Pars secundaDe principiis rerum materialium
IQuibus rationibus rerum materialium existentia certo cognoscatur.II.1
Etsi nemo non sibi satis persuadeat res materiales existere, quia tamen hoc a nobis paulo ante in dubium reuocatum est, et inter primae nostrae aetatis praeiudicia numeratum, nunc opus est ut rationes inuestigemus, per quas id certo cognoscatur. Nempe quicquid sentimus, procul dubio nobis aduenit a re aliqua, quae a mente nostra diuersa est. Neque enim est in nostra potestate efficere, ut unum potius quam aliud sentiamus; sed hoc a re illa quae sensus nostros afficit, plane pendet. Quaeri quidem potest an res illa sit Deus, an quid a Deo diuersum. Sed quia sentimus, siue potius a sensu impulsi clare ac distincte percipimus, materiam quandam extensam in longum, latum et profundum, cuius uariae partes uariis figuris praeditae sunt, ac uariis motibus cientur, ac etiam efficiunt ut uarios sensus habeamus colorum, odorum, doloris, etc: si Deus immediate per se ipsum istius materiae extensae ideam menti nostrae exhiberet, uel tantum si efficeret ut exhiberetur a re aliqua, in qua nihil esset extensionis, nec figurae, nec motus: nulla ratio potest excogitari, cur non deceptor esset putandus. Ipsam enim clare intelligimus tanquam rem a Deo et a nobis, siue a mente nostra, plane diuersam; ac etiam clare uidere nobis uidemur, eius ideam a rebus extra nos positis, quibus omnino similis est, aduenire; Dei autem naturae plane repugnare ut sit deceptor, iam ante est animaduersum. Atque ideo hic omnino concludendum est, rem quandam extensam in longum, latum et profundum, omnesque illas proprietates quas rei extensae conuenire clare percipimus habentem, existere. Estque haec res extensa, quam corpus siue materiam appellamus.
I The grounds on which the existence of material things may be known with certainty.
Although we are all sufficiently persuaded of the existence of material things, yet, since this was before called in question by us, and since we reckoned the persuasion of their existence as among the prejudices of our childhood, it is now necessary for us to investigate the grounds on which this truth may be known with certainty. In the first place, then, it cannot be doubted that every perception we have comes to us from some object different from our mind; for it is not in our power to cause ourselves to experience one perception rather than another, the perception being entirely dependent on the object which affects our senses. It may, indeed, be matter of inquiry whether that object be God, or something different from God; but because we perceive, or rather, stimulated by sense, clearly and distinctly apprehend, certain matter extended in length, breadth, and thickness, the various parts of which have different figures and motions, and give rise to the sensation we have of colours, smells, pain, etc., God would, without question, deserve to be regarded as a deceiver, if he directly and of himself presented to our mind the idea of this extended matter, or merely caused it to be presented to us by some object which possessed neither extension, figure, nor motion. For we clearly conceive this matter as entirely distinct from God, and from ourselves, or our mind; and appear even clearly to discern that the idea of it is formed in us on occasion of objects existing out of our minds, to which it is in every respect similar. But since God cannot deceive us, for this is repugnant to his nature, as has been already remarked, we must unhesitatingly conclude that there exists a certain object extended in length, breadth, and thickness, and possessing all those properties which we clearly apprehend to belong to what is extended. And this extended substance is what we call body or matter.
IIQuibus etiam cognoscatur corpus humanum menti esse arcte coniunctum.II.2
Eadem ratione, menti nostrae corpus quoddam magis arcte, quam reliqua alia corpora, coniunctum esse, concludi potest, ex eo quod perspicue aduertamus dolores aliosque sensus nobis ex improuiso aduenire; quos mens est conscia non a se sola proficisci, nec ad se posse pertinere ex eo solo quod sit res cogitans, sed tantum ex eo quod alteri cuidam rei extensae ac mobili adiuncta sit, quae res humanum corpus appellatur. Sed accuratior eius rei explicatio non est huius loci.
II How we likewise know that the human body is closely connected with the mind.
We ought also to conclude that a certain body is more closely united to our mind than any other, because we clearly observe that pain and other sensations affect us without our foreseeing them; and these, the mind is conscious, do not arise from itself alone, nor pertain to it, in so far as it is a thing which thinks, but only in so far as it is united to another thing extended and movable, which is called the human body. But this is not the place to treat in detail of this matter.
IIISensuum perceptiones, non quid reuera sit in rebus, sed quid humano composito prosit uel obsit, docere.II.3
Satis erit, si aduertamus sensuum perceptiones non referri, nisi ad istam corporis humani cum mente coniunctionem, et nobis quidem ordinarie exhibere, quid ad illam externa corpora prodesse possint aut nocere; non autem, nisi interdum et ex accidenti, nos docere, qualia in seipsis existant. Ita enim sensuum praeiudicia facile deponemus, et solo intellectu, ad ideas sibi a natura inditas diligenter attendente, hic utemur.
