem esset quod omnes partes simul tempore separarentur ab invicem et equaliter propter fugam vacui.’ [op. cit. fol.69^v col.1]).tur+oportet+quod+prius+separaretur+una+pars+quam+alia+successive+et+quantum+esset+spatium+inter+illas+partes+tantum+de+aere+ingrederetur+et+sic+successive+subintraret+aer+sicut+successive+disiungeretur.+Impossible+autem+esset+quod+omnes+partes+simul+tempore+separarentur+ab+invicem+et+equaliter+propter+fugam+vacui.’+[op.+cit.+fol.69v+col.1]).>Google Scholar

28 In referring to the passage in question, Duhem says (Le Système du monde VIII 142): ‘Chacun sait qu'un verre plongé dans l'eau se laisse soulever sans grand effort; au contraire, l'adherence de deux disques plans se peut observer sans aucune difficulté. Il est clair que notre auteur n'avait tenté ni l'une ni l'autre des deux epreuves.” Duhem's severe criticism of Bacon misses the point. We may plausibly assume that Bacon observed glasses raised from the surface of water and had occasion to witness the separation of plane surfaces. He merely explains such phenomena as resulting from slight, and perhaps undetectable, inclinations of the surfaces, without which separation could not occur.Google Scholar

29 Burley's text, summarized in this paragraph, is the following: ‘Contra sive sit sive non, non minus stat argumentum quia posito quod inequaliter elevetur, ita quod magis fiat elevatio ex una parte quam ex alia, nichilominus aer circumdans ineque cito replebit partes interiores sicud exteriores et per consequens reliquitur ibi vacuum. Ymmo dicitur quod pars tabule elevabitur ante partem in infinitum’ (Questiones super libros Physicorum IV q. 6(39) [fol.66^r col. 1]). This passage is perhaps susceptible of another plausible interpretation. Instead of the intervening space conceived as a series of minute parts, Burley may have had in mind the entire intervening space itself. Following the angular separation of the surfaces and assuming that it necessarily takes a finite time for the incoming air to sweep from the open end to the point where the surfaces remain in contact, a momentary vacuum would occur near the point of contact prior to the arrival of the air. Such an opinion was apparently reported by Pseudo-Siger of Brabant (‘Si elevetur prius secundum alteram partem, adhuc erit ponere vacuum, quia aer non potest pervenire a parte prius elevata’ [op. cit. 178]) as one of three exhaustive possibilities (the other two being parallel, simultaneous separation and denial of separation, the latter promptly dismissed as absurd). In a subsequent discussion of the experiment, Pseudo-Siger adopts the position that separation can only occur when one surface is inclined to the other. The formation of a vacuum is now dismissed, without justification or elaboration, as undemonstrated. (‘Ad aliud de experimento [i.e., the experiment concerning the separation of two surfaces] dicendum quod numquam posset superius corpus directe elevari ab inferiori nisi prius secundum unam partem, et non contingit ea separari alio modo a praedictis [i.e. in the three ways mentioned earlier], quasi videlicet contrahendo unum super alterum et quasi planando unum per aliud, et ideo non concluditur illud experimentum ad probandum vacuum esse’ [ibid., p. 180]).Google Scholar

In the very next section, Burley again rejects part-after-part separation by appeal to the nature of the continuum, which, as Aristotle says in Metaphysics X (Chapter 1?), is something whose motion is one. Now if one part is moved, the whole continuous surface must move. Hence a vacuum will form since the air will reach the outer parts before the inner parts of the space between the separated surfaces. (‘Contra per Philosophum 10 Metaphysice verum continuum est cuius motus est unus. Volo ergo quod illa tabula sit medie continua vel aliqua pars eius. Ergo quantumcumque aliqua pars eius movetur totum movetur. Si ergo tale corpus elevetur erit ibi vacuum antequam aer potest replere partes interiores spatii’ (Questiones super libros Physicorum IV q.6 (39) [fol.66^r col.1]).

