Cosmology and Theory of Weight

Strazzoni, Andrea

doi:10.1007/978-3-030-19878-7_6

Andrea Strazzoni¹¹

Part of the book series: Studies in History and Philosophy of Science ((AUST,volume 51))

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Abstract

In this chapter I consider De Volder’s approach to cosmology, which probably led him to relinquish Cartesianism around 1700. I argue that the appearance of Newton’s Principia – containing a striking criticism of Descartes’s vortex theory of planetary motion – and the failure of Huygens to provide an experimental confirmation of his own alternative model, which he used to correct Descartes’s model of gravity and oppose Newton’s idea of universal gravitation, eventually led De Volder to renounce the teaching of natural philosophy, as he could accept neither Newton’s, nor the Cartesian models. In particular, I analyse De Volder’s role in evaluating the results obtained by Huygens in two distinct trials to calculate longitude at sea by means of pendulum clocks, the shortening of which according to latitude was calculated by Huygens using his model of gravity. The outcome of these trials led De Volder to reject Huygens’s theory, and ultimately to dismiss Descartes’s model. Moreover, I consider De Volder’s attempt to combine Newton’s and Descartes’s ideas in the explanation of the movement of the Moon, a case in which Descartes’s vortex theory was immune to Newton’s criticism, but which could not be extended to the explanation of planetary movements.

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Notes

1.
Schuster 2013, 489.
2.
These three topics have been comprehensively dealt with in Schuster 2013. See also, as to Descartes’s cosmology and theory of weight, Aiton 1957, 1958a, b, 1959, 1972; Gaukroger 2002, chapters 5–6. As to Descartes’s hydrostatics, see Gaukroger 2000a; Gaukroger and Schuster 2002; Chalmers 2017, chapter 5.
3.
Descartes 1982, 60.
4.
Descartes 1982, 113–114. On Descartes’s theory of centrifugal force, see Bertoloni Meli 1990; Garber 1992, chapter 7.
5.
On Descartes’s theory of light, see Sabra 1981; Smith 1987; Schuster 2013, chapters 4 and 10.
6.
The reader can find thorough discussions of Descartes’s cosmogonic processes in Aiton 1972; Lynes 1982; Jalobeanu 2002; Schuster 2013, chapters 9–12.
7.
On the problem of an actual differentiation of individual bodies in the Cartesian continuum, see Taliaferro 1986; Grosholz 1994; Normore 2008; Thiel 2011, chapter 1; Ariew 2012; Reid 2014. See also Sect. 4.1.2, De Volder’s monist view of material substance.
8.
See Descartes’s Le monde, chapter 6, and Principia, III.46–47.
9.
See Descartes’s Le monde, chapter 8, and Principia, III.48–52.
10.
See Descartes’s Le monde, chapter 8, and Principia, III.53–54.
11.
See Descartes’s Principia, III.54 and III.61.
12.
See Descartes’s Le monde, chapter 10, and Principia, II.82–85.
13.
Again, Schuster has provided a thorough treatment of how Descartes, in providing his cosmogony, developed an all-encompassing account of these phenomena: see Schuster 2013, chapter 12. On Descartes’s theory of magnetism, see Georgescu 2017, chapter 3.
14.
“[…] some of these parts must move more quickly than others when they must change their order so as to pass from a wider path to a narrower one […]: the two balls which are between points A and B cannot pass between the other two points C and D {which I am supposing to be closer together}, unless one moves ahead of the other; and it is obvious that […], the one which precedes must move more rapidly than the other,” Descartes 1982, 129.
15.
“[…] we can suppose that speed of movement compensates for narrowness of space. Thus, in any given length of time, the same quantity of matter will pass through one section of this circle as through another,” Descartes 1982, 56; see also III.98: “the rapidity of rivers is always greater in shallow and narrow places than in deep and wide ones,” Descartes 1982, 138. Cf. Castelli 1628, 9–12. For a thorough discussion, see Bertoloni Meli 2006, 84–85 and 157.
16.
“Si canalis A sit eiusdem longitudinis, ac C, at C duplo latior, quam A, et aliqua materia fluida duplo celerius transeat per canalem A, quam quae transit per canalem C, tantundem materiae eodem temporis spatio per canalem A transibit, quantum per C; et si per canalem A tantundem transeat, atque per C, illa duplo celerius movebitur,” Spinoza 1663, 44–45. See Fig. 6.7, Spinoza 1663, 44.
17.
“Compensari. Vide Spinozam in principior. Carthes. partem secundam axiomate XIV,” Hamburg 273, 101; cf. The Hague dictata, 38a, providing the illustration.
18.
Schuster 2013, 465–466.
19.
“Let us suppose that star N is less solid, or capable of less agitation {or force to continue its movement in a straight line} than the globules of the second element near the circumference of our heaven, but that it has somewhat more than those close to {the center in which is} the Sun. Given these conditions, we shall understand that as soon as N has been carried away by the vortex of the Sun, it must continuously descend toward the center, until it reaches {the point at which are [found]} those heavenly globules which are equal to it in solidity, or in ability to continue their movement along straight lines. When it is finally at that point, it will neither move closer to nor farther from the Sun (unless driven slightly this way or that by some other causes), but will constantly revolve around the Sun among those heavenly globules {which are equal to it in force}, and will be a Planet. For if it descended closer to the Sun, it would there find itself surrounded by slightly smaller heavenly globules which it would exceed in force to recede from the center around which it revolves. These parts would also be more rapidly moved, which thus would increase its own agitation along with its force, causing it to ascend. If, on the other hand, it receded further from the Sun, it would encounter there heavenly globules which were somewhat less rapidly moved and would thus decrease its agitation, and which were slightly larger and would thus have the force to drive it back toward the Sun,” Descartes 1682, 168–169.
20.
Descartes 1682, 154.
21.
Descartes 2004, 44–45.
22.
“For we see that a spinning top acquires enough force, merely from the fact that a boy twirls it once, to continue subsequently to spin on its own for several minutes, and to rotate during that time several thousand times {around its axis}, even though it is very small and even though both the air which surrounds it and the earth on which it presses oppose its movement. Similarly, one can easily believe that if a Planet had been set in motion from the moment of its creation, that alone would be sufficient to allow it to continue its rotations from the beginning of the universe up to the present time without any significant decrease in speed, because {the greater a body is, the longer it can retain the agitation which has been communicated to it in this way; and because} the five or six thousand years for which the universe has existed are a much shorter time compared to the size of a Planet than a minute is compared to the tiny bulk of a spinning top,” Descartes 1982, 170.
23.
For a discussion, see Garber 1992, chapter 7; Slowik 2002, chapter 3. This is a sort of ‘anomaly’, or one of the “deviations” (see Descartes 1982, 169) in what would be the path of a planet which Descartes admits in order to explain the actual phenomena observed in astronomy: see III.141–145.
24.
Descartes 2004, 49.
25.
Descartes 2004, 50.
26.
Descartes 1982, 192.
27.
Descartes 1982, 193.
28.
Descartes 1982, 189.
29.
“[…] il n’y a point de raison qu’aucune des parties de leur circonference s’esloigne ny s’approche de leurs centres plus que les autres en ce sens là, vuqu’elles ny sont ne plus ne moins pressées d’vn costé que d’autre par l’air qui les enuironne,” AT VI, 281.
30.
Descartes 1982, 192.
31.
See infra, n. 132.
32.
Namely Henricus Regius’s Fundamenta physices and Philosophia naturalis (1646, 1654, 1661, 1687), Henry More’s Coniectura Cabbalistica (1653), Daniel Lipstorp’s Specimina philosophiae Cartesianae (1653), Christoph Wittich’s Dissertationes duae, quarum Prior de S. Scripturae in rebus philosophicis abusus examinat; Altera dispositionem et ordinem totius universi tradit (1653) and Consensus veritatis in Scriptura divina et infallibili revelatae cum veritate philosophica a Renato des Cartes detecta (1659), Louis de Beaufort’s Cosmopoea divina: seu Fabrica mundi explicata (1656), Johannes Amerpoel’s Cartesius mosaïzans, seu Evidens et facilis conciliatio philosophiae Cartesii cum historia creationis primo capite Geneseos per Mosem tradita (1669), Géraud de Cordemoy’s Copie d’une lettre ecrite à un sçavant religieux de la Compagnie de Jesus, pour montrer, I. Que le systeme de M. Descartes, son opinion touchant les bestes, n’ont rien de dangereux. II. Et que tout ce qu’il en a écrit semble estre tiré du premier chapitre de la Genese (1668), Jacques Rohault’s Traité de physique (1671), Claude Gadroys’s Le système du monde selon les trois hypothèses, où conformement aux loix de la mechanique l’on explique dans la supposition du mouvement de la terre (1675), Claude Mallement de Messange’s L’ouvrage de la Création: Traité physique du monde (1679), Thomas Burnet’s Telluris theoria sacra and Sacred Theory of the Earth (1681, 1684, 1689), Théodore Barin’s Le monde naissant ou La création du monde, démontrée par des principes tres simples et tres conformes à l’histoire de Moyse (1686), Fontenelle’s Entretiens sur la pluralité des mondes (1686), Pierre-Sylvain Régis’s Système de philosophie (1690) and Cours entier de philosophie ou Système général selon les principles de Descartes (1691). See Blair 2000; Harrison 2000; Anstey 2011, chapter 5, 2018.
33.
See Huygens 1888–1950, volume 19, 628–645.
34.
For an account, see Aiton 1972, chapter 4; Gabbey 1986; Snelders 1989; Dijksterhuis 2004, chapter 6; Boantza 2011.
35.
“L’on sçait que Mr. Descartes a aussi taché dans la Physique d’expliquer la pesanteur par le mouuement de certaine matiere qui tourne autour de la terre. […] [S]i l’on supposoit que la matiere celeste tournast du mesme coté que la terre mais auec beaucoup plus de vitesse il s’ensuiuroit que ce mouuement rapide d’une matiere qui se meut toute vers un mesme coté se feroit sentir et qu’elle emporteroit avec elle les corps qui sont sur la terre de mesme que l’eau emporte la poudre de bois dans notre experience, ce qui pourtant ne se fait nullement, mais outre cela ce mouuement circulaire a l’entour de l’axe de la terre, ne pourroit en tout cas chasser les corps qui ne suiuent pas le mesme mouuement que vers ce mesme axe, de sorte que nous ne verrions pas tomber les corps pesants perpendiculairement vers l’horizon mais par des lignes perpendiculaires a l’axe du monde, ce qui est encor contre l’experience,” Huygens 1669c, 631–632; cf. Huygens 1690, 134–135.
36.
“Hoc tantum adnotabo, non esse verisimile, si gravitas corporum terrestrium ex actione materiae colestis oritur, quin descensus eorum fieret ad Terram non perpendicularis, sed in angulos satis obliquos ab oriente occidentem versus, propter impactiones materiae coelestis in superficiem Terrae tardius ipsa materia coelesti in orientem circumrotatae. Sed abunde satis iam demonstratum est totam doctrinam Cartesianam de gravitate et levitate puram putam est imaginationem, ex eo animi morbo quem ego mechanicam credulitatem appellare sole genitam et prognatam,” More 1671, 114.
37.
“Evidenter enim demonstrasti […] id ipsum quod nuper admodum amicus aliquis his verbis Basilea ad me perscriptis in Cartesiana quoque desideravit: posita hac hypothesi certum esse puto, corpora gravia secundum illa lineam detrusum iri, secundum quam materia subtilis a Terra recederet; recedere conatur autem quaelibet particula […] secundum lineam talem quae in eodem iacet plano cum circulo per rotationem particulae descripto, i.e. secundum lineam parallelam aequatori. […] Quod si ergo vorticum aut orbium coelestium fluidorum talem gyrationem supponamus, qualis in orbibus aut globis solidis contingit, ut partes singulae singulos etiam circulos circa singula centra describant, totusque adeo vortex non tam circa centrum quam circa axem alique convolvatur, non solum hoc, de quo nunc sermo nobis, incommodi sequetur, sed necessum etiam foret, hoc motu vorticolos stellas et corpora mundana non sphaerica, sed cylindrica potius, facta, sub polis gravitatem nullam esse et c.,” Sturm 1685, Epistola, 22–23. The same text is reported in Bernoulli 1686b, 92–93.
38.
In the posthumously published Account of Dr. Isaac Vossius’s Hypothesis of Gravitation, with Some Animadversions thereupon, Hooke maintained that heavy bodies would be displaced towards the axis of the vortex, and that both the vortex and the Earth would have a cylindrical shape, according to the Cartesian model of gravity: see Hooke 1705, 202.
39.
“Dans l’explication que Mr. Descartes a donnée de la pesanteur je ne trouue pas qu’il ayt assez faict de reflexion sur cette action de la matiere fluide sur les parties du dedans des corps terrestres, et il semble mesme qu’il n’a point admis la liberté de son mouuement a trauers du composé de ces parties puis qu’il veult que par la rencontre de la terre elle soit empeschée de continuer ses mouuements en ligne droitte, et que pour cela elle s’en esloigne autant qu’elle peut. En quoy il ne semble pas auoir pensé aux proprietez de la pesanteur que je viens de remarquer. Car si le mouuement de cette matiere est empesché par la terre, elle ne penetrera non plus librement les Corps des metaulx, ny du verre, donc il s’ensuiuroit que du plomb enfermé dans une phiole, perdroit son poids ou que du moins il seroit diminué comme aussi que les parties du dedans d’un corps solide ne contribueroient point a sa pesanteur, comme ne ressentant pas l’action de la matiere que les doibt pousser vers en bas; de plus en portant un corps pesant au fond d’un puit ou de quelque mine profonde, il y deuroit perdre sa pesanteur ce qui ne se trouue point par experience,” Huygens 1669c, 637; cf. Huygens 1690, 140–141.
40.
“L’on peut voir cet effect par une experience fort aisée mais qui est digne de remarque parce qu’elle nous faict voir a l’oeil quelque image de la pesanteur, car en faisant tourner de l’eau dans quelque vaisseau qui ait le fond plat apres y avoir mis dedans des petites parcelles de quelque matiere un peu plus pesante que l’eau, asin qu’elle puisse aller au fond, l’on verra qu’au commencement ces petits corps flottant dans l’eau a cause de son agitation et suivant son mouvement circulaire ne s’approcheront nullement vers le centre du vaisseau, mais aussy tost qu’ils commenceront a toucher au fond et que leur mouuement circulaire sera par la interrompu ou diminué ils s’amasseront tous alentour dudict centre y tendants par des lignes spirales parce que ils suivent encore en partie le mouuement de l’eau. Que. si l’on y met un corps ajusté en sorte qu’il ne puisse point suiure du tout le mouuement de l’eau mais seulement s’approcher vers le centre il y sera poussé tout droit, comme si L. est une petite boule qui puisse rouler librement entre les filets A, B, C, K, et un troisiesme un peu plus eslevé F. H, tendus par le milieu du vaisseau pres du fonds, lesquels filets soient arrestez immobiles pendant que l’eau tourne (ce qui se peut faire en arretant subitement le vaisseau apres l’auoir fait tourner car l’eau continuera encore quelque temps le mouuement circulaire qu’elle a conceu) l’on verra qu’aussi tost cette boule s’en ira vers le centre D. et s’y tiendra arrestée. Et il faut noter que dans cette experience l’on peut rendre le corps L. de la mesme pesanteur que l’eau, et que mesme l’experience en succedera mieux, de sorte que sans aucune difference de pesanteur des corps qui sont dans le vaisseau le seul mouuement en produit icy l’effect,” Huygens 1669c, 633; cf. Huygens 1690, 132–133.
41.
Rohault accepted Descartes’s theory of weight as presented in Le monde, namely as based on the idea of a tangential tendency to movement only. To support it, he described Huygens’s experiment: see Rohault 1671, volume 2, part 2, chapter 28. Rohault does not deal with the problem of the displacement of bodies towards the axis of the vortex.
42.
“Pour entendre comment la matière subtile qui tourne autour de la terre chasse les corps pesants vers le centre, remplissez quelque vaisseau rond de menues dragées de plomb, ayant mêlé parmi ce plomb quelques pieces de bois, ou autre matiere plus legere que ce plomb, qui soient plus grosses que ces dragées; puis, faisant tourner ce vaisseau fort promptement, vous esprouuerez que ces petites dragées chasseront toutes ces pieces de bois, ou autre telle matiere, vers le centre du vaisseau, ainsy que la matiere subtile chasse les cors terrestres, & c.,” AT II, 593–594.
43.
“Ie voy bien que ie ne me suis pas assez expliqué en vous disant ce que ie prens pour la Pesanteur, que ie dis venir de ce que la Matiere subtile tournant fort viste autour de la Terre, chasse les Cors Terrestres vers le Centre de son Mouvement, ainsi que vous pourrez experimenter en faisant tourner de l’eau en rond en quelque grand vaisseau, et iettant dedans quelques petits morceaux de bois; vous verrez qu’ils iront vers le milieu de l’eau, et s’y soustiendront comme fait la Terre au milieu de la Matiere subtile,” AT III, 134–135. Later in his Principia Descartes would overtly compare planets to straws and leaves in water, moving faster as they are closer to the centre of whirlpools (III.30), thus confirming his vortical model, according to which planets closer to the Sun move faster than those far away. The comparison of planets to straws is used also in Regius’s Fundamenta physices (see Regius 1646, 55) and in Antoine Le Grand’s Institutio philosophiae secundum principia Renati Descartes (see Le Grand 1675, 266; first edition 1672).