III That the perceptions of the senses do not teach us what is in reality in things, but what is beneficial of hurtful to the composite whole of mind and body.
It will be sufficient to remark that the perceptions of the senses are merely to be referred to this intimate union of the human body and mind, and that they usually make us aware of what, in external objects, may be useful or adverse to this union, but do not present to us these objects as they are in themselves, unless occasionally and by accident. For, after this observation, we will without difficulty lay aside the prejudices of the senses, and will have recourse to our understanding alone on this question by reflecting carefully on the ideas implanted in it by nature.
IVNaturam corporis non in pondere, duritie, colore, aut similibus; sed in sola extensione consistere.II.4
Quod agentes, percipiemus naturam materiae, siue corporis in uniuersum spectati, non consistere in eo quod sit res dura, uel ponderosa, uel colorata, uel alio aliquo modo sensus afficiens: sed tantum in eo quod sit res extensa in longum, latum et profundum. Nam, quantum ad duritiem, nihil aliud de illa sensus nobis indicat, quam partes durorum corporum resistere motui manuum nostrarum, cum in illas incurrunt. Si enim, quotiescumque manus nostrae uersus aliquam partem mouentur, corpora omnia ibi existentia recederent eadem celeritate qua illae accedunt, nullam unquam duritiem sentiremus. Nec ullo modo potest intelligi, corpora quae sic recederent, idcirco naturam corporis esse amissura; nec proinde ipsa in duritie consistit. Eademque ratione ostendi potest, et pondus, et colorem, et alias omnes eiusmodi qualitates, quae in materia corporea sentiuntur, ex ea tolli posse, ipsa integra remanente: unde sequitur, a nulla ex illis eius naturam dependere.
IV That the nature of body consists not in weight hardness, colour and the like, but in extension alone.
In this way we will discern that the nature of matter or body, considered in general, does not consist in its being hard, or ponderous, or coloured, or that which affects our senses in any other way, but simply in its being a substance extended in length, breadth, and depth. For with respect to hardness, we know nothing of it by sense farther than that the parts of hard bodies resist the motion of our hands on coming into contact with them; but if every time our hands moved towards any part, all the bodies in that place receded as quickly as our hands approached, we should never feel hardness; and yet we have no reason to believe that bodies which might thus recede would on this account lose that which makes them bodies. The nature of body does not, therefore, consist in hardness. In the same way, it may be shown that weight, colour, and all the other qualities of this sort, which are perceived in corporeal matter, may be taken from it, itself meanwhile remaining entire: it thus follows that the nature of body depends on none of these.
VPraeiudicia de rarefactione et de uacuo, hanc corporis naturam obscuriorem facere.II.5
Duae uero adhuc causae supersunt, ob quas potest dubitari, an uera natura corporis in sola extensione consistat. Una est, quod multi existiment, pleraque corpora sic posse rarefieri ac condensari, ut rarefacta plus habeant extensionis quam condensata; sintque etiam nonnulli adeo subtiles, ut substantiam corporis ab eiusdem quantitate, atque ipsam quantitatem ab extensione distinguant. Altera est, quod ubi nihil aliud esse intelligimus, quam extensionem in longum, latum et profundum, non soleamus dicere ibi esse corpus, sed tantummodo spatium, et quidem spatium inane, quod fere omnes sibi persuadent esse purum nihil.
V That the truth regarding the nature of body is obscured by the opinions respecting rarefaction and a vacuum with which we are pre- occupied.
There still remain two causes to prevent its being fully admitted that the true nature of body consists in extension alone. The first is the prevalent opinion, that most bodies admit of being so rarefied and condensed that, when rarefied, they have greater extension than when condensed; and some even have subtilized to such a degree as to make a distinction between the substance of body and its quantity, and between quantity itself and extension. The second cause is this, that where we conceive only extension in length, breadth, and depth, we are not in the habit of saying that body is there, but only space and further void space, which the generality believe to be a mere negation.
VIQuomodo fiat rarefactio.II.6
Sed quantum ad rarefactionem et condensationem, quicumque ad cogitationes suas attendet, ac nihil uolet admittere nisi quod clare percipiat, non putabit in ipsis aliud quidquam contingere, quam figurae mutationem: ita scilicet, ut rara corpora illa sint, inter quorum partes multa interualla existunt, corporibus aliis repleta; et per hoc tantum densiora reddantur, quod ipsorum partes, ad inuicem accedentes, interualla ista imminuant uel plane tollant: quod ultimum si aliquando contingat, tunc corpus tam densum euadit, ut repugnet ipsum densius reddi posse. Atqui non ideo minus tunc extensum est, quam cum partes habens a se mutuo dissitas, maius spatium amplectitur: quia quicquid extensionis in poris siue interuallis a partibus eius relictis continetur, nullo modo ipsi tribui debet, sed aliis quibusuis corporibus, a quibus interualla ista replentur. Ut cum uidemus spongiam, aqua uel alio liquore turgentem, non putamus ipsam secundum singulas suas partes magis extensam, quam cum compressa est et sicca; sed tantummodo poros habere magis patentes, ac ideo per maius spatium esse diffusam.