30 That the third article contained Blasius' own opinion is evident from his declaration that ‘In the third article, I shall determine the proposed question for the affirmative side according to what seems to me must be said.’ (‘In tertio articulo determinabo propositam questionem pro parte affirmativa secundum quod mihi videbitur fore dicendum’ [see p.2 col. 2 of Blasius' treatise in the volume cited above in note 25. Since the folios are unnumbered, I have supplied the pagination]).Google Scholar

31 I have assumed that the surfaces are circular, since, as we shall see, Blasius speaks of a circumference, radius, and center.Google Scholar

32 The text of the first conclusion summarized to this point is as follows: ‘Prima est: possible est duo corpora dura plana, et cetera, adinvicem equidistanter applicari. Probatur ista conclusio, quia si non esset hoc possibile hoc immo esset quia daretur vel motus in instanti vel propter aliquid inconveniens. Sed ostendo quod nullum sequatur quia quando ista corpora equidistanter veniunt ad contactum et queritur de aere mediante: an aer centralis moveatur prius ad punctum medium semidiametri et posterius ad circumferentiam, vel simul ad hec loca? Dico quod prius ad punctum medium et posterius extra circumferentiam, quia, ut dicit tertia suppositio, omnis motus localis tempore mensuratur. Et quando infertur igitur, tunc in centro relinquiretur vacuum. Nego consequentiam, quoniam quando non erit aer in centro, ista corpora se tangent, eo quod eque cito aer centralis erit extra circumferentias istorum corporum sicut erit aer qui est iuxta circumferentiam’ (op. cit. p. 5 col. 1).Google Scholar

33 The second of five suppositions, which says that ‘whatever the velocity by which some air is moved, other air can be moved infinitely more quickly …’ (‘Secunda suppositio: quacumque velocitate data qua aliquis aer movetur in infinitum potest velocius alius aer moveri …’ [ibid. p. 4 col. 2]).Google Scholar

34 ‘Et modus est iste: quia sit b aer qui est iuxta centrum, et sit a aer qui est iuxta circumferentiam, modo dico sic ad hoc quod a aer iuxta circumferentiam exiens moveatur ad extra requiritur tempus mensurans istum motum. Sed quacumque velocitate data qua moveatur iste aer a ad extra, potest aer centralis b moveri in centecuplo velocius per unam suppositionem et in millecuplo. Quare in eodem tempore erunt isti aeres a et b moti ad extra’ (ibid. p. 5 col. 1).Google Scholar

35 ‘Tertia difficultas de eo quod dictum est in declarando unam conclusionem[i.e. the first conclusion under discussion here]. Dictum fuit enim quod in approximando duo plana ad invicem, aer centralis erat eque cito extra circumferentiam sicut erat aer qui erat iuxta circumferentiam quod non videtur esse verum cum unus et idem sit motor propellens exterius aerem centralem etaerem qui erat iuxta circumferentiam et cum una et eadem esset applicatio propellentis ad istos aeres' (ibid. p. 5 col. 1).Google Scholar

36 ‘… licet iste aer centralis et iste circumferentialis moveantur ab eodem motore, ut scilicet a lapide plane qui deorsum movetur versus alium, non tamen moventur secundum eandem proportionem eo quod aer situatus in circumferentia habet in motu suo aerem extrinsecum sibi continue magis et magis resistentem propter maiorem et maiorem condensationem eius; sed aer centralis habet continue minorem et minorem resistentiam quia aer sibi immediatus continue est minor et minor et continue est rarior et rarior. Et hoc faciliter potest intelligenti patere. Et ideo licet iste aer et ille moveantur ab eodem motore non tamen secundum eandem proportionem, ut patet’ (ibid. p. 6 col. 1).Google Scholar

37 The loci of such discussions were separate treatises usually titled De instanti, or commentaries and questiones on Aristotle's Physics, Bks. VI and VIII, which contained the fundamental concepts that gave rise to this large body of literature. Wilson, Curtis, William Heytesbury, Medieval Logic and the Rise of Mathematical Physics (Madison, Wis. 1956) 31–32, distinguishes two phases in the approach of the medieval Schoolmen. The first ‘in which, naturaliter loquendo, the Schoolmen sought to apply the distinction [i.e. of intrinsic and extrinsic boundaries] directly to the physical magnitudes of the Aristotelian world-lengths, velocities, weights, and indeed whatever physical quantity may be conceived as continuous; the other in which, logice loquendo or sophistice loquendo, and applying the distinction to problems which were imaginable but presumably not capable of physical realization, they arrived at results which are of interest for the mathematical analysis of the continuum and of infinite aggregates.’Google Scholar

38 How a quantity of air could rarefy indefinitely without occurrence of a vacuum is not explained. That it could is simply assumed. In a future article, I shall describe and interpret medieval explanations of condensation and rarefaction.Google Scholar