44.
Probably Huygens had in mind the case in which not only the water is rotating, but also the vessel: in this case, floating bodies are displaced outwards: this point is discussed in Palmerino 2007.
45.
“Ce qui n’est pas ainsy dans l’experience que Mr. Descartes propose dans une de ses lettres imprimées, car il remplit le vaisseau A. B. C. de menue dragée de plomb et y mesle parmy quelques pieces de bois ou d’autre matiere plus legere que le plomb, et faisant tout tourner ensemble, il dit que les pieces de bois seront chassées vers le milieu du vase, ce que je puis bien croire, mais c’est un effet de la differente pesanteur du bois et du plomb au lieu qu’il faut expliquer la pesanteur sans en supposer aucune et en considerant tous les corps comme faicts d’une mesme matiere. Il propose encore dans une autre lettre de jeter dans de l’eau tournante des petits morceaux de bois et dit qu’ils s’en iront vers le milieu de l’eau, auquel endroit s’il entend du bois qui nage sur l’eau, comme il y a apparence, il ne se fera point de concentration, mais s’il veut qu’il aille au fond, ce sera veritablement la mesme experience que j’ay proposée un peu auparauant, et le bois s’amassera au centre, mais ce sera a cause qu’en tombant au fond du vase son mouuement circulaire en sera retardé, de laquelle raison Mr. Descartes n’a point parlé,” Huygens 1669c, 633–634; cf. Huygens 1690, 133–134.
46.
See Palmerino 2007.
47.
“Proba, neque violentia motus mundani excuti gravia in medium. In motu circulari violento si qua petunt medium totius rei mobilis, illa oportet esse leviora reipsa mota, ut in vorticibus ligna et paleae sunt leviora, quam est aqua ipsa rotata in gyrum; ibi namque maior a rotatione fit impressio in corpus aquae, quod gravius est, ut impetu ruat et rectitudinem affectans extima circuli petat, centrumque veluti exhauriat, quo facto leviora, innatantia, cum propter minorem impressionem motus in ipsa tardioremque motum destituuntur et ab aquis velocioribus introrsum repelluntur, tum etiam propter declivitatem centri in medium naturaliter influunt,” Kepler 1618, 59
48.
“Nam ipsi primum indicium debetur verae causae gravitatis, et huius naturae legis, a qua gravitas pendet, quod corpora rotata conantur a centra recedere per tangentem, et ideo si in aqua festucae vel paleae innatent, rotato vase aqua in vorticem acta, festucis densior, atque ideo fortius quam ipsae, excussa a medio, festucas versus centrum compellit; quemadmodum ipse diserte duobus, et amplius locis, in Epitome Astronomiae exposuit; quanquam adhuc subdubitabundus, et suas ipse opes ignorans, nec satis conscius quanta inde sequerentur, tum in Physica, tum speciatim in Astronomia. Sed his deinde egregie usus est Descartes, etsi more suo autorem dissimulavit. Miratus autem saepe sum, quod Descartes legum coelestium a Keplero inventarum rationes reddere ne aggressus est quidem, quantum constat; sive quod non satis conciliare posset cum suis placitis, sive quod felicitatem inventi ignoraret, nec putaret tam studiose a natura observari,” Leibniz 1689, 83.
49.
“Nonnulla quoque Cartesianis haud absimilia prodidit Keplerus, insignis aetatis huius mathematicus, a quo multa se didicisse Cartesius profitetur. Is licet fixis singulis suos non attribuit vortices, in eoque et in mundi infinitate dissentire se a Bruno et Gilberto saepius affirmet, suum tamen dat Soli vorticem, Cartesianis et Brunianis vorticibus parem in quo Terra et planetae volvantur,” Huet 1689, 216.
50.
“Nihilo felicior fuit Cartesius in assignanda caussa gravitatis corporum terrestrium, quam confert in motum globulorum secundi elementi; qui cum a vortice in quo sunt, circumagantur in orbem, motu hoc tendere illos necesse esse, ait, ad extimum vorticis ambitum secundum lineas rectas; atque idcirco si quae terrestria corpora occurrant, cum tanta in iis non insit ad fugiendum centrum et extima petenda propensio, de loco suo decedunt, urgentibus globulis, et ab his ad alta contendentibus retruduntur ad inferiora; atque eo magis, quo plus habent materiae terrestris, minusque coelestis. Id ut commodius explicet, utitur exemplo ingentis alicuius vasis aqua pleni; quae aqua, si in orbem vertatur, et minutae alique iniiciantur ligni particulae, confluent illae statim ad centrum, et suspensae in medio aquae vortice natabunt, uti medium vorticis sui innat Terra. […] Haec quantumvis belle et ad speciem veritatis composita, fidem tamen non obtinebunt a cordatis philosophis, si observaverint aquam hanc in vase circumactam, ferri circa axem motus huius, et iniectas in eam particulas ad axem illum tendere, et quidem unamquamque particulam ad id axis punctum, in quo secatur axis ab area plana vertiginis particulae huius; non vero tendere ad centrum vasis. Nam si aqua impleatur vas aliquod in cylindri formam excavatum, et aqua in orbem agatur, tum in eam iniiciantur particulae aliquae ligneae et lapideae; conspicientur illico particulae lignae ad supremam axis partim confluere, lapideae ad infimam; neutrae vero ferri ad centrum cylindri. Nempe singulae petent centrum areae planae, in qua moventur; ac proinde cum in suprema parte aquae ligna, in inferiore lapides circumagantur, centra utriusque vertiginis in variis erunt axis partibus, in iis nempe punctis, in quibus areae vertiginis utriusque axem secabunt. Hinc sequitur, corpora terrestria a globulis materiae caelestis depressum iri, non versus Terrae centrum, sed versus centra vertiginum suarum, nempe unumquodque versus centrum vertiginis globulorum, a quibus deprimitur; hoc est, versus punctum illud axis Terrae, in quo secatur axis ab area vertiginis huius: unde fiet, ut ea sola corpora terrestria, quae sunt sub aequinoctiali, cadant in Terram ad perpendiculum […]; relique vero ferantur quidem ad perpendiculum versus axem Terrae,” Huet 1689, 160–162.
51.
“Alii vero gravitatis rationem petunt a materia subtili, inter Terram et Lunam interiecta, quae in gyrum circum Terram acta, eam, ut et Lunam, omniaque corpora interiecta, secum abriperet; et cum illius materiae motus, utpote celerior quam Terrae et c. nonnihil a Terra impediatur, quantum potest ab eadem recederet, ac recedendo versus inferiora propelleret particulas terrestres, inter materiae caelestis particulas haerentes, utpote quibus tanta vis recedendi a centro non competeret; simili ratione, qua in vase rotundo, minutioribus globulis plumbeis, quibus alterius materiae plumbo levioris fragmenta permista sunt, replet, quod celeriter circa centrum suum convertitur, a plumbo, per quem materia subtilis repraesentatur, versus centrum propelluntur aliorum corporum leviorum fragmenta: aut ut frusta ligni coniecta in aquam in gyrum actam, versus eius medium feruntur, ibidemque haerent. Verum nec horum explicatio naturae gravitatis satisfacit. Quantum enim ad citata exempla, illa arguunt gravia a Terra sursum potius propelli debere, quam versus eam, si gravium motus a materiae subtilis propulsione deducendus esset; cum in iis a centro propellantur quae graviora sunt, leviora vero versus centrum ferantur,” Senguerd 1681, 57–58.
52.
“Planeta. Si concipiamus argumenta eorum, qui impugnant authoris philosophiam nulla inveniemus mechanica, nisi circa hanc materiam, id inquiunt sc[ilicet]: si omnes vortices et materia caelestis in orbem vertantur, eas habebunt leges quas materia caelestis, siq[ue] in orbem vertentur vortex et si innatent planeta omnes accedent ad centrum, ut festuca innatans aq[uae] vortici ad eius centum confluit sed argumentum illud Voetii indicat ignorantiam authoris nostri sententiae, fatemur quidem id fieri in festuca leviori, negamus vero id de corporibus aqua gravioribus, quod non parum confirmat ea, q[uae] antea {dixi}, cur enim levia accedunt ad centrum? Quam quia sunt minus solida, sic in aquam si iniiciamus festucam accedet ad centrum, quia aqua habet maiores vi recedendi a centro: obiici quidem potest planetas esse minus solidos sed R[espondeo] aquam ubiq[ue] aeq[ue] solidam e[ss]e et ex par[ticu]lis constare homogeneis, q[uo]d si in vortice contingeret planetae ad centrum accederent, sed in vortice globuli in extremitate sunt maiores, {…} {sensim} fiunt minores minores[que], verum itaq[ue] q[ui]dem est planetam e[ss]e minus solidum respectu superiorum globulorum alias enim e[ss]et cometa, progressus autem planeta invenit minus solidos, donec omnes qui eum cingunt sunt aequales,” Hamburg 273, 208.
53.
I intend here Gijsbert Voet (1589–1676) and his sons Daniel Voet (natural philosopher, 1629–1660) and Paul Voet (writer of law and theology, 1619–1677), and Johannes Voet (1647–1714), son of Paul and writer of law. Some disputations on physical topics of Paul Voet were appended to the first edition of the Physiologia, yet, they do not deal with the argument discussed by De Volder.
54.
See Sect. 4.1.3, De Volder’s ideas on cohesion and divisibility.
55.
See Voet 1661, 49 and 138.
56.
“Substantia haec coelestis non in orbem movetur, licet in orbem moveantur astra; cum omnia corpora mota, quantum in ipsis est, conentur recedere a centro sui motus, consequenter et haec a suo recederet centro, quod prorsus absurdum: neque enim quippiam ad incrustandum hoc absurdum facit, si dixeris partes huius materiae exteriore interioribus crassiores et maiores esse; cum tale quid duntaxat fingatur, non vero ulla probabili ratione probetur. […] Ut autem absurdum est hic admittere orbes realiter distinctos, ita non minus absurdum admittere […] machinam coelestem ex diversis vorticibus fluidis conflatam esse: tum quod mox illi vortices in unum (nisi per miraculum impediatur) coalescere deberent, cum fluidum in fluidum impingens, ob non simultaneam cuiusque partis illius fluidi actionem, eidem permisceri debeat, et permisceri experientia doceat; tum quod vorticum extremus (nisi mundum infinitum posueris) ob rationem ante datam, videl. Conatum cuiusque corporis recedendi a centro, dissilire, sicque consequenter et reliqui debeant,” Voet 1661, 56. In commenting upon these passages in the second edition of the Physiologia (1678), Gerard de Vries notes that according to Descartes’s vortex theory stars would have a cylindrical shape: “[a]ccedit, quod facile sit demonstrare, secundum hanc hypothesin vorticosam, stellas esse debere figurae, non rotundae, sed oblongae, ac protensae ab uno vorticis polo ad alium,” Voet and De Vries 1678, 133.
57.
See infra, n. 202.
58.
De Volder could have found Voet’s argument in Daniel Voet’s Meletemata philosophica, in quibus antiquae et receptae philosophiae fulcra magis stabiliuntur, novatorum philosophandi methodus evertitur. This book – not listed in the Bibliotheca Volderina – was however extremely rare and is today mentioned only in the catalogues of the Universitätsbibliothek Greifswald – where it is labelled as lost – and the Bibliothèque publique et universitaire of Neuchâtel, where it is reported as printed in Utrecht in 1661. Unfortunately, the book could not be accessed during my research.
59.
“Pour parvenir donc a une cause possible de la pesanteur, je supposeray que dans l’espace spherique qui comprend la terre et les corps qui sont autour d’elle jusqu’a une grande estendue il y a une matiere fluide qui consiste en des parties tres petites et qui est diversement agitée en tous sens avec beaucoup de rapidité, laquelle matiere ne pouuant sortir de cet espace qui est entouré d’autres corps, je dis que son mouuement doibt deuenir en partie circulaire a l’entour du centre, non pas tellement pourtant qu’elle vienne a tourner toute d’un mesme sens, mais en sorte qua la plus part de ses mouuements differents se fassent dans des surfaces sphériques a l’entour du centre dudict espace, qui pour cela deuient aussi le centre de la terre. […] [D]ans la matiere celeste que j’ay supposée […]il n’y a pas de raison pourquoy le mouuement d’une partie de la matiere l’emporteroit sur celuy des autres pour faire que toute la masse tournast vers un mesme centre [sic; in Huygens 1690 this is corrected into “mesme sense”],” Huygens 1669c, 634–635; cf. Huygens 1690, 135–136.
60.
“Je suppose donc la terre au milieu du monde et au milieu des estoiles fixes et des Planetes. je fais que la terre est emportée comme il a este dict par un tourbillon du Corps aetheré d’occident en orient, et je luy en donne encore un autre pareil en force et vistesse qui va du midy au septentrion, ou du septentrion au midy, causé par un autre tourbillon qui emporte generalement tout le monde de ce sens là, cest a dire la Terre les planetes et les Estoiles fixes. Ce mouvement qui ne change rien et qui ne sçauroit repugner a aucun Phenomene parce qu’il est commun a tous les corps qui peuvent faire des Phenomenes, ne laisse pas de faire son effect sur les Corps grossiers er solides qui composent le Globe Elementaire; et le flus rapide du corps aetheré qui emporte tout le monde du midy au Septentrion qui croise celuy qui emporte la terre du couchant au levant, produit l’égalité du mouvement des Corps pesants et fait que des poles de la Terre a son centre il y a un mouvement egal a celuy qui a desia esté monttré se devoir faire de la ligne aequinoctiale au mesme centre,” Académie des Sciences, Procès-verbaux, volume 6, 220v–221r. I owe the citation to Christiaan Huygens in het Nederlands, https://adcs.home.xs4all.nl/Huygens/ (accessed 28 January 2019).
61.
On this topic, see Yoeder 1988, chapter 3, 1998; Barbour 1989, chapter 9; Bertoloni Meli 1990; Erlichson 1994; Chareix 1996, 2004; Slowik 1997; Ducheyne 2008.
62.
See Sect. 2.4.1, De Volder as editor of Huygens’s posthumous works; cf. Molhuysen 1913–1924, volume 4, 58∗–59∗.
63.
They also corrected some errors they found in the demonstrations provided in 1701 by Antoine Parent, in a communication to the Journal des Sçavans: “[…] sequitur libellus de Vi centrifuga, quem in scedis auctoris, sed nequaquam convenienti ordine dispositum invenimus. Quare factu optimum et auctoris menti convenientissimum extimavimus, si, quantum pote, sequeremur ordinem theorematum de Vi centrifuga, quae ad finem Horologii oscillatorii divulgavit iam ante multos annos; licet ad ipsum necessarium fuerit, quaedam ex iis theoremata, ut puta VII, IX, X, XI, prout hic numerantur, ex fundamentis ab Ill. Hugenio positis deducere, sed ne sic quidem praecise licuit eundem numerum propositionum obtinere, ne quidpiam, quod de his conscripserat auctor, publico invideremus. Quae dum scribimus incidi forte fortuna in manus nostras Diarium Gallicum anni 1702, quod dum obiter pervolvimus, animadvertimus 23 Maii 1701 adduci demonstrationes horum 13 theorematum; et simul in iis erroris accusari auctorem nostrum […],” Huygens 1703, Praefatio, 11–12 (unnumbered). In the light of De Volder’s and Fullenius’s editing, Joella Yoeder has asked, in her analysis of Huygens’s posthumous works, whether “[i]s the edited De Vi Centrifuga a treatise by Huygens? He did not reorder the manuscript, insert additional proofs, and have it copied […]. Nor did he acknowledge its existence in his will. In fact, Fullenius and de Volder felt the need to justify what they had done, particularly defending their added proofs as in the style of Huygens. The editors of Oeuvres completes point out that the proofs are not that Huygenian,” Yoeder 1998, 103.
64.
See Yoeder 1998, 103.
65.
“Reprenant donc la figure dont je me suis servy cy dessus puisque la pesanteur du corps E est justement egale a l’effort qu’a une portion aussi grande de la matiere fluide a s’esloigner du centre D, ou que c’est plustost la mesme chose; il fault dire qu’une liure de plomb par exemple icy sur terre pese autant vers le centre, qu’une masse de la matiere fluide de la grandeur de ce plomb pese vers en haut pour s’en esloigner par la vertu de son mouuement circulaire. Or puisque la matiere de plomb et la matiere fluide ne different en rien selon notre hypothese l’on peut dire que la liure de plomb, pese autant vers en bas qu’elle peseroit vers en hault si elle tournoit autour du centre de la terre et a la distance qu’elle en est auec autant de vitesse que faict la matiere fluide, mais je trouve par ma Theorie du mouuement circulaire qui s’accorde parfaictement auec l’experience qu’un corps tournant en cercle, si l’on veut que son effort a s’esloigner du centre egalle justement l’effort de sa simple pesanteur […],” Huygens 1669c, 638–639; cf. Huygens 1690, 142–143.
66.