VI In what way rarefaction takes place.
But with regard to rarefaction and condensation, whoever gives his attention to his own thoughts, and admits nothing of which he is not clearly conscious, will not suppose that there is anything in those processes further than a change of figure in the body rarefied or condensed: so that, in other words, rare bodies are those between the parts of which there are numerous distances filled with other bodies; and dense bodies, on the other hand, those whose parts approaching each other, either diminish these distances or take them wholly away, in the latter of which cases the body is rendered absolutely dense. The body, however, when condensed, has not, therefore, less extension than when the parts embrace a greater space, owing to their removal from each other, and their dispersion into branches. For we ought not to attribute to it the extension of the pores or distances which its parts do not occupy when it is rarefied, but to the other bodies that fill these interstices; just as when we see a sponge full of water or any other liquid, we do not suppose that each part of the sponge has on this account greater extension than when compressed and dry, but only that its pores are wider, and therefore that the body is diffused over a larger space.
VIIEam non posse ullo alio modo intelligibili explicari.II.7
Et sane non uideo, quid mouerit nonnullos, ut mallent dicere rarefactionem fieri per augmentationem quantitatis, quam ipsam hoc spongiae exemplo explicare. Nam etsi, cum aÎr aut aqua rarefiunt, non uideamus ullos ipsorum poros qui ampliores reddantur, nec ullum nouum corpus, quod ad illos replendos accedat: non est tamen rationi tam consentaneum, aliquid non intelligibile effingere, ad eorum rarefactionem uerbotenus explicandam, quam ex hoc quod rarefiant, concludere in ipsis esse poros, siue interualla quae ampliora redduntur, et nouum aliquod corpus accedere quod ipsa implet, etsi hoc nouum corpus nullo sensu percipiamus. Nulla enim ratio nos cogit ad credendum, corpora omnia quae existunt debere sensus nostros afficere. Ac rarefactionem perfacile hoc modo, non autem ullo alio, fieri posse percipimus. Ac denique plane repugnat aliquid noua quantitate uel noua extensione augeri, quin simul etiam noua substantia extensa, hoc est, nouum corpus ei accedat. Neque enim ullum additamentum extensionis uel quantitatis, sine additamento substantiae quae sit quanta et extensa, potest intelligi, ut ex sequentibus clarius patebit.
VII That rarefaction cannot be intelligibly explained unless in the way here proposed.
And indeed I am unable to discover the force of the reasons which have induced some to say that rarefaction is the result of the augmentation of the quantity of body, rather than to explain it on the principle exemplified in the case of a sponge. For although when air or water is rarefied we do not see any of the pores that are rendered large, or the new body that is added to occupy them, it is yet less agreeable to reason to suppose something that is unintelligible for the purpose of giving a verbal and merely apparent explanation of the rarefaction of bodies, than to conclude, because of their rarefaction, that there are pores or distances between the parts which are increased in size, and filled with some new body. Nor ought we to refrain from assenting to this explanation, because we perceive this new body by none of our senses, for there is no reason which obliges us to believe that we should perceive by our senses all the bodies in existence. And we see that it is very easy to explain rarefaction in this manner, but impossible in any other; for, in fine, there would be, as appears to me, a manifest contradiction in supposing that any body was increased by a quantity or extension which it had not before, without the addition to it of a new extended substance, in other words, of another body, because it is impossible to conceive any addition of extension or quantity to a thing without supposing the addition of a substance having quantity or extension, as will more clearly appear from what follows.
VIIIQuantitatem et numerum differre tantum ratione a re quanta et numerata.II.8
Quippe quantitas a substantia extensa in re non differt, sed tantum ex parte nostri conceptus, ut et numerus a re numerata. Ita scilicet ut totam naturam substantiae corporeae, quae est in spatio decem pedum, possimus considerare, quamuis ad istam mensuram decem pedum non attendamus: quia plane eadem intelligitur in qualibet istius spatii parte ac in toto. Et uice uersa, potest intelligi numerus denarius, ut etiam quantitas continua decem pedum, etsi ad istam determinatam substantiam non attendamus: quia plane idem est conceptus numeri denarii, siue ad hanc mensuram decem pedum, siue ad quidlibet aliud referatur; et quantitas continua decem pedum, etsi non possit intelligi sine aliqua substantia extensa, cuius sit quantitas, potest tamen sine hac determinata. In re autem fieri non potest, ut uel minimum quid ex ista quantitate aut extensione tollatur, quin tantundem etiam de substantia detrahatur; nec uice uersa, ut tantillum de substantia detrahatur, quin tantundem de quantitate ac extensione tollatur.