39 A reference to the fourth supposition, which declares: ‘No minimum distance can be assigned by which distant bodies are separated, so that I wish to say that if any bodies are newly separated, they will previously have been separated by half that distance. And this is true unless we should say that any bodies are first separated now when they begin to exist, since two bodies could now be generated, one in the east and one in the west. However, the supposition [excludes the latter case and] comprehends [only] bodies which begin their separation by local motion [rather than by distinct generations in widely separated places].’ (‘Quarta suppositio. Non est dare minimam distantiam per quam corpora distantia distant, ut velim dicere quod si aliqua corpora nunc noviter distant prius per medietatem distantie distabant. Et hoc est verum nisi diceremus aliqua corpora nunc primo distare cum inceperunt esse quia nunc possent generari duo corpora, unum in oriente et reliquum in occidente. Suppositio autem intelligitur de corporibus que inceperunt distare per motum localem’ [op. cit. p. 5 col. 1]).Google Scholar

40 ‘Secunda conclusio. Possibile est duo corpora dura et plana abinvicem equidistanter elevari. Probatur conclusio quia si non, hoc esset: vel eo quod daretur vacuum vel motus in instanti, ut communiter dicitur. Sed quod hoc non sequatur declaro quia cum tu queris de aere existente in circumferentia vel eque cito movetur ad centrum sicut ad punctum medium semidiametri vel prius ad punctum medium semidiametri quam ad centrum, dico quod prius movetur ad punctum medium semidiametri quam ad centrum. Et cum tu concludis ergo est tunc vacuum in centro, nego adhuc consequentiam quia quandocumque fuit aer in puncto medio semidiametri prius fuit alius aer in centro. Volo tamen quod omnis aer qui est in centro prius fuit in puncto medio semidiametri. Unde nullus est primus aer qui primo fuerit in centro quia sicut nulla est prima distantia qua ista corpora plana nunc distant, ut dicit una suppositio, sic non est aliquis aer qui primo subingressus est. Et ideo quicumque aer est nunc in centro prius fuit in puncto medio semidiametri. Et sic non sequitur aliquid inconveniens’ (ibid.).Google Scholar

41 Bacon insisted that nothing could intervene between a plane surface and air in air or a plane surface and water in water. Therefore, ‘if my palm touches the Seine, then, if the palm is raised from the water, it is necessary to assume that in the central point [of my palm] there would be a dimension without air and water. Hence there is a void, or at least a disposition toward a void, which is false.’ (‘… ponamus quod nichil tangat se in aere vel in aqua, set tangat immediate aquam, ut si palma mea tangat Secanam, tunc, si elevetur palma ab aqua, tunc necesse est ponere in punctum centralem esse dimensionem sine aere et aqua, et ita adhuc vacuum vel ad minus aptitudinem vacuitatis: quod est falsum’ [Questiones supra libros octo Physicorum Aristotelis IV (in Opera hactenus inedita Rogeri Baconi fasc. XIII 226)]).Google Scholar

Even more to the point was John of Jandun's criticism: ‘… someone might say that two bodies could never be so perfectly joined and in mutual contact in air or in water without there being air or water between them, as Aristotle seems to intend in the second [book] of De anima, in the chapter on touch. But whoever [argues this way] assumes a false thing, for this might not suffice because although two solid bodies cannot be brought into mutual contiguity and contact in air unless air intervenes, nevertheless a solid and plane body could be applied to a surface of water so that nothing could lie between. And then if this body were raised simultaneously and separated from the water, the doubt would return as before because air cannot immediately [i.e. instantaneously] arrive at the middle of the space between them [i.e. the surfaces]. Therefore it seems that a vacuum will remain.’ (‘… diceret aliquis quod nunquam duo corpora possunt sibi invicem ita perfecte uniri et coniungi in aere vel in aqua quin sit aer medius vel aqua ut videtur Aristoteles intendere in secundo De anima capitulo de tactu. Et immo supponit unum falsum, sed forte non sufficeret istud quia licet duo corpora solida non possunt sibi invicem coniungi et contiguari in aere quin sit aer medius, tamen unum corpus solidum et planissimum posset applicari superficiei aque ita quod nullum esset medium. Et tunc si simul elevetur illud corpus et disiungatur ab aqua redit dubitatio ut prius quia aer non statim poterit pervenire ad medium spatii inter illa. Unde remanebit vacuum ut videtur’ (op. cit. [n. 26 above] fol. 69^v col.1).