See theorems 2 and 3 in the 1673 version: “II. Si duo mobilia aequalia, aequali celeritate ferantur, in circumferentiis inaequalibus; erunt eorum vires centrifugae in ratione contraria diametrorum. III. Si duo mobilia aequalia in circumferentiis aequalibus ferantur, celeritate inaequali, sed utraque motu aequabili, qualem in his omnibus intelligi volumus; erit vis centrifuga velocioris, ad vim tardioris, in ratione duplicata celeritatum,” Huygens 1673, 160.
67.
Yoeder 1988, chapter 3.
68.
Cf. Huygen’s account: “[c]aeterum ad illorum demonstrationem, quae nos hic tractabimus, sufficit in minimis quamlibet spatiis a quietis puncto accelerationem crescere secundum impares numeros 1, 3, 5, 7, ut Galileus statuit […] Cum itaque globus cum rota circumactus curvam describere conetur respectu radii in quo situs est, ac talem quidem quae radium contingat, apparet conatu hoc filum cui alligatus est, non secus tendi debere quam si secundum ipsum radium productum globus ire conetur. Sunt autem et spatia quae in dicta curva globus peracturus esset temporibus aequaliter crescentibus, sicut series quadratorum ab unitate 1, 4, 9, 16, etc. si videlicet principium motus spatiaque minima attendamus; quod apposita figura ostendit, ubi arcus aequales in circumferentia rotae accepti sunt BE, EF, FM; et in tangente BS rectae dictis arcubus aequales BK, KL, LN; lineae vero ex centro sunt EC, FD, MS. Hic itaque si globus a circumeunte rota divelleretur in B; tum ubi punctum B pervenisset in E globus esset in K, particulamque curvae supra descriptae percurrisset EK. post secundum vero tempus exactum cum B venisset in F, globus in L reperiretur, iamque curvae partem FL percurrisset. Similiterque cum B venisset in M, globus peregisset curvae portionem MN. Hae vero curvae lineae partes tanquam eaedem cum rectis EC, FD, MS, quas contingunt, in principio separationis globi ab rota, considerandae sunt. Quoniam tam parvi arcus a puncto B accipi possunt ut differentiola quae est inter rectas curvasque hasce, minorem rationem habeat ad ipsarum longitudinem, quavis ratione imaginabili. Proinde igitur et spatia EK, FL, MN tanquam crescentia secundum seriem quadratorum ab unitate 1, 4, 9, 16, spectanda sunt. Atque ita conatus globi in circumeunte rota retenti haud alius erit, ac si secundum rectam quae ex centro per ipsum ducitur progredi contenderet, idque motu accelerato quo aequalibus temporibus crescentia percurreret spatia secundum numeros 1, 3, 5, 7, etc.,” Huygens 1703, 402–407.
69.
“Momentis. Concipit sic autor canalem rotundum, in quo globus contentus non potest ab eo recedere, sed in eo tubulo manere debet, manifestum enim, est globulum si sibi relinquatur, per rectam lineam permoturum, si sc[ilicet]: non moveatur circulariter, sed per rectam lineam ad tubi extremitatem, canalis enim non esto impedimento, quominus pergat recta, ideoq[ue] movebit[ur] per lineam AY, ex quibus certum est, si ostendamus in vorticibus tales e[ss]e tubulos aut latera, omnes e[ti]am in iis globulos recedere a centro: qua in parte notandum est tangentem in A circulo e[ss]e proximam, adeo ut inter illam et circulum nulla linea dici possit, adeoq[ue] ut parva sit recessio, sed cum ideam motus perseveret, accelerabitur, et si consideremus divisibilibus, gradatim augeri debet, primo itaq[ue] momento si habeamus unicum gradum motus, secundo habebimus duos, tertio tres, et sic porro, adeo ut tandem evadat celerrimus,” Hamburg 273, 156. Cf. the other series of dictata: “[d]um sortitur effectum, augetur. Manente enim eadem causa, necesse est, ut continuo novus accedat conatus: sic primo ex. gr. est momento vis q[uae]dam recedendi a centro. Secundo momento, quia durat adhuc motus circularis accedit nova q[uae]dam vis priori quia iam aderat, tertio adhuc alia, et sic porro: unde motus is, qui huic virium augmento respondet, continuo maior maiorq[ue] fiet. Et ut loquuntur uniformiter accelerabitur. Demonstravit autem Galileus in suo libello De motu, ea spacia, q[uae] tali moti absolvuntur esse inter sese, ut quadrata temporum, hoc est, si uno momento absolvatur spacium unius E[xempli] G[ratia] pedis, duobus {absolvitum} iri spacium 4 pedum. Tribus, 9 pedum, quatuor deniq[ue] momentis 16 pedum, et sic porro, ita ut velocitas acceleretur secundum ordinem numerorum imparium, 1, 3, 5, 7, 9, 11, 13 […],” Hamburg 274, 66.
70.
“Een houte circul drajende op een ax ad demonstrandam vim centrifugam,” Molhuysen 1913–1924, volume 4, 105∗.
71.
Huygens provides his demonstration by considering the oscillations of a pendulum whose length is equal to the radius of the Earth: “si l’on veut que son effort a s’esloigner du centre egalle justement l’effort de sa simple pesanteur, il faut qu’il fasse chaque tour en autant de temps qu’un pendule de la longueur du demy diametre de ce cercle employe a faire deux vibrations. Il faut donc voir en combien de temps un pendule de la longueur du demy Diametre de la Terre feroit ces deux vibrations; ce qui est aisé par la proprieté connüe des pendules et par la longueur de celuy qui bat les secondes qui est de trois pieds 8½ lignes. Et je trouue qu’il faudroit pour ces deux vibrations une heure 25 la mesure de Snellius le demy Diametre de la terre de 19,595,154 pieds. La vitesse donc de la matiere fluide a l’endroit de la surface de la Terre doibt estre egale a celle d’un corps qui feroit le tour de la Terre dans ledict temps d’une heure 25. minutes, laquelle vistesse est a peu pres 17. fois plus grande que celle d’un poinct de la Terre situé soubs l’Equateur qui faict le mesme tour en 24. heures, comme il paroist par la proportion entre 24. heures et une heure 25. minutes,” Huygens 1669c, 639; cf. Huygens 1690, 143–144.
72.
“[P]aravit mensam, eo artificio constructam, ut in horizontali situ circa suum centrum circumrotari posset: centrum tamen ita erat perforatum ut transitum praeberet filo, cuius extremis alligati erant duo globi aequales quorum alter infra mensam pendulus in linea axis sustinebatur; alter vero in mensa iacebat, ita aut ab alterius globi pondere statim versus centrum attraheretur, nisi ipsum vis aliqua retineret: tum circumrotabatur mensa circa axem velocissime, dum autem ad certum velocitatis gradum pervenerat globus in mensa iacens, observabatur quod tanta vi tendebat a centro sui motus recedere, ut posset globi alterius infra mensam dependentis gravitari resistere: tunc enim non descendebat pendulus ille globus, quanquam a nulla alia potentia retineretur, nisi a vi centrifuga globi alterius cum mensa circumacti: tunc igitur, mensurando circumferentiam, a globo illo descriptam dicebar per experientiam ostendere, quanta velocitas, in data circumferentia centrifugam habeat vi gravitatis aequalem,” Papin 1689, 184–185.
73.
“Demonstravit praeterea Cl. Hugenius, quod in magnis circumferentiis maior quam in parvis celeritas requiratur, ut aequalis utrobique centrifuga vis habeatur: in circumferentiis igitur maiorum in superficie Telluris circulorum, quae circumferentias in mensa descriptas tam immani superant intervallo, necesse est ut materia gravitatem efficiens celerrime moveatur, quo possit tantam vim centrifugam habere: illa enim materia non deprimit gravia versus centrum Telluris nisi eadem vi qua ipsa ab eodem centro conatur recedere: ac revera, calculo rite subductum venit idem Cl. Hugenium quod materia gravitatem efficiens tanto debeat impetu moveri, ut singulis horis totum Telluris ambitum millies ferme percurrere possit: illa autem velocitas, respectu celeritatum a gravibus cadentibus acquisitarum infinita meritissime censeri potest,” Papin 1689, 185.
74.
“[L]a mesme vistesse de cette matiere jointe a la maniere dont nous auons dict qu’elle agit sur les corps qu’elle rend pesants faict voir la raison du principe que Galilée a pris pour demonstrer la proportion de l’acceleration des corps qui tombent qui est que leur vitesse s’augmente également en des temps egaux. Car ces Corps estant poussez successiuement par les parties de la matiere voisine, qui tachent de monter en leur place et dont le mouuement est tousiours infiniment plus viste que celuy qu’ils peuuent auoir acquis par des cheutes qui tombent soubs notre experience, cela fait que l’action de la matiere qui les presse peut estre considerée tousiours aussi forte que lors quelle les trouue au repos, d’ou l’on conclud ensuitte assez facilement l’accroissement des vitesses proportionné a celuy des temps,” Huygens 1669c, 640; cf. Huygens 1690, 144–145. Cf. Papin 1689, 183–184: “Galilaeus in Dialogis suis mechanicis supponit, quod gravi cadenti aequales velocitatis gradus aequalibus temporibus accrescant: et […] eandem illam veritatem experimentis multis conatur a posteriori evincere, quasi nulla dari possit demonstratio a priori. Verum illustrissimus Hugenius praestantiori rem methodo peregit: illam enim propositionem, quam alii pro primo principio assumunt, demonstravit ipse a priori per aliam veritate, quae sic se habet: potentia quae gravitatis causa est, celeritatem habet infinitam prae velocitatibus gravium cadentium, quas nobis observare licet.” For a thorough account, see Freudenthal 2002.
75.
Cf. the original texts, in Varia astronomica, in Huygens 1888–1950, volume 21, 437–439: “[t]ourbillons détruits par Newton. Tourbillons de mouvement sphérique à la place. Rectifier l’idée des tourbillons. Tourbillons nécessaires, […]” and in some marginalia written in the same day on the manuscript Projet de 1680–1681, partiellement exécuté à Paris, d’un planétaire tenant compte de la variation des vitesses des planètes: “[…] omnes difficultates abstulit Clar. vir. Neutonus, simul cum vorticibus Cartesianis; docuitque planetas retineri in orbitis suis gravitatione versus solem. Et excentricos necessario fieri figurae Ellipticae,” Huygens 1888–1950, volume 21, 143.
76.
The reader can find a thorough account in Westfall 1981, chapter 10; Pourciau 1991; Weinstock 1992; Wilson 1994; Gal 2005; Guicciardini 2005; Nauenberg 2005; Ducheyne 2011, chapter 3.
77.
I relied on the translation of Andrew Motte: Newton 1803, volume 1, 40.
78.
Newton 1803, volume 1, 2.
79.
Newton 1803, volume 1, 54.
80.
Mahoney 1993, 187. I owe this reference to Guicciardini 1999, 51.
81.
Guicciardini 1999, 90.
82.
Descartes 1982, 56. For De Volder’s commentary, see Sect. 6.1.2, Descartes’s cosmogony and cosmology.
83.
Descartes 1982, 169. De Volder comments upon this article only in the Hamburg 273 series of his dictata, without adding anything substantial to it: see Hamburg 273, 208.
84.
Newton 1803, volume 1, 378–379. Cf. the original text: “[h]inc liquet planetas a vorticibus corporeis non deferri. Nam planetae secundum hypothesin Copernicaeam circa solem delati revolvuntur in ellipsibus umbilicum habentibus in sole, et radiis ad solem ductis areas describunt temporibus proportionales. At partes vorticis tali motu revolvi nequeunt. Designent AD, BE, CF, orbes tres circa solem S descriptos, quorum extimus CF circulus sit Soli concentricus, et interiorum duorum aphelia sint A, B et perihelia D, E. Ergo corpus quod revolvitur in orbe CF, radio ad solem ducto areas temporibus proportionales describendo, movebitur uniformi cum motu. Corpus autem, quod revolvitur in orbe BE, tardius movebitur in aphelio B et velocius in perihelio E, secundum leges astronomicas; cum tamen secundum leges mechanicas materia vorticis in spatio angustiore inter A et C velocius moveri debeat quam in spatio latiore inter D et F; id est, in aphelia velocius quam in perihelio. Quae duo repugnant inter se,” Newton 1687, 399–400.
85.
Descartes 1982, 207.
86.
Cf. his Le monde: “[t]o this end, consider the Moon to be at B for example […], where you can assume that it is stationary in comparison to the speed at which the celestial matter below it moves. Consider also that this celestial matter, having less space to traverse […] and consequently having to move a little more quickly there, cannot but have the force to push the whole Earth […]. In this way, since the surface […] of the Earth remains round, because it is hard, that of the water […] and the air […], which are fluid, must take the shape of an oval,” Descartes 2004, 52.
87.
“[L]‘on peut voir malgré Descartes que le tourbillon de la Lune n’est pas disposé comme il s’imagine, & que le Diametre apparent de cette Planete est quelque fois plus grand aux Quadratures qu’aux Syzygies,” Tinelis de Castelet 1677, 12. See Aiton 1955a, 1972, chapter 4.
88.
See Aiton 1955b.
89.
“[L]‘auteur preuve que les planetes ne sont pas emportées par des turbillons corporels. La raison en est que, selon l’hypothese de Copernic, elles font leurs révolutions par des ellipses dont le Soleil est le foyer, & décrivent des aire proportionnelles aux temps, par des rayons tirez jusqu’au Soleil. Or les parties d’un Tourbillon ne peuvent pas se mouvoir de cette maniere; come on le voit dans la figure suivante. Qu’AD, BE, CF, soient trois Orbes decrits autour du Soleil S. que l’exterieur CF soit consentrique au Soleil, & que les Aphelies des deux interieurs soient AB, & leurs perihelies DE. Le Corps, qui fait sa revolution dans l’Orbe CF, décrivant des aires proportionnelles aux temps par un rayon tiré jusqu’au Soleil, aura un mouvement uniforme. Mais le corps qui fait son tour dans l’Orbe BE, se mouvra plus lentement dans l’Alphelie B & plus prontement dans le perihelie D, conformémement aux Loix Astronomiques: au lieu que selon les Loix des Méchaniques, la matiere du tourbillon, qui est en AC l’espace le plus étroit, doit se mouvoir plus vite que celle qui est en DF, où elle se peut étendre davantage: de sorte qu’il faudroit qu’une Planete fut emportée par son tourbillon avec plus de rapidité, lorsqu’elle est le plus éloignée du Soleil, & qu’elle allât plus lentement lorsqu’elle en est le plus proche,” Locke 1688a, 440–442. See, for more details, Anstey 2011, chapter 5.
90.
“153. Why the Moon travels more rapidly, and deviates less from its mean motion [when] in conjunction than in quadrature, and why its heaven is not spherical. Neither shall we marvel at the fact that the Moon is seen to be somewhat more rapidly moved, and to deviate less from its course in any direction when it is full or new (that is, when it is near parts B or D of the Heaven); than when only half of it is visible, that is, when it is near A or C. Since the heavenly globules in the space ABCD differ in size and motion from those which are below D near K and from those above B near L, but are similar to those near N and Z; they spread more freely toward A and C than toward B and D. From this it follows that the orbit ABCD is not a perfect circle, but closer to the figure of an ellipse; and that the matter of the heaven is transported more slowly when in the regions near C and A than when near B and D. Therefore, the Moon, which is carried along by this matter of the heaven, {must also move more slowly and deviate more from its course near C and A and} must move closer to the Earth if it is waxing and further away if it is waning; that is, further away when it happens to be near A or C, than when it is near B or D,” Descartes 1982, 175.
91.
See Snow 1924; Rosenfeld 1969; Anstey 2005; Kochiras 2017.
92.
“Je n’ay donc rien contre la Vis Centripeta, comme Mr. Newton l’appelle, par la quelle il fait peser les Planetes vers le Soleil, & la Lune vers la Terre, mais j’en demeure d’accord sans difficulté: parce que non seulement on sçait par experience qu’il y a une telle maniere d’attraction ou d’impulsion dans la nature, mais qu’aussi elle s’explique par les loix du mouvement, comme on a vû dans ce que j’ay écrit cy dessus de la pesanteur. Car rien n’empêche que la cause, de cette Vis Centripeta vers le Soleil, ne soit semblable à celle qui pousse les corps, qu’on appelle pesants, à descendre vers la Terre,” Huygens 1690, 160.
93.
“Il y avoit long temps que je m’estois imaginé, que la figure spherique du Soleil pouvoit estre produite de mesme que celle qui, selon moy, produit la sphericité de la Terre); mais je n’avois point etendu l’action de la pesanteur à de si grandes distances, comme du Soleil aux Planetes, ni de la Terre à la Lune; parce que les Tourbillons de Mr. Des Cartes, qui m’avoient autrefois paru fort vraisemblables, & que j’avois encore dans l’esprit, venoient à la traverse,” Huygens 1690, 160.
94.