VIII That quantity and number differ only in thought (RATIONE) from that which has quantity and is numbered.
For quantity differs from extended substance, and number from what is numbered, not in reality but merely in our thought; so that, for example, we may consider the whole nature of a corporeal substance which is comprised in a space of ten feet, although we do not attend to this measure of ten feet, for the obvious reason that the thing conceived is of the same nature in any part of that space as in the whole; and, on the other hand, we can conceive the number ten, as also a continuous quantity of ten feet, without thinking of this determinate substance, because the concept of the number ten is manifestly the same whether we consider a number of ten feet or ten of anything else; and we can conceive a continuous quantity of ten feet without thinking of this or that determinate substance, although we cannot conceive it without some extended substance of which it is the quantity. It is in reality, however, impossible that any, even the least part, of such quantity or extension, can be taken away, without the retrenchment at the same time of as much of the substance, nor, on the other hand, can we lessen the substance, without at the same time taking as much from the quantity or extension.
IXSubstantiam corpoream, cum a quantitate sua distinguitur, confuse concipi tanquam incorpoream.II.9
Et quamuis forte nonnulli aliud dicant, non puto tamen ipsos aliud ea de re percipere; sed cum substantiam ab extensione aut quantitate distinguunt, uel nihil per nomen substantiae intelligunt, uel confusam tantum substantiae incorporeae ideam habent, quam falso tribuunt corporeae, huiusque substantiae corporeae ueram ideam extensioni relinquunt, quam tamen accidens uocant, atque ita plane aliud efferunt uerbis, quam mente comprehendunt.
IX That corporeal substance, when distinguished from its quantity, is confusedly conceived as something incorporeal.
Although perhaps some express themselves otherwise on this matter, I am nevertheless convinced that they do not think differently from what I have now said: for when they distinguish (corporeal) substance from extension or quantity, they either mean nothing by the word (corporeal) substance, or they form in their minds merely a confused idea of incorporeal substance, which they falsely attribute to corporeal, and leave to extension the true idea of this corporeal substance; which extension they call an accident, but with such impropriety as to make it easy to discover that their words are not in harmony with their thoughts.
XQuid sit spatium, siue locus internus.II.10
Non etiam in re differunt spatium, siue locus internus, et substantia corporea in eo contenta, sed tantum in modo, quo a nobis concipi solent. Reuera enim extensio in longum, latum et profundum, quae spatium constituit, eadem plane est cum illa quae constituit corpus. Sed in hoc differentia est, quod ipsam in corpore ut singularem consideremus, et putemus semper mutari quoties mutatur corpus: in spatio uero unitatem tantum genericam ipsi tribuamus, adeo ut, mutato corpore quod spatium implet, non tamen extensio spatii mutari censeatur, sed remanere una et eadem, quamdiu manet eiusdem magnitudinis ac figurae, seruatque eundem situm inter externa quaedam corpora, per quae illud spatium determinamus.
X What space or internal place is.
Space or internal place, and the corporeal substance which is comprised in it, are not different in reality, but merely in the mode in which they are wont to be conceived by us. For, in truth, the same extension in length, breadth, and depth, which constitutes space, constitutes body; and the difference between them lies only in this, that in body we consider extension as particular, and conceive it to change with the body; whereas in space we attribute to extension a generic unity, so that after taking from a certain space the body which occupied it, we do not suppose that we have at the same time removed the extension of the space, because it appears to us that the same extension remains there so long as it is of the same magnitude and figure, and preserves the same situation in respect to certain bodies around it, by means of which we determine this space.
XIQuomodo in re non differat a substantia corporea.II.11
Et quidem facile agnoscemus, eandem esse extensionem, quae naturam corporis et naturam spatii constituit, nec magis haec duo a se mutuo differre, quam natura generis aut speciei differt a natura indiuidui: si attendentes ad ideam quam habemus alicuius corporis, exempli causa, lapidis, reiiciamus ab illa id omne quod ad corporis naturam non requiri cognoscimus: nempe reiiciamus primo duritiem, quia si lapis liquefiat aut in puluisculos quam minutissimos diuidatur, illam amittet, neque tamen ideo desinet esse corpus; reiiciamus etiam colorem, quia uidimus saepe lapides adeo pellucidos, ut nullus in iis esset color; reiiciamus grauitatem, quia quamuis ignis sit leuissimus, non ideo minus putatur esse corpus; ac denique reiiciamus frigus et calorem, aliasque omnes qualitates, quia uel non considerantur in lapide, uel iis mutatis, non ideo lapis corporis naturam amisisse existimatur. Ita enim aduertemus, nihil plane in eius idea remanere, praeterquam quod sit quid extensum in longum, latum et profundum: quod idem continetur in idea spatii, non modo corporibus pleni, sed eius etiam quod uacuum appellatur.