42 ‘Ymmo dicitur aliter quod impossibile est aliqua corpora solida tangere se in aere vel in aqua nisi aer vel aqua intercipiatur. Hoc enim dicit Philosophus secundo De anima. Unde si duo corpora solida coniunguntur et deinde separentur ab invicem aer interceptus rarefit et replet locum quam potest quousque adveniat aer circumstans’ (Questiones super libros Physicorum IV q.6 (39) [fol. 66^r col.1]).Google Scholar

43 ‘Contra, possibile est quod aer interceptus sit ita rarus quod non possit iterum rarefieri ut repleat tantum locum quantum intercipitur [text: incipitur] inter illa corpora post separationem. Possibile enim est quod ille aer interceptus sit aer rarissimus. Volo enim quod duo corpora tangant se in aere rarissimo vel in igne rarissimo et redit argumentum’ (ibid. fol. 66^r cols. 1–2).Google Scholar

44 How bending or folding one of the two surfaces, which implies a part-after-part separation, would avoid either instantaneous motion of the inrushing medium or the dreaded vacuum is left unexplained. We have already seen that Burley rejected part-by-part separation of surfaces. At this point in the text, it does not seem that Burley intended that one of the original surfaces be conceived as bent or folded prior to contact, as the words ‘nisi altera tabularum flecteretur sive plicaretur’ might also suggest (for the full context, see note 45). Plausibility for this claim derives from the fact that in what immediately follows, Burley argues that whether the original surfaces are plane or not, separation cannot occur.Google Scholar

45 The text on which this paragraph is based follows: ‘Ad primum: in contrarium quando arguitur de igne rarissimo intercepto dicendum quod si ignis rarissimus interciperetur inter duas tabulas, tunc una tabula non posset elevari nisi altera tabularum flecteretur sive plicaretur. Tamen licet tabula non posset elevari a tabula potest tamen separari ab alia tabula trahendo a latere tabulam a tabula. Nec est cura quantum sive sint tabule plane sive non plane et sive equaliter fiat elevatio in partibus tabule sive inequaliter quia nullum corpus interceptum posset rarefieri ad replendum locum. Nullo modo potest tabula elevari a tabula nec equaliter nec inequaliter’ (ibid. fol. 67^r col. 1).Google Scholar

46 ‘Item si aliquis magnus saxus [sic] supponitur alteri posito, tunc quod ibi est aer medius, magnus lapis superpositus posset moveri per ilium aerem. Lapis enim potest esse tante gravitatis quod ille aer non sufficit ad resistendum lapidi. Ergo lapis superpositus permoveri [potest] per ilium aerem interceptum et per consequens potest ita approximari alteri lapidi quod nullus aer intercipitur quia possibile est corpus esse tante gravitatis quod aer non resistet motu suo’ (ibid. fol. 66^r col. 2).Google Scholar

47 Here now is the relevant passage, including the quotations, for this portion of Burley's discussion: ‘Si enim lapis moveatur et debeat in fine motus coniungi cum aere vel cum aqua eque cito coniungitur medium superficiei lapidis ad superficiem aque sicud partes exteriores illius superficiei quia totus lapis simul movetur et aliqua superficies lapidis tota simul coniungitur aque. Sed corpus prius interceptum inter lapidem et aquam non eque cito recedit a medio sicud a partibus exterioribus illius spacii. Ergo ibi derelinquitur vacuum’ (ibid.).Google Scholar

48 I now give the text for the brief summary that follows: ‘Propter istas rationes dicitur quod si duo corpora debeant adinvicem coniungi tunc partes exteriores aeris intercepti et similiter partes interiores simul recesserunt ab illo loco qui erat inter illa corpora. Licet enim partes aeris successive recedant, tamen ille partes aeris simul recesse sunt et ideo possunt tam partes exteriores quam interiores illorum corporum simul et semel coniungi’ (ibid).Google Scholar

49 Since Burley omits discussion of these alleged arguments, we cannot determine whether they were similar to those employed by Blasius of Parma, as described above.Google Scholar

50 Here is the text for the summary that follows in this paragraph: ‘Ad aliud quando dicitur quod magnus lapis alteri superpositus moveri posset per ilium aerem interceptum dicendum quod quantumcumque sit lapis magnus et gravis non movebitur propter hoc per ilium aerem nterceptum: quia infinita pars lapidis equaliter tendit deorsum versus aliam lapidem in partibus exterioribus et interioribus. Ymmo si lapis superior deorsum moveretur [text: moveri] per aerem interceptum, eque cito tangeret alium lapidem secundum suas partes exteriores sicud secundum partes interiores centrales. Et hoc non posset esse nisi aer interceptus recederet eque cito secundum omnes partes suas extra circumferentias. Et sic recederet sine motu, quod est impossibile. Ideo quantumcumque sit magnus lapis superpositus non descendet per ilium aerem interceptum quia tunc est possibile quod totus aer interceptus cedat subito’ (ibid. fol. 67^r col. 1).Google Scholar