“Je n’avois pas pensé non plus à cette diminution reglée de la pesanteur, sçavoir qu’elle estoit en raison reciproque des quarrez des distances du centre: qui est une nouvelle & fort remarquable proprieté de la pesanteur, dont il vaut bien la peine de chercher la raison. Mais voyant maintenant par les demonstrations de Mr. Newton, qu’en supposant une telle pesanteur vers le Soleil, & qui diminue suivant la dite proportion, elle contrebalance si bien les forces centrifuges des Planetes, & produit justement l’effet du mouvement Elliptique, que Kepler avoit deviné, & verifié par les observations, je ne puis guere douter que ces Hypotheses touchant la pesanteur ne soient vrayes, ni que le Systeme de Mr. Newton, autant qu’il est fondé la dessus, ne le soit de mesme. Qui doit paroitre d’autant plus probable, qu’on y trouve la solution de plusieurs difficultez, qui faisoient de la peine dans les Tourbillons supposez de Des Cartes. On voit maintenant comment les excentricitez des Planetes peuvent demeurer constamment les mesmes: pourquoy les plans de leurs Orbes ne s’unissent point, mais gardent leurs differentes inclinaisons à l’égard du plan de l’Ecliptique, & pourquoy les plans de tous ces Orbes passent necessairement par le Soleil. Comment les mouvemens des Planetes peuvent s’accelerer & se ralentir par les degrez qu’on y observe; qui malaisement pouvoient estre tels, si elles nageoient dans un Tourbillon autour du Soleil,” Huygens 1690, 160–161.
95.
For a thorough account, see Schliesser and Smith 2000. See also Mahoney 1980; Schliesser and Smith 1996; Howard 2008; De Grijs 2015. Please note that Huygens had already organized a sort of pre-trial in the Zuiderzee in 1685.
96.
Similar observations were carried out in the same years by Jean Picard (1671), Edmond Halley (1677), Varin, Jean Deshayes and Guillaume de Glos (1682): see Olmsted 1942; Débarbat 1986; Matthews 2000; Howarth 2007; Dew 2013.
97.
Schliesser and Smith 2000, 16. In fact, the original difference between the ‘virtual’ final point of the voyage and the actual location of Texel (i.e. what Huygens thought it to be on the basis of Tachard’s estimations, to which I shall return below) calculated by Huygens was circa 0° 25′, resulting from the calculated last point of the Alcmaer (14° 1′ west of the Cape, in the first calculation), and the location of Texel (14° 25′ west of the Cape). The version reproduced in the Oeuvres, i.e. Huygens’s own copy, in fact, was modified by Huygens after De Volder provided some corrections on Huygens’s table in his report. In the report (which I analyse below), De Volder provided corrections to the calculated positions of the Alcmaer, locating its final point 14° 8′ west to the Cape: “[…] [w]aer bij komt dat de horologien soodanigh verschil van lenghte tussen de Caep en Texel geven, […] sijnde dit verschil volgens de Horologien, niet 14 gr. 1 minuut, als de Hr. Huijgens seyt, tgeen uijt het voorseijde abuijs in ’t adderen komt te spruijten maer 14 gr. 8 m.,” De Volder to the Directors of the VOC (letter 2547), 22 July 1689, in Huygens 1888–1950, volume 9, 343. Huygens wrote a marginal note in his copy of his own report about this: “[m]ijn misrekening in de 7e colomme en ’t geen in de verdere colommen daer uijt volgden, is hier van daen gecorrigeert volgens de rekening van de Hr. de Volder,” Huygens to the Directors of the VOC (letter 2519), 24 April 1688, in Huygens 1888–1950, volume 9, 280; see Schliesser and Smith 2000, 2 (n. 3), 16 (n. 41) and 50 (n. 108). Of course, De Volder’s correction made Huygens’s result even more compelling.
98.
“Doch eyndelijck, nae langh wachten, kan ick seggen seer goede tijdinghe te brengen aengaende dese Inventie, als bevonden hebbende dat door middel der voors, horologien de Lengdens tusschen de Caep de Bonne Esper.^ce en Texel doorgaens seer wel sijn afgemeten, en de geheele Lengde tusschen dese twee plaetsen soo perfect, dat het maer 5 à 6 mijlen en verscheelt, ’t welck ick bekenne met sonderlingh vergenoegen gesien te hebben; als sijnde een seeckere preuve van de moghelijckheydt deser soo lang nae gewenschte saeck,” Huygens to the Directors of the VOC (letter 2519), 24 April 1688, in Huygens 1888–1950, volume 9, 272.
99.
Cf. the beginning of the Addition: “[q]uelque temps aprés que j’eus achevé d’escrire ce qui precede, ayant receu & examiné le journal du voiage, qui, par ordre de Messieurs les Directeurs de la Compagnie des Indes Orientales, a esté fait, avec nos Horloges à pendule, jusqu’au Cap de Bonne Esperance; & du dépuis ayant encore lû le tres sçavant ouvrage de Mr. Newton, dont le titre est Philosophiae Naturalis principia Mathematica; l’un & l’autre me fournit de la matiere pour étendre d’avantage ce Discours. Et premierement, quant aux differentes longueurs des Pendules dans divers Climats, dont il a aussi traité, je crois avoir, par le moien de ces Horloges, non seulement une confirmation évidente de cet effect du mouvement de la Terre, mais aussi de la mesure de ces longueurs, qui s’accorde tres bien avec le calcul que je viens d’en donner. Car ayant corrigé & rectifié, suivant ce calcul, les Longitudes qu’on avoit mesurées par les Horloges, au retour du Cap de B. Espe. jusqu’au Texel en Hollande, (car en allant elles n’avoient point servi) j’ay trouvé que la route du vaisseau en estoit beaucoup mieux marquée sur la Carte, qu’elle n’estoit sans cette correction; & si bien, qu’en arrivant à ce Port, il n’y avoit pas 5 ou 6 lieues d’erreur dans la Longitude ainsi rectifiée,” Huygens 1690, 152–153.
100.
See Schliesser and Smith 2000, 4 (n. 8): “[a] copy of de Volder’s review can be found in Hudde’s personal archives at the Algemeen Rijksarchief (signature: 1.10.48 no. 44) in The Hague.”
101.
“Aengaende het gemelte effect van het draeijen der aerde sal VEdt. misschien gesien hebben ’t geen onlanghs daervan geschreven is door den Professor Newton in sijn boeck genaemt Philosophiae Naturalis principia Mathematica, stellende verscheyde hypotheses die ick niet en kan approberen, waeruyt dan oock ander besluijt treckt als mijn rekeningh uytgeeft. De fondamenten waerop ick gebouwt hebbe sijn in mijn Raport vermelt, welcke voor soo veel der Lichaemen swaerheydt aengaet, weynigh verschelen van die van des Cartes en Rohault,” Huygens to Hudde, 24 April 1688 (letter 2517), in Huygens 1888–1950, volume 9, 267. Hudde did not write a review on Huygens’s report.
102.
“En wat aengaet het gansche fondament deser Calculatie, en wat ick daer ontrent in acht genomen hebbe, ’t selve heb ick verhandelt in een apart Tractaet van de Oorsaeck der Swaerte), ’t welck ick geerne wil, en oock voor genomen hebbe te onderwerpen aen alle Ervarene Mathematici haer examen, om te doen sien dat ick in mijn stellingh nochte uytrekeningh niet in ’t minste toegegeven hebbe om de gevonden Lengdens goedt te maecken,” Huygens to the Directors of the VOC (letter 2519), 24 April 1688, in Huygens 1888–1950, volume 9, 276.
103.
Cf. Huygens’s own words: “ayant trouvé, comme on a vû, que, si la Terre tournoit 17 fois plus viste qu’elle ne fait, la force Centrifuge sous l’Equateur seroit égale à toute la pesanteur d’un corps; il faut que le mouvement de la Terre, tel qu’il est maintenant, oste une partie de la pesanteur, qui soit à la pesanteur entiere comme 1 au quarré de 17, c’est-à- dire 1/289; parce que les forces des corps, à s’éloigner du centre autour du quel ils tournent, sont entre elles comme les quarrez de leurs vitesses, suivant mon Theoreme 3e. de Vi Centrifuga). Chaque corps, sous l’Equateur, estant donc moins pesant de 1/289 de ce qu’il seroit si la Terre ne tournoit point sur son axe; il s’ensuit, par les loix de la Mechanique, que la longueur d’un Pendule, en cet endroit, doit aussi estre diminuée de 1/289, pour faire ses allées dans le mesme temps qu’il les feroit sur la Terre immobile,” Huygens 1690, 146–147.
104.
“[…] l’on trouvera que ces retardemens, entre eux, suivent assez precisément la mesme proportion que les diminutions de la longueur du pendule: & que le plus grand retardement, tel que seroit celuy d’une Horloge sous l’Equateur, lors qu’elle auroit esté reglée sous le Pole, seroit par jour fort prés de 2½ min. En ayant donc calculé des Tables, on pourroit corriger, par leur moien, le mouvement des Horloges, & s’en servir avec la mesme sureté que si ce mouvement estoit par tout égal,” Huygens 1690, 150.
105.
“Le canal qu’il suppose est representé dans nostre figure par ECP, faisant un angle droit au centre de la Terre. Il faut le concevoir comme ayant quelque peu de creux, & rempli d’eau. Ce qui estant, il est certain que les deux jambes, EC, CP [respectively, the canal connecting the equator and a pole to the center of the Earth], se doivent tenir en équilibre, si l’on suppose que la Terre, estant toute composée d’eau, prend une figure, dont les diametres soient EA & PQ [respectively, the ‘equatorial’ canal and the ‘polar’ canal]: parce qu’autrement, cette eau du canal, ne demeureroit pas non plus dans son assiette en la concevant sans canal, contre ce qu’on suppose. d’où il est aisé de trouver la raison de EA à PQ. Car en posant EC = a; CP = b, & representant la pesanteur absoluë par une ligne p; & la force centrifuge en E par la ligne n; le poids du canal PC est pb, sçavoir ce qui se fait en multipliant toutes les parties de ce canal egalement par la ligne p. Mais le poids du canal EC, qui seroit pa, est diminué par la force centrifuge de toutes ses parties, des quelles la plus élevée, qui est en E, a la force n; & toutes les autres parties l’ont proportionée à celle cy, suivant leur distances du centre D. ce qui fait 1/2 na pour toute la force centrifuge de l’eau du canal EC, qui estant ostée de son poids pa, reste pa − 1/2 na; qui doit estre égal à pb poids du canal PC. d’où il paroit que a est à b comme p à p − 1/2 n. C’est-à-dire que le diametre EA de la Terre, est à son axe PQ, comme 289 à 288 1/2, ou comme 578 à 577; car la raison de p à n estoit comme 289 à 1,” Huygens 1690, 155. On the other hand, Newton discovered a difference, between the equator and the poles, of 1/231: he used the example of the canals later used by Huygens, applying to them the effect of centrifugal force and of gravitation: see his Principia, book 3, propositions 18–20, where Newton proposes various adjustments to the lengths of pendulum clocks, for different latitudes.
106.
“[…] cet exemple de la Lune prouve si bien la diminution du poids, suivant la raison reciproque des quarrez des distances du centre de la Terre [Huygens had just (successfully) applied Newton’s law of inverse square to the gravitation of the Moon]; on pourroit douter s’il n’y auroit pas aux Pendules une autre inégalité, outre celle qui estoit causée par le mouvement journalier. Car si la Terre n’est pas spherique, mais assez pres spheroïde, & qu’un point sous l’Equateur est plus eloigné du centre, que n’est un point sous le Pole, dans la raison de 578 à 577, comme il a esté dit cy-devant; les pesanteurs estant en ces endroits en raison contraire des quarrez de ces distances, il faudroit aussi que le pendule sous l’Equateur fust plus court, que celuy dessous le Pole, dans cette mesme raison contraire). C’est à dire que ces pendules seroient comme 288 à 289; ou que le pendule sous l’Equateur seroit plus court de 1/289 de ce qu’il seroit sous le Pole. Qui est justement la mesme difference, qui provenoit cy dessus du mouvement journalier, ou de la force centrifuge. De sorte qu’une Horloge, avec la mesme longueur de pendule, iroit plus lentement sous l’Equateur que sous le Pole, du double de ce qu’elle retardoit par le mouvement de la Terre; & ainsi cette difference journaliere sous l’Equateur seroit de pres de 5 minutes. Et sous les autres paralleles, on la trouveroit par tout plus que double de ce qu’elle y estoit auparavant. Mais je doute fort que l’experience confirme cette grande variation), puisque j’ay vû que, dans le voiage dont j’ay fait mention, la seule premiere équation suffit, & que la plus que double mettroit, vers le milieu du chemin, trop de difference entre la route du vaisseau, calculée sur le Pendule, & celle qu’il tenoit par l’Estime des Pilotes,” Huygens 1690, 166–167. Please note that if the theoretical delay calculated by Huygens on the basis of the idea of universal gravitation amounts of 5 minutes, according to Newton’s Principia it amounts in fact to a delay of 3 minutes and 7 seconds, as Newton takes into account local variations of gravity, due to the spheroidal shape of the Earth, and to its internal density: see Newton 1687, 425–426, discussed in Schliesser and Smith 2000, 21. Also by considering this variation, however, Huygens’s calculation of the longitude at the ship’s arrival in Texel would have been more precise than Newton’s: see Schliesser and Smith 2000, 18.
107.
See De Volder to the Directors of the VOC, 22 July 1689 (letter 2547), and De Volder to Huygens, 6 April 1693 (letter 2800), in Huygens 1888–1950, volume 9, 276, 339–343, volume 10, 435–436. For Huygens’s reaction to De Volder’s comments, see the letters of Huygens to De Volder of 14 March 1693 (letters 2798–2799), 19 April 1688 (letters 2802–2803), and the letter of Huygens to the Directors of the VOC of 6 March 1693 (letter 2796). No official report for the VOC on the second trial could be retrieved.
108.
On him, see Dijkstra 2012, chapter 10.
109.
On it, see Dijkstra 2007.
110.
Dijkstra 2012, 322.
111.
De Volder asked him how he determined the longitude, and Graaf answered him that he could do so by the movement of the moon in the firmament. As De Volder asked whether he could observe such movement, Graaf asked the members of the States of Holland whether they would not misinterpret what he was going to answer, and stated that De Volder had posed a misleading question, because longitude cannot be found by observation. Eventually, De Volder looked at him severely, without words: “[w]aar op d’Heer Professor Volder hem liet hooren vragende; Waar door ik de langte zoude vinden? Ik antwoorde hem, door het verachteren van de Maan aan het Sterredak. Daar op hy heel for vraagde, wat Starredak? Ik zeide, dat het even veel was, of ik zeyde firmament of uitspansel. Daar op hy weder heel spijtig sprak, en vraagde; of ik dat wel eens konde observeren? Waar op ik verzochte, dat Haar Ho: Mog: my niet qualijk geliefden af te neemen, ’t geen ik daar op nu dacht te zeggen: die my verlofgaven, om vry uit te spreken. Dies ik zeyde, dat de Heer Professor my vraagde ’t geene niet ter zaake dien de. Alzoo men door het observeren die lengte niet konde bekomen […]. Ik dan sprak tegen Volder: Laat ons een goed fundament leggen, op dat het Hemelsch gebouw niet om verre raakt, wanneer wy ten halven gekoomen zijn: Ook moeten wy betoonen, dat wy mannen zijn in ’t verstand; en geen woorden spreken, die in den wind of lucht vervliegen: Maar die tot de zaak en des zelfs waarheid dienen. Dewijl hy my daar op sterk aanzag, zeide ik vorder tot hem; Laat ons nu eerst het geen men ’t lichtste meint te wesen bezien, of het met de waarheid over een komt, te weeten, de beweginge van de Son. Ik vrage dan, hoe groot de cyclus of cirkel van de Son is? Hy my noch al sterk aanziende, en sprak niet. Ik zeide, vraag my: Hy sweeg noch al stil,” Graaf 1689, 2–3. See also the commentary of the editors of Huygens’s Oeuvres: Huygens 1888–1950, volume 9, 315 and 317.
112.
“In de volgende, of tweede Sessie, ontrent 14 dagen daar na vermidts de traage en weerwillige wederkomst van d’Heer Professor Volder, is niets besonders voorgevallen, […]” Graaf 1689, 9.
113.
See Graaf 1689, 12–16.
114.
“Quanto in silentio audivimus lectam fuisse in consessu Potentissimorum Hollandiae Ordinum Epistolam Volderi, quum de oriente et occidente excitatum esset negotium?” Gronovius 1709, 28.
115.
See, for instance, his letter to Lodewijk Huygens of 14 May 1689 (letter 2538). See Dijkstra 2012, 321–331.
116.