XI How space is not in reality different from corporeal substance.
And indeed it will be easy to discern that it is the same extension which constitutes the nature of body as of space, and that these two things are mutually diverse only as the nature of the genus and species differs from that of the individual, provided we reflect on the idea we have of any body, taking a stone for example, and reject all that is not essential to the nature of body. In the first place, then, hardness may be rejected, because if the stone were liquefied or reduced to powder, it would no longer possess hardness, and yet would not cease to be a body; colour also may be thrown out of account, because we have frequently seen stones so transparent as to have no colour; again, we may reject weight, because we have the case of fire, which, though very light, is still a body; and, finally, we may reject cold, heat, and all the other qualities of this sort, either because they are not considered as in the stone, or because, with the change of these qualities, the stone is not supposed to have lost the nature of body. After this examination we will find that nothing remains in the idea of body, except that it is something extended in length, breadth, and depth; and this something is comprised in our idea of space, not only of that which is full of body, but even of what is called void space.
XIIQuomodo ab eadem differat in modo, quo concipitur.II.12
Est autem differentia in modo concipiendi; nam, sublato lapide ex spatio uel loco in quo est, putamus etiam eius extensionem esse sublatam, utpote quam ut singularem et ab ipso inseparabilem spectamus. Sed interim extensionem loci, in quo erat lapis, remanere arbitramur, eandemque esse, quamuis iam ille locus lapidis a ligno, uel aqua, uel aÎre, uel alio quouis corpore occupetur, uel etiam uacuus esse credatur: quia ibi consideratur extensio in genere, censeturque eadem esse lapidis, ligni, aquae, aÎris, aliorumque corporum, uel etiam ipsius uacui, si quod detur, modo tantum sit eiusdem magnitudinis ac figurae, seruetque eundem situm inter corpora externa, quae spatium illud determinant.
XII How space differs from body in our mode of conceiving it.
There is, however, some difference between them in the mode of conception; for if we remove a stone from the space or place in which it was, we conceive that its extension also is taken away, because we regard this as particular, and inseparable from the stone itself: but meanwhile we suppose that the same extension of place in which this stone was remains, although the place of the stone be occupied by wood, water, air, or by any other body, or be even supposed vacant, because we now consider extension in general, and think that the same is common to stones, wood, water, air, and other bodies, and even to a vacuum itself, if there is any such thing, provided it be of the same magnitude and figure as before, and preserve the same situation among the external bodies which determine this space.
XIIIQuid sit locus externus.II.13
Quippe nomina loci aut spatii non significant quicquam diuersum a corpore quod dicitur esse in loco, sed tantum eius magnitudinem, figuram, et situm inter alia corpora designant. Et quidem, ut ille situs determinetur, respicere debemus ad alia aliqua corpora, quae ut immobilia spectemus; ac prout ad diuersa respicimus, dicere possumus eandem rem, eodem tempore, locum mutare ac non mutare. Ut, cum nauis in mari prouehitur, qui sedet in puppi manet semper uno in loco, si ratio habeatur partium nauis inter quas eundem situm seruat; et ille idem assidue locum mutat, si ratio littorum habeatur, quoniam assidue ab unis recedit et ad alia accedit. Ac praeterea, si putemus terram moueri, tantumque praecise procedere ab Occidente uersus Orientem, quantum nauis interim ex Oriente in Occidentem promouetur, dicemus rursus illum qui sedet in puppi, locum suum non mutare: quia nempe loci determinationem ab immotis quibusdam coeli punctis desumemus. Sed si tandem cogitemus, nulla eiusmodi puncta uere immota in uniuerso reperiri, ut probabile esse infra ostendetur, inde concludemus nullum esse permanentem ullius rei locum, nisi quatenus a cogitatione nostra determinatur.
XIII What external place is.
The reason of which is, that the words place and space signify nothing really different from body which is said to be in place, but merely designate its magnitude, figure, and situation among other bodies. For it is necessary, in order to determine this situation, to regard certain other bodies which we consider as immovable; and, according as we look to different bodies, we may see that the same thing at the same time does and does not change place. For example, when a vessel is being carried out to sea, a person sitting at the stern may be said to remain always in one place, if we look to the parts of the vessel, since with respect to these he preserves the same situation; and on the other hand, if regard be had to the neighbouring shores, the same person will seem to be perpetually changing place, seeing he is constantly receding from one shore and approaching another. And besides, if we suppose that the earth moves, and that it makes precisely as much way from west to east as the vessel from east to west, we will again say that the person at the stern does not change his place, because this place will be determined by certain immovable points which we imagine to be in the heavens. But if at length we are persuaded that there are no points really immovable in the universe, as will hereafter be shown to be probable, we will thence conclude that nothing has a permanent place unless in so far as it is fixed by our thought.