51 ‘Et quando accipitur quod lapis potest esse tante gravitatis quod aer non sufficiet ad resistendum, dicendum quod licet aer in propria virtute non sufficeret ad resistendum lapidi, tamen, in virtute agentis superioris salvantis perfectionem et plenitudinem universi, sufficit aer motus ad resistendum lapidi quantumcumque gravi. Unde aer interceptus ideo non cedit lapidi quia detinetur ab agente superiori prohibente vacuum forte’ (ibid.).Google Scholar

52 ‘Tamen corpus multum grave propinquius tangit aliud quam corpus minus grave, licet enim semper sit aer medius inter corpora solida, aliquando est spissior, aliquando magis tenuis’ (ibid.).Google Scholar

53 ‘Item contra istam responsionem [i.e. Burley's theory] videtur sequi derisoria, puta quod animal semper ambulet super aerem vel aquam quia animal in ambulando numquam attingeret terram, sed semper ambularet super aerem qui, scilicet, intercipitur inter pedem et terram’ (ibid. fol. 66^r col. 2).Google Scholar

54 ‘Ad aliud quando accipitur quod animal numquam ambularet super terram sed semper super aerem vel aquam dicendum quod nullum est inconveniens.† Hoc concedere nec est hoc deridendum ex quo est verum.† Verumptamen secundum communem usum loquendi animal dicitur ambulare super illud quod supportat: huiusmodi est terra et non aer. Ideo dicitur animal ambulare super terram et non super aerem quia terra sustinet et supportat et non aer’ (ibid. fol. 67^r cols. 1–2).Google Scholar

55 See Schmitt, , art. cit. (above n. 1) 365 n.31.Google Scholar

56 Galileo had discussed the same problem in his earlier Dialogue on Motion. For a translation, see Stillman, Drake and Drabkin, I. E. (translators and annotators), Mechanics in Sixteenth-Century Italy (Madison, Wis. 1969) 361–362.Google Scholar

57 Dialogues Concerning Two New Sciences by Galileo Galilei (translated from the Italian and Latin into English by Henry Crew and Alfonso de Salvio; New York 1914; reprinted by Dover Publications). The summary and quotations below are from pp. 11–12.Google Scholar

58 I. e., parallel.Google Scholar

59 Although instantaneous motion in a void was frequently rejected in the Middle Ages (see Grant, E., ‘Motion in the Void and the Principle of Inertia in the Middle Ages,’ Isis 55 [1964] 265–292 and ‘Bradwardine and Galileo: Equality of Velocities in the Void,’ Archive for History of Exact Sciences 2 [1965] 344–364), it was probably maintained by most sixteenth-century Italian Aristotelians whose opinions and attitudes Galileo consistently and vigorously opposed.Google Scholar

60 It is challenged only to the extent that Sagredo himself raises a perplexing question. If, as Salviati argued, void functions as a resistance to material separation, void itself must be the cause of the initial resistance to separation of the plates. But if a vacuum does not form until the plates are separated, how is resistance to separation attributable to an as yet unformed void? The effect would precede the cause I Galileo's explanation of this paradox is left vague and uncertain. Somewhat later on in the First Day, he reiterates that ‘experiment leaves no doubt that the reason why two plates cannot be separated except with violent effort is that they are held together by the resistance of the vacuum’ (p.18 [66]). But does the vacuum occur before or after separation?Google Scholar

The solution may lie in Galileo's further and quite important claim that solid bodies are held together by the attractive force of minute, indivisible, dimensionless, interparticulate vacua whose collective cohesive force must be overcome before a material body can be broken or fractured. For, as Salviati says, ‘one may say that although each particular vacuum is exceedingly minute and therefore easily overcome, yet their number is so extraordinarily great that their combined resistance is, so to speak, multiplied almost without limit’ (ibid. p. 19 [67]). Salviati goes on to prove ‘that within a finite extent it is possible to discover an infinite number of vacua’ (ibid. p. 20 [68]). From all this, are we to understand that the total resistance to separation of two perfectly polished plates in direct contact arises from the infinite number of interparticulate vacua disseminated not only between the particles of each plate but also between the particles of the surfaces at every point of contact? May we then infer that when sufficient force is applied to cause separation, an actually extended, though momentary, vacuum will result before the inrushing air fills the intervening space? On this interpretation, the proper cause of resistance to separation is attributable to the infinity of indivisible, interparticulate vacua, and the actually extended vacuum is but the effect or consequence of separation.

Evidence that Galileo believed in the existence of minute, actually extended vacua — in contrast to his more widely discussed dimensionless vacua — may be inferred from Salviati's remarks on pp. 61 [105] and 67 [112].