“Pendant que Mr. de Volder s’appliquoit à étudier & à enseigner les Mathematiques, de trés-habiles gens découvrirent ces nouvelles Méthodes aux quelles on a donné les noms de Calcul differentiel & de Calcul integral, & faisoient de tems en tems paroître quelque chose en public, qu’ils avoient découvert, par ces Méthodes. Nôtre Philosophe s’applica aussi à ces nouvelles manieres, & dès que le livre de l’Illustre Mr. Newton, des Principes Mathematiques de la Philosophie Naturelle, eut paru en MDCLXXXVII. Il s’attacha fortement à cette lecture, pour découvrir les principes sur les quels l’Auteur s’étoit fondé; & l’on a encore trouvé parmi ses papiers les calculs de ses démonstrations. On sait que ce livre suppose une connoissance des Mathematiques, qui n’est pas commune. Je me souviens même d’avoir ouï dire à Mr. de Volder, que peu de tems après qu’il parut, feu Mr. Huygens, qui étoit un grand Mathematicien, mais à qui les nouvelles méthodes, dont j’ai parlé, étoient inconnuës, le vint voir à Leide & le mit sur le sujet du livre de Mr. Newton. Il avoüa à Mr. de Volder, qu’il trouvoit ce livre extrémement obscur, & lui demanda ce qu’il en pensoit. Nôtre Philosophe lui répondit qu’il n’étoit pas en effet facile de pénetrer les principes des démonstrations de l’Auteur, mais qu’il avoit trouvées veritables celles qu’il avoit examinées. On ne peut pas néanmoins douter que Mr. Huygens ne fût un excellent Mathematicien, & que la Physique & les Mathematiques ne lui soient très-redevables. […] Je ne doute pas que le Livre de Mr. Newton ne lui eût ouvert les yeux, sur la doctrine des tourbillons de Descartes; que ce Livre a entierement renversée, à cela près, qu’il établit le Systeme de Copernic, comme lui; en reconnoissant le Soleil, comme le centre commun des mouvemens de la Terre & des autres Planetes. Cette partie de la Physique de Descartes avoit né an moins paru à bien des gens la mieux imaginée. On voit en cette rencontre, comme en plusieurs autres, l’exemple d’un grand Mathematicien, qui ne raisonnoit point mathematiquement, ni même conséquemment,” Le Clerc 1709, 379–380 and 382. Le Clerc also more generally refers to some “Englishmen” as having brought De Volder to reject Cartesianism (may be referring also to Locke: see Sect. 2.2.3, The mid-1670s clash at Leiden and the foundation of the experimental theatre): “[i]l n’étoit nullement entêté de la Philosophie, qu’il enseignoit; sur la fin de ses jours, & même quelques années auparavant, il avoit reconnu le foible du Cartesianisme; autant apparemment, par sa propre méditation, que par le secours des habiles Anglois, qui ont établi d’autres principes,” Le Clerc 1709, 398.
117.
On him, see Font 2014; Balázs et al. 2016. See also Réka 2009.
118.
See, for instance, the defence of Descartes’s matter theory in the De lumine, Pars prima, thesis 3, which goes along with an overall presentation of Descartes’s theory of light developed in the whole text, and the use of Descartes’s definition of relative motion as given in Principia II. 25 (De systemate mundi, thesis 8).
119.
Köleséri 1681, thesis 11.
120.
“Systema Mundi quod a Nobiliss. Cartesio delineatur, non pro mera hypothesi; sed pro rei veritate habendum est,” Köleséri 1681, Annexa physica, annexum 14. See Ruestow 1973, 80–81.
121.
“44. That I nevertheless wish those [causes] I am proposing here to be taken only as hypotheses. […] That I shall even assume here some which it is certain are false. Indeed, in order to better explain natural things. I may even retrace their causes here to a stage earlier than any I think they ever passed through. For example, I do not doubt that the world was created in the beginning with all the perfection which it now possesses; so that the Sun, the Earth, the Moon. and the Stars existed in it, and so that the Earth did not only contain the seeds of plants but was covered by actual plants; and that Adam and Eve were not born as children but created as adults. The Christian faith teaches us this, and natural reason convinces us that this is true; because, taking into account the omnipotence of God, we must believe that everything He created was perfect in every way. But nevertheless, just as for an understanding of the nature of plants or men it is better by far to consider how they can gradually grow from seeds than how they were created [entire] by God in the very beginning of the world,” Descartes 1982, 105. On the topic, see Harrison 2000; Ariew 2011b; Torero-Ibad 2011.
122.
“I. […] Hypotheses enim et principia ea sunt, quibus bene, firmiterque positis, accuratissime omnes sequentur consequentiae; […] nec unquam certior, evidentiorque ad assequendam veritatis cognitionem via esse potest firmis principiis et hypothesibus; utpote quales etiam ipsi scientiae certissimae mathematicae sectatores suis praemittunt problematibus et theorematibus, tantumque hypotheses in astronomia, quantum axiomata in geometria praestant, Ea siquidem quis invenerit, tum dum invenit maximam veritatum obtinuit partem, nam veritates tam indissolubili et mutuo nexu sunt sibi ipsis nexae, ut una posita reliquae sponte sequantur. Oportet interim ea principia et hypotheses ex quibus consequentias deducere, variasque rerum causas reddere contendit philosophus tam clara et evidentia esse, ut mens earum veritatem in dubium vocare nec possit, nec debeat; tam concatenata, connexave cum suis consequentiis ut tota consequentiarum cognitio, illis suum debeat ortum, sed non vicissim illorum his: talibus ita positis, adniti philosophum oportet ut notitia rerum, ex principiis hisce, a quibus dependent ita deducat, ut nihil in tota deductionum serie inveniatur, quod non sit manifestissimum. […] XII. […] Habes itaque hic lector veritatis avide, ex hac hypothesi systema ordinatissumum, mirandam mundi fabricam potiori tum ratione, tum experientia nixam. Quia autem hypothesin et principium invenimus, quo firmiter asserto, et vindicato, evidentes phaenomenωn caelestium causas obtinemus, quorum demonstrationem ulterius persequi nunc non licet,” Köleséri 1681, theses 1 and 12.
123.
See Sect. 3.2.3.3, The role of experience in De Volder’s natural philosophy.
124.
On him, and on the presence of Hungarian students at Leiden, see Réka 2009.
125.
Cf. the closing scholium: “[…] sideribus lucidis (de quibus solis nobis sermo est),” De Volder and Derecskei 1682, Scholium. In the Annexa, it is reported a standard Cartesian proposition on gravity: “Omnia copora terrestria sunt levia, et ea tantum dicuntur gravia, quae sunt minus levia,” De Volder and Derecskei 1682, annexum 9.
126.
Cf. De Volder and Derecskei 1682, lemma 10: “[o]mne corpus circulariter motum continuo determinatur, ut secundum tangentem pergat moveri, idque obtinet, nisi a causis externis impediatur. Circulus, (iuxta Archimedem) est polygonum infinitorum laterum seu est figura constans ex infinitis lineis rectis. Adeo ut quamdiu numerus laterum certus est, eousque semper est differentia, inter circulum, et polygonum. Si vero numerus laterum sit infinitus, seu omni numero maior, iam illud polygonum erit circulus. Unde sequitur. Corpus circulariter motum, in quolibet puncto sit; semper haerere in aliqua linea recta, nec ab ea deflectet, nisi a causa externa cogatur […]. At illa linea recta, si producatur est tangens circuli.” See Hamburg 273, 105–106: “[t]angens circuli. Tangere linea dicit[ur] circulum {q[uod]} circulum tangit ut AB, non vero secat ut CB. Circulus nihil aliud est quam infinita congeries tangentium ex definitione Archimedis. Cum itaq[ue] corpus in orbem movetur, ex una tangente in alias progreditur, ex quo sequitur, si in illa tangente in qua est, sibi relinquatur, moveri oportere per eandem.” See Fig. 6.17, Hamburg 273, 105. See also Hamburg 274, 43: “[t]angens circuli. Hoc equidem patet, quia circulus potest considerari, ut fit ab Archimede aliisq[ue] mathematicis, tanquam poligonum infinitorum laterum, unde lapis in A haerebit in uno latere istius poligoni, et si a funda dimittatur per illud {latus} perget moveri, {latus} illud autem productum ut manifestum est, est tangens circuli, q[uae] demonstratio non {…} omnibus cuiusq[ue] generis curvis potest applicari, cum ea eodem modo possum {…} constare ex infinitis tangentibus pro curvarum varietate varie dispositis.” In the copy of the dictata extant in Pretoria, consistent annotations are added in an unnumbered page between pages 34 and 35.
127.
“Si hoc incrementum qualibet alia proportione procedat, potest autem qualibet, neque enim ulla ratio est, quae hanc potius stabiliat, quam illam, iam quaelibet potest esse Solis magnitudo, et concidit omnis vis mathematicae huius, si dis placet, demonstrationis, Certe cum nihil assumat Cartesius nec assumere debeat, quam ex angularibus corpusculis, aequalibus et, si ita velis, inter se similibus exsculpi globulos, longe plurimis in corpusculis maximos, in pauculis vero reliquorum si spectemus multitudinem, aliquantulum minores, hoc enim tantum requiritur, ut plura fiant ramenta, quam ut globulorum intervallulis replendis sufficiant, nec quicquam cogatur determinare de huius incrementi quantitate, imo nec ratio sinat determinare, quamtum hoc sit incrementum, cum per data possit esse quodlibet; multo rectius ratiocinatus foret Vir. Ill. si ex hisce conclusisset, quamlibet posse sequi ex principiis a Cartesio positis Solis magnitudinem; nec posse certam determinari ulla alia ratione quam per experientiam,” De Volder 1695, De tribus Cartesii elementis, thesis 13.
128.
The author lists 9 astronomical difficultates raised by the attribution of rest to Earth, and resolves them by considering Earth as a planet. In this, the disputation is kindred to a shorter disputation presided over by De Volder in 1684, authored by Hieronymus Simons van Alphen, Exercitatio philosophica utrum Sol, an vero Tellus, in planetarum numerum referenda sit, inquirens, in which, as in the 1694 disputation, the Tychonic system is criticized as presupposing an enormous speed in the stars (thesis 9), and it is supposed that planets are carried in a vortex (thesis 12).
129.
“Atque ita iuxta ipsorum hypothesin ratio, cur motus sit Terrae tribuendus, est certa et evidens, ratio vero, cur illum coelo tribuant et Terrae quietem, est incerta, et a sola illorum imaginatione efficta: Phil. pr. parte 3 § 38,” De Volder and Casembroot 1694, thesis 11. Cf. Descartes’s text: “[t]hus, according to their hypothesis, the reason for which we ought to attribute motion to the heaven and immobility to the Earth is uncertain and depends entirely on their imagination; while, on the other hand, the reason for which they should say that the Earth moves is obvious and certain,” Descartes 1982, 102.
130.
“Obi. Tellurem a materia coeli ambiente deferri non posse, cum secundum ipsam Cartesii hypothesin tardius ipso fluido moveatur, adeoque fore, ut tractu temporis ei obtemperet, ac eadem cum celeritate feratur. R. Utinam adduceretur locus, in quo ita ratiocinatur Cartesius, sic enim melius pateret, an vere an falso haec illi adscribantur: memini quidem me alicubi legisse, illud fluidum secundum partes celerius ipsa Tellure, aliove planeta moveri, id est, nunc has nunc illas fluidi particulas a Terra recedere, et ad ipsam rursus accedere; sed tamen illius fluidi motum, quo simul cum eo ferri, accurate aequare,” De Volder and Casembroot 1694, thesis 13. See Descartes’s Principia, III.28: “[t]hat the Earth, properly speaking, is not moved, nor are any of the Planets; although they are carried along by the heaven. And it is important to remember here what was said earlier concerning the nature of movement; i.e., that (if we are speaking properly and in accordance with the truth of the matter) it is only the transference of a body from the vicinity of those bodies which are immediately contiguous to it, and considered to be at rest, into the vicinity of others. However, in common usage, all action by which any body travels from one place to another is often also called movement; and in this sense of the term it can be said that the same thing is simultaneously moved and not moved, according to the way we diversely determine its location. From this it follows that no movement, in the strict sense, is found in the Earth or even in the other Planets; because they are not transported from the vicinity of the parts of the heaven immediately contiguous to them, inasmuch as we consider these parts of the heaven to be at rest,” Descartes 1982, 94.
131.
“Terra non fertur suo motu, defert[ur] vero a materia coelesti eius poros pervadente, si itaq[ue] co[rpor]is {motus} telluri et materiae coelesti nil efficiet in tellure, et ratione {suiis} nulla in eo fiet mutatio, a materia coelesti, manet haec ratione eius in eodem loco, praeter hunc {[n]a[m] motum alium} adest materiae subtili per quam a tellure recedit, in tellurem ergo eius motum impedientem incidens, ab ea recedit, et erit levis. Sicq[ue] apparet q[uo]d ante in o[mni]bus vorticibus levior habere diximus, o[mn]ia sc. corpora recedere conari a centro, circa quod moventur, c[um]q[que] non possint o[mn]ia, subtiliora saltem, et celerius mota, sicq[ue] sola materia coelestis a tellure recedit, non a[utem] alia corpora, quia sic daretur vacuum, aliud[que] in eius locum succedere debet, q[uo]d vocatur grave,” Hamburg 273, 232. Cf. the other series: “[q]uantum possunt recedunt. Nam cum in terram incidant, et ab ea in determinatione sua mutentur, necesse est, ut reflectantur, aeq[ue] ac pila, q[uae] incidit in parietem, non potest autem reflecti, {quin} a terra recedat, ut evidens est,” Hamburg 274, 99.
132.
See the corollaria respondentis (i.e. of Jacob Copper, who would translate Descartes’s De homine into Dutch (as De verhandeling van den mensch en de makinge van de vrugt in ’s moeders lichaam, 1682)) appended to the third disputation, and the corollaria (whose author is not specified) of the fourth one: “[…] quia in omni motu est circulus, alia corpora minoris motus capacia, deprimuntur versus centrum materia caelesti recedente,” De Volder 1676–1678, disputation 3, corollary 11; “gravitas corporum dependet a minori vi qua pollent a centro recedendi”, De Volder 1676–1678, disputation 4, corollary 7. The latter corollary is compatible both with Le monde’s and Principia’s accounts. In the main text of disputation 3, De Volder is uncommitted on the gravity of subtle matter: “[…] materia subtiliori ipso aëre multo minus gravi, (si modo ullius gravitatis sit particeps, quod hic non determino),” De Volder 1676–1678, disputation 3, thesis 4.
133.
“X. Quam rem si paulo inspiciamus accuratius, reperturi sumus corpora, quae sua natura nec gravia nec levia sunt, suam vel gravitatem vel levitatem debere causae externae; imo magis proprie et simplicius dici corpora terrestria omnia esse levia et ea quae vocantur gravia respectu aliorum esse tantum minus levia et ea quae vocantur levia esse tantum minus gravia: ex rotatione enim Telluris circa axem concludere licet, omnia a centro quantum possent recessura, quod autem non recedant, sed contra versus centrum deprimantur, hoc oriri ex alia causa, quia sc. dantur corpora ad motum aptiora, maioremque propterea vim habentia ad recedendum. XII. Sed ubi omnis materia aequalem a centro recedendi vim habet nullus potest esse gravitatis effectus; aequalia enim in aequalia agere non possunt: quod clarissime exempli vasis aqua referti illustrabitur: in vase enim aqua pleno omnis illa aqua tam quae est in superficie, quam quae est prope fundum aequali vi premit deorsum; si enim illa quae est in superficie maiori vi premeret quam quae est prope fundum, eo ipso descendere et alia in eius locum adscendere deberet. Hinc sequitur, si ponamus omnia corpora aequalem habere vim recedendi, quod nulla eorum nec adscendere, nec descendere ulterius possint, nulla enim est ratio, cur unum magis descendat alterum,” De Volder and Van Bronchorst 1685, theses 10–11.
134.
“Circa Solem, tanquam centrum, ingens materiae moles, in orbem movetur; similiter et circa Tellurem nostra, quae in vortice illo Solis continetur, alius quidam minor vortex datur, quicum et circa proprium axem in orbem movetur. Quod postulatum, a posteriori saltem, si non a priori, ex motu Lunae circa Tellurem, ut et reliquorum planetarum circa Solem, tanquam ipsorum centra in orbem, demonstrari apodictice potest,” Schuyl 1688a, Postulatum.
135.
“Posito (per postulat. Praeced.) quod omnia in orbem moveantur, sequitur […] quod omnia corpora conatum habeant recedendi a centro, secundum tangentem circuli, quare […] actu, nisi quid impediat, a centro recedent. Et licet quidem impediatur, quod omnis materia simul a centro recedeat, ea tamen corpora, quae ad recedendum plus virium habent longius […] a centro recedere debent, quam quae habent minus virium. Unde sequitur, quod, licet in principio merum fuerit chaos, tandem nihilominus omnia ad aequilibrium reduci debuerint, ita ut unaquaeque pars eum sibi vindicaverit locum, in quo aequalem tum a centro recedendi, tum ad centrum accedendi conatum habet, quare et in eo […] haerere debet, ex eoque nec a centro, nec versus centrum excedere potest, prement tamen se invicem […] cum mutuis obstent conatibus, sed ex diametro aequaliter, quae pressio, cum non tantum fiat secundum lineam rectam e centro eductam, sed versus quascunque alias imaginabiles plagas (circulus enim ex infinitis tangentibus aliter, et aliter continuo determinatis est compositus). Hinc unaquaeque pars istius materiae, quae vortices istos constituit, quaquaversum ex diametro premetur aequaliter,” Schuyl 1688a, chapter 1, 2–3 (unnumbered).
136.
“Ex eodem etiam ratiocinio sponte sua se prodit causa, tum gravitatis, et descensus corporum gravium,” Schuyl 1688a, chapter 1, 3 (unnumbered).
137.
“De Hr. Huijgens onderstelt dat de oorsaeck van de swaarte der lichamen bestaet in een seer subtile materie van een en selfde natuyr met alle andere lichamen, dewelcke rondom het centrum van de aarde naer alle kanten seer snel bewogen wort,” De Volder to the Directors of the VOC (letter 2547), 22 July 1689, in Huygens 1888–1950, volume 9, 339–340.
138.