XIVIn quo differant locus et spatium.II.14
Differunt autem nomina loci et spatii, quia locus magis expresse designat situm quam magnitudinem aut figuram, et e contra, magis ad has attendimus, cum loquimur de spatio. Dicimus enim frequenter unam rem in locum alterius succedere, quamuis non sit accurate eiusdem magnitudinis, nec figurae; sed tunc negamus illam idem spatium occupare; ac semper, cum ille situs mutatur, dicimus locum mutari, quamuis eadem magnitudo ac figura permaneat. Cumque dicimus rem esse in hoc loco, nihil aliud intelligimus, quam illam obtinere hunc situm inter alias res; et cum addimus ipsam implere hoc spatium uel hunc locum, intelligimus praeterea ipsam esse huius determinatae magnitudinis ac figurae.
XIV Wherein place and space differ.
The terms place and space, however, differ in signification, because place more expressly designates situation than magnitude or figure, while, on the other hand, we think of the latter when we speak of space. For we frequently say that a thing succeeds to the place of another, although it be not exactly of the same magnitude or figure; but we do not therefore admit that it occupies the same space as the other; and when the situation is changed we say that the place also is changed, although there are the same magnitude and figure as before: so that when we say that a thing is in a particular place, we mean merely that it is situated in a determinate way in respect of certain other objects; and when we add that it occupies such a space or place, we understand besides that it is of such determinate magnitude and figure as exactly to fill this space.
XVQuomodo locus externus pro superficie corporis ambientis recte sumatur.II.15
Atque ita spatium quidem semper sumimus pro extensione in longum, latum et profundum. Locum autem aliquando consideramus ut rei, quae in loco est, internum, et aliquando ut ipsi externum. Et quidem internus idem plane est quod spatium; externus autem sumi potest pro superficie quae proxime ambit locatum. Notandumque est, per superficiem non hic intelligi ullam corporis ambientis partem, sed solum terminum, qui medius est inter ipsum corpus ambiens et id quod ambitur, quique nihil aliud est quam modus: uel certe intelligi superficiem in communi, quae non sit pars unius corporis magis quam alterius, sed eadem semper esse censeatur, cum retinet eandem magnitudinem et figuram. Etsi enim omne corpus ambiens cum sua superficie mutetur, non ideo res quam ambit locum mutare existimatur, si eundem interim situm seruet inter illa externa, quae tanquam immobilia spectantur. Ut si nauim in unam partem a fluminis lapsu, et in contrariam a uento tam aequaliter impelli supponamus, ut situm suum inter ripas non mutet, facile aliquis credet ipsam manere in eodem loco, quamuis omnis superficies ambiens mutetur.
XV How external place is rightly taken for the superficies of the surrounding body.
And thus we never indeed distinguish space from extension in length, breadth, and depth; we sometimes, however, consider place as in the thing placed, and at other times as out of it. Internal place indeed differs in no way from space; but external place may be taken for the superficies that immediately surrounds the thing placed. It ought to be remarked that by superficies we do not here understand any part of the surrounding body, but only the boundary between the surrounding and surrounded bodies, which is nothing more than a mode; or at least that we speak of superficies in general which is no part of one body rather than another, but is always considered the same, provided it retain the same magnitude and figure. For although the whole surrounding body with its superficies were changed, it would not be supposed that the body which was surrounded by it had therefore changed its place, if it meanwhile preserved the same situation with respect to the other bodies that are regarded as immovable. Thus, if we suppose that a boat is carried in one direction by the current of a stream, and impelled by the wind in the opposite with an equal force, so that its situation with respect to the banks is not changed, we will readily admit that it remains in the same place, although the whole superficies which surrounds it is incessantly changing.
XVIRepugnare ut detur uacuum, siue in quo nulla plane sit res.II.16
Vacuum autem philosophico more sumptum, hoc est, in quo nulla plane sit substantia, dari non posse manifestum est, ex eo quod extensio spatii, uel loci interni, non differat ab extensione corporis. Nam cum ex hoc solo quod corpus sit extensum in longum, latum et profundum, recte concludamus illud esse substantiam, quia omnino repugnat ut nihili sit aliqua extensio, idem etiam de spatio, quod uacuum supponitur, est concludendum: quod nempe, cum in eo sit extensio, necessario etiam in ipso sit substantia.