According to Huygens’s Adversaria, a copy was sent on 17 February: “Mr. Huet Evesque de Soissons, Mr. Cuper St. Gen. M. Papin prof.r a Marpurg. Dierkens. de Volder. Fullenius correctum. 17 feb.,” Huygens 1888–1950, volume 9, 379. However, it seems that De Volder got his copy only on 16 May: see the letter of Huygens to Hudde of 25 May 1689 (letter 2539): “[a]en de Heer Hudde genotificeert mijn reys naer Engelandt. en dat het tractaet de la Cause de la Pesanteur aen de Volder behandight hebben,” Huygens 1888–1950, volume 9, 319; cf. Huygens’s Adversaria: “16 Maj. aan Burchardus de Volder Prof. matheseos tot Leyden mijn Discours de la cause de la Pesanteur gebracht om te examineeren ’t geen daer uyt geallegueert werdt in mijn Bericht aen de Bewindthebbers van de O. Indische Compagnie, aengaende de Vindingh der Lengden door mijn Horologien, die aen de Caep de B. Esperance geweest zijn. Welck bericht bij Haer Ed. aen gemelte de Volder in handen gestelt is om het zelve te examineeren,” Huygens 1888–1950, volume 9, 319.
139.
“Unde non tantum patet, cur fluidorum partes sine ulla sensibili resistentia quaquaversum moveri, et ab invicem separari possint, sed et, cur, simul ac ab una parte fortius prematur, quam ab altera, eo statim cedant, quaquaversum illud sit, sive sursum, sive deorsum sive versus latera; imo ex unico hoc fundamento omnes fluidorum proprietates, omniaque hydrostaticorum paradoxa facillimo negotio explicari possunt. Ex eodem etiam ratiocinio sponte sua se prodit causa […] duritiei, et cohaesionis, quae profecto nulla alia est, quam sublatum hocce aequilibrium, ita ut corpus, vel partes ipsius ex diametro premantur inaequaliter. Premuntur enim omnia, ut ex circulari omnium corporum motu iam demonstravi. Illa autem pressio vel est ex diametro aequalis, vel inaequalis. Si aequalis, quiescet quidem corpus illud […] sed minima tamen vi moveri potest. Sin vero inaequalis, movebitur […] nisi a parte, qua minus premitur maior sit resistentia, quam est ab altera vis pressionis, quo in casu quiescet non tantum, sed nec moveri poterit […] nisi a causa, quae pressionem, vel resistentiam illam superare potest,” Schuyl 1688a, chapter 1, 2–3 (unnumbered).
140.
“Quin imo cum haec demonstratio sit universalis, eaque proprietas, quod sc. unaquaeque ipsorum pars minima vi quaquaversum moveri queat, omnibus fluidis sit essentialis, sequitur omnium fluidorum partes, quaquaversum ex diametro premi aequaliter. Quod cum verum sit de quacunque fluidorum parte, partesque ipsorum singulae seorsim omnem effugiant sensum, in minutissimas partes fluida ut sint divisa oportet, hoc est, ut singulae separatim ab invicem, et diversis inter se agitentur motibus (nihil enim aliud per divisionem in materia intelligo) cumque nihilo moveatur a se ipso […] debent hae partes ab alia quadam materia fluida moveri per ipsarum intervalla fluenti, quae rursus ab alia, et alia, in infinitum usque,” Schuyl 1688a, chapter 1, 3 (unnumbered).
141.
“Or comme il y a toujours beaucoup de parties de cette matière invisible qui passe par les pores des corps durs, elles ne les rendent pas seulement durs comme nous venons d’expliquer, mais de plus elles sont causes qu’il y en a quelques-uns qui font ressort et se redressent, d’autres qui demeurent ployés, d’autres qui sont fluides et liquides; et enfin, elles sont cause non-seulement de la force que les parties des corps durs ont pour demeurer les unes auprès des autres. Mais aussi de celle que les parties des corps fluides ont de s’en séparer, c’est-à-dire que c’est elle qui rend quelques corps durs, et quelques autres fluides,” Malebranche 1842, 598. De Volder owned Malebranche’s Recherche in the Paris edition in 12° (1678–1679), whose third volume (in which book 6 is contained) appeared in 1679: see Bibliotheca Volderina, 51. On this ground, Malebranche rejected the validity of Descartes’s rules of collision involving bodies at rest: for a discussion, see Nadler 2000; Schmaltz 2015.
142.
“Postquam itaque satis, ut opinor, constiterit, cohaesionem durorum corporum nulli alii causae, quam compressioni alicuius corporis externi deberi, non multum porro illi determinando insudabimus, cum praeter aërem nullum detur, quod corpus durum immediate tangat et ambiat,” Bernoulli 1683, 51. As to air, Bernoulli draws his conclusion from the example of the cohering marbles, explained, according to him, as an effect of the pressure of the lateral columns of atmosphere – i.e. in an Archimedean manner, as in De Volder’s and in Boyle’s explanations: “[c]ui assertioni stabiliendae opportune incidit celebre illud experimentum de duobus marmoribus politis et laevigatis, quae sibi iuncta, ut nullus aër intermediare possit, quovis caemento tenacius cohaerescunt, adeo ut nisi maxima adhibita vi avelli a se mutuo nequeant. Quod phaenomenum, ubi per pressionem vel gravitatem atmosphaerae explicant scriptores hydrostaticorum, hoc volunt: cum duo marmora ita sibi iuncta in altum elevantur, vel ex alto suspenduntur, per hanc elevationem vel suspensionem fit, ut marmor inferius nullum amplius supra se pondus habens, quo deprimatur, a pondere lateralis aëris sursum impelli debeat contra superficiem inferiorem superioris marmoris, atque ita suspensum teneri, quamdiu una cum pondere annexo, si quod annexum fuerit, non praeponderat simili cylindro aërio […] a marmoribus ad ultimos atmosphaerae limites protenso,” Bernoulli 1683, 54–55. Against the idea that the mere pressure of air can explain cohesion, however, Bernoulli notes that very heavy bodies can be appended to chains or nails for years, even if they are much heavier than the column of air which would supposedly sustain them. Accordingly, he supposes that this is due to the action of subtle matter or aether, which being much higher than the columns of atmosphere, can exert enough pressure to keep bodies cohering: “[f]ateor, nos primo ne cogitando quidem assecuturos, quae unquam possit esse causa, quale caementum, qualeve gluten, quod has ingentis ponderis catenas a lapsu sustentet; cum absurdum sit, effectum hunc proficisci posse a tantillo pondere cylindri atmosphaerici toties minori. Sed quoniam ex superioribus clare quoque percepisse nobis persuademus, pertinacem hanc cohaesionem partium duri corporis nulli alii deberi causae, ne quieti quidem ipsi, praeterquam soli pressioni corporis alicuius externi, concludere non dubitamus, omnino necessum esse, ut suspensio et cohaesio partium baculi proficiscatur quidem a pondere corporis alicuius externi, sed a pondere longe maiori, quam est pondus solius atmosphaerae: unde in suspicionem hanc incidemus, non solum aërem crassiorem, sed aetherem ipsum, omnemque materiam subtiliorem, longe supra atmosphaerae limites diffusam, aliqua quoque gravitate praedita esse, quae iuncta cum gravitate atmosphaere effectum producat, quem haec sola producere nequibat,” Bernoulli 1683, 129–130.
143.
To this idea, Bernoulli opposes empirical arguments: for instance, he considers the case of a piece of wood, such as a rod, which can be broken by pushing it according to a line perpendicular to its centre, but it cannot be broken by pulling it from its two extremities: “[n]on parum etiam gestio audire rationem, ob quam lignum satis crassum applicato genu vel etiam sola manu […] facile dirumpi queat, conatu frangendi facto iuxta lineam […] perpendicularem longitudini baculi […] cum tamen tenuis bacillus, aut corpus adhuc fragilius nullis humanis viribus diffringi possit, ubi conatus adhibetur in directum […] tametsi enim obtendi posset, id fieri ob naturae a vacuo abhorrentiam, eo quod facta hoc ultimo casu separatione aër non posset eodem momento a lateribus bacilli ad eius medium irruere, non tamen ita respondebunt vacuistae, nec inter plenistas illi qui quietem cohaesionis causam statuunt,” Bernoulli 1683, 41.
144.
See the footnote in Bernoulli 1683, 57: “[c]um hanc dissertationem ad umbilicum fere perduxissem, incidi in Exc. Dn. Boylii Tractatum de historia firmitatis corporum, e quo perspexi, Nob. Authori iam olim suboluisse vim aëris in connectendus duobus corporibus sensibili mole constantibus […]. Tametsi vero non parvam inde lucem istis afferre potuissem, et nonnulla alio disponere ordine; consultius tamen iudicavi, nihil mediationibus meis addere, easque hic recensere, quo primum naturalissimo ordine sese menti meae obtulerunt.”
145.
See Sect. 5.6.3.3, De Volder’s assumption of Boyle’s law in the works of his students.
146.
“Cum bona pars huius dissertationis sub prelo prodiisset, ferebat occasio, ut inter confabulandum cum amico, varii praecipue de praesentibus, ut fit, studiis miscerentur sermones, interque alia mentio incideret causae firmitudinis corporum durorum, ubi monuit amicus, eam a Malebrancio compressioni aetheris ambientis ascribi. Ego illum per iocum haec dixisse, postquam in adversaria mea, vel impressa dissertationis folia forte casu quodam incidisset, suspicatus, sesquiannus est, regessi, ex quo auctoris istius Scrutinium veritatis (Recherche de la verité) fugitivo quidem, fateor, oculo perlustravi; sed non observavi, saltem non memini, illum circa cohaesionem partium duri corporis ultra Cartesii quietem penetrasse. Amicus vero asseverare dicta sua, et ne dubitem, commodare librum, ac monstrare locum, qui fidem dictis faceret. Quo sane perlecto mirabar, non tam quod dictus auctor in cohaesione partium duri corporis iam ante me pressionem aetheris repererit, sed praecipue quod in cognitionem huius veritatis eodem filo Ariadnaeo deductus, eique comprobandae iisdem rationibus, iisdemque adeo exemplis mecum usus sit; uti e Scrutinii veritatis et Dissertationis nostrae collatione patere poterit,” Bernoulli 1683, Monitum, 1–2 (unnumbered).
147.
“M. Bernouli qui a tâché de rendre raison de la cohésion des particules de tous les corps, par la pression de l’Ether, a omis deux choses de grande importance. 1. Il n’a point consideré que quelque grande que puisse être la pression d’un ambiant fluide, s’il n’ya autre chose pour tenir jointes les particules des corps, encore qu’on ne les puisse pas éloigner l’une de l’autre perpendiculairement, néanmoins on peut démontrer qu’on peut pousser l’une de dessus l’autre, aussi aisément que s’il n’y avoit point de semblable pression. L’experience de deux marbres polis posez l’un sur l’autre, que la pression de l’Atmosphere tient en cet état, fait voir à l’eouil ce que je veux dire, puis qu’on les peut séparer fort aisément, en les poussant de côté, au lieu qu’ils ne le peuvent être perpendiculairement. 2. Il n’a aucun égard aux particules de l’Ether, qui étant aussi bien des corps formez d’autres particules, doivent avoir quelque chose qui les tienne uniës, ce qui ne peut pas venir d’elles mêmes; car il est aussi difficile de concevoir comment les parties du moindre Atome de matiere demeurent uniës les unes aux autres, que celles des plus grosses masses,” Locke 1688b, 76–77. Notably, experiments with marbles disposed vertically and horizontally were performed and described by Senguerd in chapter 19 his Rationis atque experientiae connubium (1715), where he noted that they can sustain the same weight in both cases (see Sect. 4.1.3, De Volder’s ideas on cohesion and divisibility) and criticized the idea of an infinite regress entailed by the recourse to the pressure of subtle matter as a factor of cohesion. Rather, he claimed that circular thrust of corpuscles can account for the cohesion of discrete bodies such as the cylinders of marbles: “[n]eque iuvat pressione aëris ac materiae caelestis et aetherea combinare: quia hoc posito pressionis progressus in infinitum admittendus foret. Etiam, si immensa aetheris, cohaesionem procurantis, pressio supponeretur, nullius corporis soliditas exaequaret potentiam huius pressionis. Porro, cum subtilissimi corporum pori caelestis materiae transfluxum sistere nequeant, quantum particulae solidum constituentes earum pressione introrsus et versus invicem adigerentur, indeque consolidantur, aequali impetu a particulis transfluentibus dissociarentur, ac soliditatis fieret eversio. Ne etiam quaeram unde extremorum corpusculorum, ut et ipsarum caelestium particularum soliditatis ratio petenda foret, quave sit premendi vis, qua et ipsae ex subtilioribus particulis coaluere. Rectius iudico, ut quorumvis corpusculorum, et particularum […] non cohaerentium concretio, mutua agglutinatio, et in unum corpus solidum, aut durum conversio, fluidorumque in summe dura transmutatio, unice exoritur ex earundem approximatione, superficierum adsimilatione, congruentia, et immediata contiguitate. Cuius causa aliorum corpusculorum, in locum illorum quae separanda veniunt, successio, ac circularis propulsio, in quavis corporum translatione requisita, difficilior redditur, vel etiam impeditur,” Senguerd 1715, 174–175. In his Philosophia naturalis, Senguerd explained the cohesion of cylinders by the circumpulsion of air, and explained the different degrees of cohesion of cylinders of different materials as a consequence of their porosity: see Senguerd 1681, 45–46; discussed in Sect. 5.6.3.2, The background of De Volder’s theories.
148.
Le Clerc’s Bibliotheque is present in the Bibliotheca Volderina, 93.
149.
On 29 February 1696, moreover, Casembroot was the defender (but not the author), of the Exercitium experimentale decimum de aëris fluiditate, part of 17 disputations presided by Senguerd between 1687 and 1698. As reconstructed by Wiesenfeldt, some of these Exercitia would be the basis of Senguerd’s Inquisitiones experimentales (second edition, 1699): see Wiesenfeldt 2002, 162. Please note that Senguerd rejected, in his Philosophia naturalis, the Copernican system (preferring to it the Tychonic one) so that Casembroot cannot be labelled as defending Senguerd’s ideas in his 1694 and 1696 disputations. Moreover, both the disputations are dedicated to De Volder.
150.
“Ut autem haec phaenomena exponamus, supponimus mundi systema ex innumeris constare vorticibus, atque in his unum esse, cuius Sol centrum est, circa quod omnes planetae, ipsaque Terra, et cum Tellure Luna circumvolvitur, uti Cartesius demonstrat in suis Philosophiae principiis, et ego quoque pro virili […] etiam clare in nostra De mundi systemate dissertatione ostendi,” Casembroot 1696, thesis 9.
151.
“Systema mundi, quod a Nobilissimo Cartesio delineatur non pro mera hypothesi, sed pro ipsa rei veritate est habendum,” Casembroot 1696, Annexa physica, annexum 6. Cf. Sect. 3.2.3.3, The role of experience in De Volder’s natural philosophy.
152.
“Nobilissimus non modo natalium splendore, sed et eruditionis fama Renatus Descartes Lunae in aquas subiacentes pressionem aestus et recessus marini causam iudicavit, sed ita tamen, ut eas difficultates, quas modo attulimus, plane sustulerit. Incredibili enim mentis sagacitate veras causas indagavit, ex quibus omnia fluxus refluxusque phaenomena explicari possunt. Certe non potui non, caeteris reiectis opinionibus huic uni assensum praebere: quapropter incomparabilis philosophi vestigiis insistens, hanc aestus marini causam explanare et quantum potero, ab omni difficultate liberare conabor,” Casembroot 1696, thesis 7.
153.
“Hisce ita positis, notandum est 1. Lunam in vortice Terrae circa ipsam singulis mensibus deferri, atque ipsum vorticem, qui Terram Lunamque continet, annuo spatio a vortice solari circum Solem abripi. 2. Tellurem in medio sui vorticis haerere, ubi aequalis ab omni parte existit pressio. Agedum, concipe ita libere in vorticis sui centro haerere Terram, et per eiusdem vorticis extremitates vagari Lunam. Quid fiet? Evidentissimum est, spatium vorticis, quod inter Lunam et Terram est, coarctari, et materiam caelestem velocius per angustiam inter illa duo corpora interceptam fluere, motusque celeritate spatii angustiam compensare; quum id in omni naturali motu constat, ut via coarctata, fluida corpora celerius fluant, et impetu sic satis valido in latera impingant. Ex quo rursus clare intelligitur, Terram, quae tantum in aethere ob aequalem materiae ambientis pressionem subsistit, hoc impulsu cessuram versus oppositum vorticis latus donec via ab utraque parte aeque angusta evadat, et aequalis reddatur pressio: quum igitur in duabus et quidem oppositis Telluris partibus tanta pressio sit, necessum est, ut aër et aqua, quae corpora fluida sunt, et pressioni faciliae [sic] cedunt, huic etiam pressioni cedant, et subsidant in ea, cui Luna imminet, et huic opposita Terrae parte, atque e contrario versus latera extollantur,” Casembroot 1696, thesis 10.
154.
“Hunc quidem vorticem ellipticam habere figuram Keplerus supposuit, sed Newton eleganter demonstrat,” Casembroot 1696, thesis 12. Wiesenfeldt labels this as the earliest evidence of the teaching of Newton’s ideas at Leiden: “[…] [d]amit stellt diese Disputation den frühesten Nachweis einer inhaltlichen Auseinandersetzung mit den Arbeiten Newtons im Rahmen philosophischer Lehrveranstaltungen in Leiden dar,” Wiesenfeldt 2002, 182–183.
155.
“[…] nec adeo obscura huius rei ratio est, quippe quo propriores sunt Soli coelestes globuli, eo minores; et quo remotiores eo maiores existunt: nam secundum leges circularis motus magis a centro recedet ea materia quae plus habet virium, et ad centrum confluet ea, quae minus habet. Quum autem omnes lunaris vorticis globuli in orbem vertantur, laterales, ubi ad superiores pervenerunt, versabuntur inter globulos paulo maiores, et habentes plus virium ad recedendum a centro: ubi vero tetigerunt inferiores, versabuntur inter globulos minores, et consequenter minori vi pollentes: unde necessarium est ut lunaris vortex non circuli perfecti, sed ellipseos figuram induat. Quae cum ita sint, manifestum est, quamvis Luna sui mole spatium aequale tam in maiori, quam in minori diametro occupet, spatium tamen in minori diametro, ubi Luna plenilunii tempore versatur, magis coarctari, (ubi enim a minori quantitate idem decrementum tollitur, quod a maiori, differentia: ratio in minori maior, quam in maiori erit) ac per consequens materiam caelestem per illas angustias transeuntem maiori celeritate maiores aestus efficere,” Casembroot 1696, thesis 12. Cf. Descartes’s Principia, III.153: “[s]ince the heavenly globules in the space ABCD differ in size and motion from those which are below D near K and from those above B near L, but are similar to those near N and Z; they spread more freely toward A and C than toward B and D. From this it follows that the orbit ABCD is not a perfect circle, but closer to the figure of an ellipse,” Descartes 1982, 175. On the composition of the planetary vortex, see Principia III.151: “both [i.e. Earth and Moon] are transported by the same heavenly matter, which probably moves at least as rapidly in the vicinity of the Earth as in that of the Moon,” Descartes 1982, 174.
156.
See Sect. 6.2.2.1, Newton’s critique of Descartes’s vortex theory. We have seen above that Tinelis de Castelet criticized Descartes’s idea that anomalies in tides occur when the Moon is closer to the Earth, namely when it is in the perigee, for the reason that such tides are independent from the distance between the Earth and the Moon, as the perigee (i.e. the closest distance between the Moon and the Earth can occur also when the Moon is at the quadratures – i.e. when it is not on the same line with the Earth and the Sun, and thus the tides are weaker). This kind of objection is taken into account in Casembroot’s De aestu marino: the answer to the objection is that Moon can be equally far from the Earth both at the syzygies and at the quadratures: yet, from this it does not follow that when it is at the syzygies, it is not in the part of the diameter of the vortex closer to Earth: “[o]bi. Supponitur Lunae apogaeum in quadraturis, perigaeum in coniunctione et oppositione; sequitur ergo, Lunam, quando in coniunctione et oppositione est, versari in minori vorticis diametro, et in maiori, ubi Luna in quadraturis haeret: sed constat ex diligentissimis astronomorum observationibus, Lunam in oppositione et coniunctione saepe tantum a Terra distare, quantum ab ea nonnunquam distat in quadraturis: unde aperte colligitur, in oppositione et coniunctione eandem fore Lunae pressionem, quae est in quadratis Lunae aspectibus. R. Me lubenter dare, Lunam quandoque in coniunctione et oppositione aeque remotam, quam in quadraturis, imo interdum remotiorem esse. Sed nego et pernego, hinc sequi, Lunam eo tempore non esse in minori vorticis diametro: nam quamvis sit Luna in apogaeo tamen in minori sui vorticis diametro quandoque haerebit, ut etiam potest esse in maiori diametro, licet sit in perigaeo: quo in casu eadem quoque pressio in aquis erit, quia, ut hanc Luna efficiat, non opus est, ut ipsa in sui vorticis extremitate versetur, sed tantum in minori diametro, in qua ubi existit, habita proportione, plus de ea sua mole tollit, quam si in maiori versaretur, et consequenter spatium illud, per quod materia subtilis celerius fluit, perangustum reddit,” Casembroot 1696, thesis 16.
157.
In the Annexa, also, we do find a reference to Huygens’s Systema Saturnium (1659): “Solum Systema Hugenianum mirandis Saturni phaenomenis satisfacit,” Casembroot 1696, Annexa astronomica, annexum 2. A reference to Huygens’s Systema Saturnium is given also in De Volder’s dictata, commenting upon Principia III.146: cf. Hamburg 273, 212.
158.
See supra, n. 97.
159.
On Tachard, see Vongsuravatana 1992. See supra, n. 159.
160.
“En alhoewel dese fauten wel haest door het gebruijck der horologien sullen konnen verbetert werden, soo waer het nochtans seer dienstigh dat men van eenighe voornaeme plaetsen de rechte Lengde ten respect van de Meridiaen van Texel of Amsterdam ondersocht, door observatie aen de omloopers van Jupiter, waer van hier te voren mentie gemaeckt is. Sijnde dese manier van Lengdevindingh van vaste plaetsen onfeilbaer, besonder als men een Eclipsis, of wederverschijningh van de binnenste omlooper, op een selfde tijdt, komt te observeren op beyde de plaetsen daer van de Lengde tusschen beijde gesocht werdt; en daer nae de uren deser observatien met malkander compareert,” Huygens to the Directors of the VOC (letter 2519), 24 April 1688, in Huygens 1888–1950, volume 9, 290.
161.
“[…] de Lengde van de Caep ten respect van Parijs was effen van 18 graden ten Oosten dewijl nu Texel 3 graden 35 minuten oostelijcker leght als Parijs, gelijck bij Riccioli in sijn Geographie pag. 378 door neerstigh ondersoeck der observatien van Eclipsen werdt bethoont soo komt de Caep oostelijcker als Texel 14 graden 25 minuten,” Huygens to the Directors of the VOC (letter 2519), 24 April 1688, in Huygens 1888–1950, volume 9, 274.
162.
Riccioli 1661, 378.
163.
See Riccioli 1661, 423. As signalled by Schliesser and Smith, in his workbook Huygens overtly followed such longitudes in his calculation: see Schliesser and Smith 2000, 34 (n. 77), referring to ms. HUG 1, f. 163 (Leiden University Library).
164.
“[…] is nootsaaekelijck dat men weete het waare verschil der lenghte tusschen de Caap en texel, waertoe seer wel te pas komt, dat door de observatien van de Eclipsen der omloopers van jupiter gevonden is het verschil der lenghte tusschen de Caep en Parijs van 18 graden soodat maer rest te weten het verschil tusschen Parijs en Texel. Uijt de Eclipsen van de maan, die Riccioli op de plaets bij den Hr. Huijgens geciteert, aenhaelt vint men omtrent het verschil tusschen Parijs en Amsterdam van 3 gr. 52 minuten, en dien volgens het verschil tussen de Caep en Amsterdam, 14 graden 8 min. Waerbij soo men nu doet 17 min. Die texel na sommige caarten omtrent westelijcker leyt als Amsterdam, sal men het onderscheyt tusschen Texel en de Caep vinden op 14 gr. 25 minuten gelijck het de Hr. Huijgens stelt,” De Volder to the Directors of the VOC (letter 2547), 22 July 1689, in Huygens 1888–1950, volume 9, 341.
165.
See, for instance, Riccioli 1667, 378, 380, 403 and 419.
166.
Only one letter (from Albert Jansz. van Dam to De Volder) has survived, dated 8 November 1677. In his letter, Van Dam asks De Volder a solution to the criticisms raised by Henry More to Descartes’s cosmology: “[…] ik omtrent de beginselen der wysbegeerte heb doet dit zoo daanig verminderen dat ik my eyndeling verstoute om met alle beleeftheyd UE dezelve zwarigheden voor te stellen dewelke Hendrik Morus eertyds den zeer doorlugtigen Heer en voortreffelykste wysbegeerige Renatus des Cartes voorgesteld heeft, te weeten; hoe ’t komt dat alle de Dwaalsterren niet in een zelfde plat omgevoert worden, te weten, in ’t plat van ’t Taanront, gelyk ook de Zonne vlakken, of ten minsten in platten die gelykwydig met het Taanront zyn, ja de Maan selfs of in de Evenaar of in een plat dat met de Evenaar gelykwydig is, dewyl zy van geen inwendige kragt bestiert, maar alleenlyk van een inwendige drift gedreven worden. Dit zelve heb ik voor dezen andere wel meer voorgestelt, maar heb nooyt geen oplossinge konne bekomen, en alzo ik tot dezelve zeer begeerig ben, en geen ander reden hebbe konnen bedenken, om daar aan te geraaken, ten zy ik myn toevlugt t’ u waarts wende, vriendelyk aan UE verzoekende, my hier op een toeverlatig antwoord te wille laaten toekomen,” Rijks 2012, 249. No answer by De Volder is extant.
167.
Huygens included a map of his own in his report, which was based, for the European part, on Van Nierop’s Wassende graade paskaart, vertonende alle de zeekusten van Europa, de geheele Middelandsche Zee, als oock ten Noordwesten, en Noordoosten (circa 1660), corrected, in its African part in order for it to fit with the distance between Texel and Cape calculated by De Volder: it is discussed in Schliesser and Smith 2000, appendix 1; see also Schliesser 1997 and Schliesser 2000. The map can be found, at high resolution, on the website of the University of Amsterdam: hdl.handle.net/11245/3.1326 (accessed 3 December 2018). De Volder owned Van Nierop’s Nederduytsche astronomia (1653), Des Aertrycks beweging en de Sonne stilstant (1661), Eenige oefeningen in Godlijcke, wiskonstige en natuerlijcke dingen (1669): see Bibliotheca Volderina, 24–25. According to the Bibliotheca Volderina, De Volder owned the apt instruments to measure the longitudes on maps: namely, a “[d]oekmeter om een platte Globus of Landkaart te meten,” Bibliotheca Volderina, 95.
168.
Mentioned in a letter to De Volder of 6 April 1693 concerning the second expedition with Huygens’s clocks: see infra, n. 187. De Volder owned certain “Groote Geographise Caarten van Holland en Zeelend door Nic. Visscher,” Bibliotheca Volderina, 65
169.
The map can be found, at high resolution, on the website of the Vrije Universiteit van Amsterdam: http://imagebase.ubvu.vu.nl/getobj.php?ppn=330047426 (accessed 3 December 2018).
170.
Bibliotheca Volderina, 65; De Volder also owned De Wit’s Nieuw Kaertboeck van de XVII Nederlandse Provinciën (circa 1667): see Bibliotheca Volderina, 65.
171.
The map can be found, at high resolution, on the website of the national Spanish Ministerio de Educación, Cultura y Deporte: http://bvpb.mcu.es/es/consulta/registro.cmd?id=477833 (accessed 3 December 2018). In any case, De Volder was right in placing Texel west to Amsterdam, as the actual longitude of Den Burg (the main town of Texel) is 4° 48′ 31.205″ east, Oudeschild (the VOC’s port, in the eastern part of the island) is 4° 50′ 59″, and Amsterdam is 4° 53′ 42.605″.
172.
“T’welck evenwel mijns aghtens soo seecker niet gaet of soude wel eenige minuten en mischien wel meerder konnen verschillen soo ten respecten dat alle de observateurs niet een ende selfde precies heijt hebben gebruijckt om de nette tijt van de Eclipsis van de maan vast te stellen als ten respecten van het onderscheyt der lenghte, tgeen men uyt diverse observatien der Eclipsen bevint. Riccioli stelt het onderscheijt tussen Parijs en Amsterdam op 4 gr. andere als de la Hire, op 2 gr. en 32 a 33 min. Soo dat het om seecker te gaen wel te wenschen was, dat men dit onderscheyt van lenghte door de observatien van de omlopers van jupiter nauwkeurigh geobserveert hadt,” De Volder to the Directors of the VOC (letter 2547), 22 July 1689, in Huygens 1888–1950, volume 9, 341. This follows the previous quotation (see supra, n. 164).
173.
La Hire 1687, 4.
174.
See Sect. 6.2.2.2, Huygens’s criticisms of universal gravitation – and the voyage of the Alcmaer; or, in the first version of the report, 0° 25′ (see supra, n. 97). Schliesser and Smith have pointed out how Huygens did not challenge De Volder’s result, and that in his report to the VOC he complained about the reliability of the maps at his disposal (see Huygens 1888–1950, volume 9, 287).
175.
Schliesser and Smith 2000, 35.
176.
“Twelck alles, hoewel seer goede hoop geeft van succes om door middel van Horologien soodanigh gecorrigeert de waere lenghtens te bekomen; soo soude ick evenwel twijffelen of men uijt het succes van dese eenige reijs soude mogen absolut concluderen, dat er geen andere oorsaeken in de natuur gevonden worden, die het effect van ’t drayen der aarde in de swaarte der lichamen op welck dese correctie der Horologies steunt soude konnen of beletten of veranderen, als oock of niet het langhsamer gaen onder de linie, als onder noorderlijcker of zuijderlijcker plaetsen van eenige andere oorsaecken soude mogen dependeren, en of misschien onder andere hier toe niet wel iets soude konnen contribueren de veranderingh der hitte door dewelcke veele oock harde lichamen uijt geset, en langer gemaeckt worden. Twelk omtrent het pendulum onder de linie gebeurende door de hitte aldaer nootsaekelijck een langsamer dogh irregulier langsamer gangh der Horologien soude maeken. Maer wat van dese ofte andere oorsaeken ons misschien nu nogh onbekent soude konnen sijn, en of die eenige ingressie in dese saek soude konnen hebben is niet als door de ervarentheijt te determineren, sullende een tweede proef, die uwelEd. met de scheepen die tegen September naer jndia staen te gaen van meeningh sijn te nemen, hier van meerder elucidatie en seeckerheyt konnen geven,” De Volder to the Directors of the VOC (letter 2547), 22 July 1689, in Huygens 1888–1950, volume 9, 343.
177.
Huygens briefly discusses De Volder’s first report – which he received on 9 September 1689 (see the letter of Huygens to the Directors of the VOC of 9 September 1689 (letter 2546), in Huygens 1888–1950, volume 9, 338.) – in a letter to the Directors of 10 May 1690, in which the performing of a second trial is treated: “[s]edert U WelEd. mij in Sept. des voorleden jaers de Horologien tot de Lengdevindingh gedestineert, beneffens het oordeel van de Hr. Prof. de Volder daer ontrent hebben gelieven te laeten toekomen en met eenen te kennen gegeven VWelEd. intentie van een naeder Preuve deser Inventie te nemen, soo hebbe het gheene noodigh was aen deselve doen repareren, oock met eenen iets tot verbetering daer aen doen veranderen, ende voorts door gedurighe observatie haer gangh geexamineert, om te sien hoe nae deselve over een konde brengen, waer in niet sonder effect gearbeijt hebbende soo twijffele oock niet of men sal sich op de reys noch beter daerop konnen vertrouwen als voor desen,” Huygens to the Directors of the VOC, 10 May 1690 (letter 2588), in Huygens 1888–1950, volume 9, 418. In a letter to his brother Constantijn of 9 September 1689, Christiaan Huygens’s reported De Volder’s favourable opinion: “[i]l semble que sur l’avis du Professeur de Volder, a qui ils ont donnè a examiner le rapport que je leur avois fait du premier essay, ils ont conceu bonne opinion de cette affaire,” Christiaan to Constantijn Huygens, 9 September 1689 (letter 2545), in Huygens 1888–1950, volume 9, 337.
178.
On the whole trial, see again Schliesser and Smith 2000.
179.
Namely, Huygens’s Verklaeringh en aenmerckingen op het Journael van Jo. de Graef en ’t geen ontrent de Horologien is voorgevallen in de laetste proeve der Lengdevindingh Ao 1690, 1691 en 1692, in Huygens 1888–1950, volume 18, 643–651.
180.
Huygens owned Visscher’s map, and attached it to his letter to De Volder of 24 March 1693 (letter 2798): see Huygens 1888–1950, volume 10, 433–434. See also Schliesser 2000.
181.
“Het gheen de Heer van de Blocquerij mij heeft gelieven te doen weten bij sijn […] schrijvens van den 16 Novembr. des voorleden jaers, aengaende het weynigh succes van mijne Horologien in de laetste proeve naer de Caep de B. Esp.^ce laet mij niet toe te twijffelen of UEd. G. achb. Sullen seer gepersuadeert sijn van de onvolmaecktheydt deser Lenghdevindingh en niet sonder reden, dewijl de Persoon selfs die het bewint daer van gehadt heeft van die opinie is. […] Doch siende evenwel dat het noodigh was soo tot UEd. Gr. Achtb.^re als mijn eyghen satisfactie, soo hebbe nae het mondelingh raport gehoort te hebben van Mr. de Graef, voorts sijn Journael, op den 19 Nov. mij toegesonden, met aendacht geexamineert. ’T welck beyde mij geheel andere gedachten ontrent het succes deser proeve gegeven heeft. Alsoo bevonden hebbe dat daer het effect der horologien bij onvermijdelijcke toevallen os misverstandt niet en is beter geworden, of door misrekeningh verkeert verstaen, sij seer wel en precijs de Lengdemetingh hebben volbracht: Te weten op de uyt reyse van het Eylandt S.^t Jago af tot aen de Caep de B. Esp.^ce daer d horologien alleen hebben konnen dienen: accorderende perfect met de nieuwste Caerten en Globen die de Lengde tusschen dese twee plaetsen stellen van ontrent 48 graden,” Huygens to the Directors of the VOC, 6 Marc 1693 (letter 2795), in Huygens 1888–1950, volume 10, 423–424. Huygens refers to letters 2773 and 2774.