XVI That a vacuum or space in which there is absolutely no body is repugnant to reason.
With regard to a vacuum, in the philosophical sense of the term, that is, a space in which there is no substance, it is evident that such does not exist, seeing the extension of space or internal place is not different from that of body. For since from this alone, that a body has extension in length, breadth, and depth, we have reason to conclude that it is a substance, it being absolutely contradictory that nothing should possess extension, we ought to form a similar inference regarding the space which is supposed void, viz., that since there is extension in it there is necessarily also substance.
XVIIVacuum ex uulgi usu non excludcre omne corpus.II.17
Et quidem ex uulgi usu, per nomen uacui non solemus significare locum uel spatium in quo nulla plane sit res, sed tantummodo locum in quo nulla sit ex iis rebus, quas in eo esse debere cogitamus. Sic, quia urna facta est ad aquas continendas, uacua dicitur, cum aÎre tantum est plena. Sic nihil est in piscina, licet aquis abundet, si in ea desint pisces. Sic inane est nauigium, quod comparatum erat ad uehendas merces, si solis arenis, quibus frangat impetus uenti, sit onustum. Sic denique inane est spatium, in quo nihil est sensibile, quamuis materia creata et per se subsistente plenum sit: quia non solemus considerare, nisi eas res quae a sensibus attinguntur. Atqui si postea, non attendentes quid per nomina uacui et nihili sit intelligendum, in spatio quod uacuum esse diximus, non modo nihil sensibile, sed omnino nullam rem contineri existimemus: in eundem errorem incidemus, ac si ex eo quod usitatum sit dicere urnam, in qua nihil est nisi aÎr, uacuam esse, ideo iudicaremus aÎrem in ea contentum non esse rem subsistentem.
XVII That a vacuum in the ordinary use of the term does not exclude all body.
And, in truth, by the term vacuum in its common use, we do not mean a place or space in which there is absolutely nothing, but only a place in which there is none of those things we presume ought to be there. Thus, because a pitcher is made to hold water, it is said to be empty when it is merely filled with air; or if there are no fish in a fish-pond, we say there is nothing in it, although it be full of water; thus a vessel is said to be empty, when, in place of the merchandise which it was designed to carry, it is loaded with sand only, to enable it to resist the violence of the wind; and, finally, it is in the same sense that we say space is void when it contains nothing sensible, although it contain created and self-subsisting matter; for we are not in the habit of considering the bodies near us, unless in so far as they cause in our organs of sense, impressions strong enough to enable us to perceive them. And if, in place of keeping in mind what ought to be understood by these terms a vacuum and nothing, we afterwards suppose that in the space we called a vacuum, there is not only no sensible object, but no object at all, we will fall into the same error as if, because a pitcher in which there is nothing but air, is, in common speech, said to be empty, we were therefore to judge that the air contained in it is not a substance (RES SUBSISTENS).
XVIIIQuomodo emendandum sit praeiudicium de pacuo absolute sumpto.II.18
Lapsique sumus fere omnes a prima aetate in hunc errorem, propterea quod, non aduertentes ullam esse inter uas et corpus in eo contentum necessariam coniunctionem, non putauimus quicquam obstare, quominus saltem Deus efficiat, ut corpus, quod uas aliquod replet, inde auferatur, et nullum aliud in eius locum succedat. Iam autem, ut errorem illum emendemus, considerare oportet nullam quidem esse connexionem inter uas et hoc uel illud corpus particulare quod in eo continetur, sed esse maximam, ac omnino necessariam, inter uasis figuram concauam et extensionem in genere sumptam, quae in ea cauitate debet contineri. Adeo ut non magis repugnet nos concipere montem sine ualle, quam intelligere istam cauitatem absque extensione in ea contenta, uel hanc extensionem absque substantia quae sit extensa: quia, ut saepe dictum est, nihili nulla potest esse extensio. Ac proinde, si quaeratur quid fiet, si Deus auferat omne corpus quod in aliquo uase continetur, et nullum aliud in ablati locum uenire permittat: respondendum est, uasis latera sibi inuicem hoc ipso fore contigua. Cum enim inter duo corpora nihil interiacet, necesse est ut se mutuo tangant; ac manifeste repugnat ut distent, siue ut inter ipsa sit distantia, et tamen ut ista distantia sit nihil: quia omnis distantia est modus extensionis, et ideo sine substantia extensa esse non potest.
XVIII How the prejudice of an absolute vacuum is to be corrected.