182.
“Alle deze noodsaeckelijcke verbeteringen in de Tafel van ’t Journael gemaeckt en bewesen hebbende, soo siet men dat de Lenghde tusschen ’t Eyland S. Jago en de Caep de B. Espe. door de horologien is gevonden van 48 gr. 14 min. 3,” Huygens 1888–1950, volume 18, 646.
183.
“Ick send UE hier neffens weder het Journael van M. de Graef met mijne aenmerkingen ende gepointeert de Caert van Africa nae dat ick volgens UE goede advisen verbetert hebbe ’t geen ik bij abuis anders gestelt hadde als mijn eygen raisonnement mede bracht,” Huygens to De Volder, 24 March 1693 (letter 2798), in Huygens 1888–1950, volume 10, 433. In the letter, Huygens explains to De Volder his own corrections.
184.
“[…] ick voor vast houde, dat het schip, ontrent dese daghen van den 23 en 23^en Apr. door de vloedt uijt den Oosten seer verre vervoert is geweest. Ick weet wel dat volgens dese gestipte Cours de Lengde tusschen St. Jago en de Caep ontrent 2 ½ gr. meerder soude komen als de 48 gr. die ick te vooren, met de caert accorderende, bevonden hebbe, en ick beken dat het horologie voor soo veel kan gemanqueert hebben, maer het kan oock de faut van de Caert sijn, daer men niet vast op gaen kan, soo langh men door onfeilbare observatien, gelijck die aan de omloopers van Jupiter de voorsz. Lengde niet perfect heeft gedetermineert,” Huygens to De Volder, 24 March 1693 (letter 2798), in Huygens 1888–1950, volume 10, 434.
185.
Huygens, following Riccioli, assumed La Palma as meridian 0; De Volder assumes El Hierro. Riccioli located El Hierro 44 minutes east to La Palma: Riccioli 1661, 322.
186.
“En om dat volgens de Caert van N. Visscher hier nevensgaende St. Jago 7 graden westelijcker leght als de Pico de Teneriffe, daer het begin der Lengden gestelt werdt, soo komt de lengde van de Caep 41 gr. 14 min. t welck seer net met de voorsz. Caert over een komt,” Huygens 1888–1950, volume 18, 646. Cf. supra, n. 182.
187.
“Ick hebbe UEdts aangename van den 24^ste maart nevens de bijlagen wel ontfangen, maar door indispositie niet konnen examineren als heden, en gisteren. Nu de saack insiende, weet ick bijna niet wat conclusie te formeren. Want onseecker sijnde hoe groot de dagelyxse vertragingh van ’t Horologie is geweest op St. Jago, en wel sodanigh onseecker, dat het een verschil van 2 ½ of oock wel meer graden op dese wijs soude komen te importeren, hoe kan men met eenige seeckerheijd van de rest concluderen? T’is wel waarschijnelyck, gelijck UEdt it aanmerckt, dat in de observatie van den 1^ste April een misslagh is begaan, en misschien is ’t oock wel soodanigh een, als UEdt. bybrengt, maar dit schijnen mij ten minsten altijdt het laatste, alleen gissingen. Tis oock waar, dat de lengde van de Caap, die de caart aanwijst soo vast niet is, dat men dese 2 ½ graden verschil, seeckerlyk tot een fout aan de Horologien soude konnen toeschrijven; maar aan de andere kant is ’t oock waar, dat de caart soo wel kan missen met de Caap oostelijcker te leggen, als Westelijcker alst behoort. Twelck soo waar mocht sijn, en dat de Caap inderdaat minder ten oosten van St. Jago verscheelde, als de caart van Visser medebrengt sou dit de fout der Horologien noch grooter maacken. Waarbij komt, dat de observatie van de Franse Jesuiten gaande naar Siam, die misschien de seeckerste is, die wij omtrent des Caaps lengde hebben, den Horologien gansch niet schijnt te favoriseren. Want die determineren de lengde van de Caap naar de meridiaan gaande door l’isle de fer op 40 ½ gr. dat is, naar de meridiaan van onse caarten gaande door Tenariffe, wat meer als 38 gr. waarmede de caarten van de Compagnie schijnen overeen te komen. So dat na dese observatien het Horologie een verschil van lengde tusschen St. Jago en de Caap soude hebben aangewesen, ’tgeen van het waare over de 5 gr. soude verschillen, ten minsten altydt incas dat St. Jago, te recht 7 gr. westelijcker gestelt wert als de meridiaan van Tenariffe. Uyt welck alles ick dan niet anders sie te concluderen, als dat dese proeve ten besten genomen de saacke laat genoechsaam in deselfde staat als voorheen, als hebbende de observateur door de daaghelyxse vertragingh vant Horologie niet accuraat genoech geobserveert te hebben, ons buijten postuur gestelt, om met eenige seeckerheijt vant qualyck of wel uijtvallen der Horologien, uijt dese proeve te konnen oordelen,” De Volder to Huygens, 6 April 1693 (letter 2800), in Huygens 1888–1950, volume 10, 436–437.
188.
“Ick bedanck UE. nochmaels van UE gedaene Correctie in mijn Rekening, en UE verderene aenmerckingen die in dat tegenwoordigh Examen der genomene Proeve van Lengdemetingh seer considerabel sijn. Evenwel soo blijft dit seecker dat volgens de Observatien van M. de Graat (sijn misrekeningen verbetert sijnde, en mijne Instructie simpelijck naegekomen) de Lengde tusschen S. Jago en de Caep de B. Esp.^e van seer nae 48 gr. door het horologie is afgemeten, en dat dit met de Caerten van Visscher en Blaeuw seer wel overeenkomt Mijn abuijs in ’t pointeren van eenighe Lenghdens van ’t schip en beletten niet, gelijck UE weet, dat die conclusie waer zij, alhoewel dit abuijs bij mij geredresseert sijnde in de nevens gaende Caert, de cours nu veel naeder aen de Cust van Brasilien komt te vallen dan ick gemeent hadde. […] Dat men nu hier uijt soude konnen besluyten de perfectie deser Lengde metingh genoegsaem gedemonstreert te sijn, of naerder als door de voorgaende proef van A^o. 1687 wil ick niet pretenderen want niet alleen UE remarque ontrent de veranderlycke daghelycksche verachtering van thorologie van S. Jago waergenomen, en laet sulx niet toe, maer oock de onsekerheijdt der stellinge van Lengden in de Caerten soude sulk besluyt twijffelachtigh maecken al hadde het horologie noch soo wel gegaen. en sal altydt soo doen behalven als men gelegentheijdt heeft om de Lengde van 2 selfde plaetsen, op de heen en weerreys te meten, of dat het Lengde-verschil door seeckere observatie aen de omloopers van Jupiter geobserveert zij,” Huygens to De Volder, 19 April 1693 (letter 2803), in Huygens 1888–1950, volume 10, 443–444.
189.
He was the author of a Circuli quadraturae nodum per helicem enodatum (Utrecht, 1698).
190.
Preserved, like a copy of his referral on Huygens’s first report, among the papers of Hudde (The Hague. Algemeen Rijksarchief, signature: 1.10.48 no. 44). It is given as appendix in Mac Lean 1971.
191.
See Howse 1989.
192.
“Hier in bestaat, mijns oordeels, het voorgeven van Monsr Pottier, omtrent het welke te considereren valt, dat in al de manieren, die men ooyt of ooyt heeft bijgebracht om door waarneminge van de maan de lenghtens te vinden, sigh twee swarigheden hebben opgedaan, die die manieren ’t onbruyck hebben gemaakt; de eerste is, dat de maansloop so volmaakt niet bekent is, als tot de lenghtevindingh van noden is. De tweede, dat als dese loop selfs al ten accuraatste bekent was, dat men evenwel te scheep so net en seeker niet kan observeren, of men sal eenige minuten komen te seylen en daardoor bij gevolgh groote fijl in de lenghtevindingh begaan,” Mac Lean 1971, 159.
193.
“[…] ik wel gewenscht had, dien Hr eerst te hebben hooren spreeken, eer ik mijn oordeel over sijn saak gaf, soo om hem te beneemen ist niet alle klachten (’t welck door de liefde die de Inventeurs ordinary tot haar concepten hebben genoegsaam onmogelijk schijnt, als men de inventie niet komt te approberen;) ten minsten altijt die, van niet gehoort te sijn, als ook om hier door voor te komen alle verdere aanloop, die hij misschien sal willen doen, als hij daar naar sal komen te vernemen, dat sijn Inventie door mij mede niet goedgekeurt is,” Mac Lean 1971, 157.
194.
In Serrurier’s disputation the problem of the cause of weight is just not mentioned. In turn, Westhovius’s De fluminibus concerns the various conditions of depth, breadth, and direction of water in a river. Amongst the natural-philosophical premises of the demonstrations of 13 propositions on the topic, it is stated that bodies heavier than water sink, and lighter ones float; the cause of their weight, however, is assumed as “already demonstrated.” In fact, as noted by the author, this topic exceeds the scope of the disputation: “[n]otiones communes. I. Notum cuilibet est, aquam habere gravitatem, qua ad Terrae centrum prolabi conatur. II. Eandem porro graviorem his, leviorem aliis corporibus esse, item graviora in aqua subsidere, leviora vero ei innatare. Supervacaneum prorsus foret, et a scopo nostro alienum, si causam gravitatis corporum hic demonstrare susciperemus: nobis illam diu demonstratam supponere sufficiat,” De Volder and Westhovius 1698, 5. Westhovius was also the respondens of one of Senguerd’s Exercitia, namely the Exercitium experimentale quintum decimum, quod est de aëris gravitate, secundum (1698). He would later become professor of eloquence at the Latin School of Gorinchem. No evidences on his graduation at Leiden could be found.
195.
“Si omnia circa Terram spatia vacua essent, id est quae aliorum corporum motum ne iuvarent, nec impedirent, illud ipsum fore; iam vero omnes Telluris partes a coelesti materia undique comprimi, impedirique, ne dissolvantur: cum enim globuli coelestes per lineas rectas, vel parum a rectis devias a Terra recedant, ac proinde efficiunt, ut aequali vi omnes eius partes ad centrum protrudantur, impediunt, ne versus coelos desiliant,” De Volder and Casembroot 1694, thesis 12.
196.
See De Volder and Bashuysen 1698, thesis 2 (providing a Cartesian definition of motion), thesis 9 (defending Descartes’s theory of tides), thesis 15 (endorsing Descartes’s theory solar spots). Besides Descartes, the author reports the astronomical observations of Galileo and Huygens (viz. on the phases of Venus and on the rings of Saturn: see theses 9 and 15–16).
197.
The very short preface reports no name, however, in his Éloge Le Clerc reveals that De Volder took care of the last phase of the publication, and wrote the preface itself (Le Clerc 1709, 389). The editors of Huygens’s Oeuvres, however, do not mention De Volder in their reconstruction of the genesis of this work: see Huygens 1888–1950, volume 21, 655–657.
198.
On the Cosmotheoros, see Ait-Touati 2011, chapter 4; Van der Schoot 2014. Notably, in the preface De Volder notes that the work does not contain mathematical demonstrations, being however based on conjectures grounded on reason: “[d]emonstrationes equidem mathematicas non invenient ubique, neque enim res patitur, sed, quo in his rebus nihil ultra desiderari iure posse videtur, verisimiles et ingeniosas coniecturas. Quae ex coelorum notitia depromi potuerunt, ea hic videbunt ratione demonstrata; quae ex iis non patent, ex coelestium corporum cum Tellure nostra affinitate solerter coniecta,” Huygens 1698a, Lectori, 2 (unnumbered). On Huygens’s use of conjectures, see Elzinga 1971. De Volder, as seen above, was already warned by Huygens that clarity and distinctness could not be deemed as absolute signs of truth: see Sect. 3.2.1, De Volder on clarity and distinctness.
199.
Huygens 1698b, 157.
200.
For Descartes (Principia, III.61), the Sun is spherical because the matter of the vortex strives to recede from it: yet, in his argument – and in his illustration of it (see Fig. 6.19, Descartes 1644a, 102) – Descartes assumes that the particles of the vortex describe circular paths: “from the fact that all the globules which rotate around S in the vortex AEI attempt to move away from the center S, as has already been shown, we can conclude that those situated on the straight line SA all push one another toward A, and that those situated on the straight line SE push one another toward E. and so on; so that if there are not enough of them to occupy all the space between S and the circumference AEI, all the unoccupied space will be in the vicinity of S. And inasmuch as those which rest upon one another (for example, those which are situated on the straight line SE) do not rotate in a body, like a rod, but complete their revolutions in varying lengths of time (as I shall explain later); the space which they leave around S must be spherical,” Descartes 1982, 115.
201.
“I am of opinion then that every Sun is surrounded with a Whirl-pool or Vortex of Matter in a very swift Motion; tho not in the least like Cartes’s […] manner of Motion. For Cartes makes his […] as every one of them to touch all the others round them, in a flat Surface, just as you have seen the Bladders that Boys blow up in Soap-suds do: and would have the whole Vortex to move round the same way. But the Angles of every Vortex will be no small hindrance to such a Motion. Then the whole matter moving round at once, upon the Axis as it were of a Cylinder, did not a little puzzle him in giving Reasons for the Roundness of the Sun: which however they may satisfy some People that do not consider them, really prove nothing of the matter. In this æthereal matter the Planets float, and are carry’d round by its motion: and the thing that keeps them in their own Orbs is, that they themselves, and the matter in which they swim. Equally strive to fly out from the Center of this Motion. Against all which […] I touch’d upon in my Essay of the Causes of Gravity. Where I gave another account of the Planets not deserting their own Orbs; which is their Gravitation towards the Sun. […]. Plutarch in his Book of the Moon above mentioned says, that some of the Antients were of opinion, that the reason of the Moon’s keeping her Orbit was, that the force of her Circular Motion was exactly equal to her Gravity, the one of which pull’d her to, as much as the Other forc’d her off from the Centre. And in our Age Alphonsus Borellus, who was of this same opinion in the other Planets as well as the Moon […]: Which Mr. Isaac Newton has more fully explained, with a great deal of pains and subtilty; and how from that cause proceeds the Ellipticity of the Orbs of the Planets, found out by Kepler,” Huygens 1698b, 157–158. As to Plutarch, see Furley 1989, chapter 16; Russo 2013, chapter 11. As to Borelli, see Koyré 1973; Hall 1983, chapter 11; Capecchi 2017, chapter 5.
202.
“According to my Notion of the Gravitation of the Planets to the Sun, the matter of his Vortex must not all move the same way, but after such a manner as to have its parts carry’d different ways on all sides. And yet there is no fear of its being destroy’d by such an irregular motion, because the æther round it, which is at rest, keeps the parts of it from flying out. With the help of such a Vortex as this I have pretended in that Essay to explain the Gravity of Bodies on this Earth, and all the effects of it. And I suppose there may be the same cause as well of the Gravitation of the Planers, and of our Earth among the rest, towards the Sun, as of their Roundness: a thing so very hard to give an account of in Cartes’s System. I must differ from him too in the bigness of the Vortices, for I cannot allow them to be so large as he would make them. I would have them dispers’d all about the immense space, like so many little Whirl-pools of Water, that one makes by the stirring of a stick in any large Pond or River, a great way distant from one another. And as their motions do not all intermix or communicate with one another; so in my opinion must the Vortices of Stars be plac’d as not to hinder one anothers free Circumrotations. So that we may be secure, and never fear that they will swallow up or destroy one another; for that was a mere fancy of Cartes’s; when he was showing how a fix’d Star or Sun might be turn’d into a Planet. And ’tis plain, that when he writ it, he had no thoughts of the immense distance of the Stars from one another; particularly, by this one thing, that he would have a Comet as soon as ever it comes into our Vortex, to be seen by us. Which is as absurd as can be. For how could a Star, which gives us such a vast Light only from the Reflection of the Beams of the Sun, as he himself owns they do; how I say could that be so plainly seen at a distance ten thousand times larger than the Diameter of the Earth’s Orbit? He could not but know that all round the Sun there is a vast Extensum; so vast, that in Copernicus’s System the magnus Orbis is counted but a point in comparison with it. But indeed all the whole story of Comets and Planets, and the Production of the World, is founded upon such poor and trifling grounds, that I have often wonder’d how an ingenious man could spend all that pains in making such fancies hang together. For my part, I shall be very well contented, and shall count I have done a great matter, if I can but come to any knowlege of the nature of things, as they now are, never troubling my head about their beginning, or how they were made, knowing that to be out of the reach of human Knowlege, or even Conjecture,” Huygens 1698b, 158–160.

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Strazzoni, A. (2019). Cosmology and Theory of Weight. In: Burchard de Volder and the Age of the Scientific Revolution. Studies in History and Philosophy of Science, vol 51. Springer, Cham. https://doi.org/10.1007/978-3-030-19878-7_6

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