We have almost all fallen into this error from the earliest age, for, observing that there is no necessary connection between a vessel and the body it contains, we thought that God at least could take from a vessel the body which occupied it, without it being necessary that any other should be put in the place of the one removed. But that we may be able now to correct this false opinion, it is necessary to remark that there is in truth no connection between the vessel and the particular body which it contains, but that there is an absolutely necessary connection between the concave figure of the vessel and the extension considered generally which must be comprised in this cavity; so that it is not more contradictory to conceive a mountain without a valley than such a cavity without the extension it contains, or this extension apart from an extended substance, for, as we have often said, of nothing there can be no extension. And accordingly, if it be asked what would happen were God to remove from a vessel all the body contained in it, without permitting another body to occupy its place, the answer must be that the sides of the vessel would thus come into proximity with each other. For two bodies must touch each other when there is nothing between them, and it is manifestly contradictory for two bodies to be apart, in other words, that there should be a distance between them, and this distance yet be nothing; for all distance is a mode of extension, and cannot therefore exist without an extended substance.
XIXEx his ea confirmari, quae de rarefactione dicta sunt.II.19
Postquam sic aduertimus substantiae corporeae naturam in eo tantum consistere, quod sit res extensa; eiusque extensionem non esse diuersam ab ea, quae spatio quantumuis inani tribui solet: facile cognoscimus fieri non posse, ut aliqua eius pars plus spatii occupet una uice quam alia, sicque aliter rarefiat, quam modo paullo ante explicato; uel ut plus sit materiae, siue substantiae corporeae, in uase, cum plumbo, uel auro, uel alio quantumuis graui ac duro corpore plenum est, quam cum aÎrem tantum continet, uacuumque existimatur: quia partium materiae quantitas non pendet ab earum grauitate aut duritie, sed a sola extensione, quae semper in eodem uase est aequalis.
XIX That this confirms what was said of rarefaction.
After we have thus remarked that the nature of corporeal substance consists only in its being an extended thing, and that its extension is not different from that which we attribute to space, however empty, it is easy to discover the impossibility of any one of its parts in any way whatsoever occupying more space at one time than at another, and thus of being otherwise rarefied than in the way explained above; and it is easy to perceive also that there cannot be more matter or body in a vessel when it is filled with lead or gold, or any other body however heavy and hard, than when it but contains air and is supposed to be empty: for the quantity of the parts of which a body is composed does not depend on their weight or hardness, but only on the extension, which is always equal in the same vase.
XXEx his etiam demonstrari, nullas atomos dari posse.II.20
Cognoscimus etiam fieri non posse ut aliquae atomi, siue materiae partes ex natura sua indiuisibiles, existant. Cum enim, si quae sint, necessario debeant esse extensae, quantumuis paruae fingantur, possumus adhuc unamquamque ex ipsis in duas aut plures minores cogitatione diuidere, ac proinde agnoscere esse diuisibiles. Nihil enim possumus cogitatione diuidere, quin hoc ipso cognoscamus esse diuisibile; atque ideo, si iudicaremus id ipsum esse indiuisibile, iudicium nostrum a cognitione dissentiret. Quin etiam si fingamus, Deum efficere uoluisse, ut aliqua materiae particula in alias minores diuidi non possit, non tamen illa proprie indiuisibilis erit dicenda. Ut etenim effecerit eam a nullis creaturis diuidi posse, non certe sibi ipsi eiusdem diuidendae facultatem potuit adimere: quia fieri plane non potest, ut propriam suam potentiam imminuat, quemadmodum supra notatum est. Atque ideo, absolute loquendo, illa diuisibilis remanebit, quoniam ex natura sua est talis.
XX That from this the non-existence of atoms may likewise be demonstrated.
We likewise discover that there cannot exist any atoms or parts of matter that are of their own nature indivisible. For however small we suppose these parts to be, yet because they are necessarily extended, we are always able in thought to divide any one of them into two or more smaller parts, and may accordingly admit their divisibility. For there is nothing we can divide in thought which we do not thereby recognize to be divisible; and, therefore, were we to judge it indivisible our judgment would not be in harmony with the knowledge we have of the thing; and although we should even suppose that God had reduced any particle of matter to a smallness so extreme that it did not admit of being further divided, it would nevertheless be improperly styled indivisible, for though God had rendered the particle so small that it was not in the power of any creature to divide it, he could not however deprive himself of the ability to do so, since it is absolutely impossible for him to lessen his own omnipotence, as was before observed. Wherefore, absolutely speaking, the smallest extended particle is always divisible, since it is such of its very nature.
XXIItem mundum esse indefinite extensum.II.21
Cognoscimus praeterea hunc mundum, siue substantiae corporeae uniuersitatem, nullos extensionis suae fines habere. Ubicumque enim fines illos esse fingamus, semper ultra ipsos aliqua spatia indefinite extensa non modo imaginamur, sed etiam uere imaginabilia, hoc est, realia esse percipimus; ac proinde, etiam substantiam corpoream indefinite extensam in iis contineri. Quia, ut iam fuse ostensum est, idea eius extensionis, quam in spatio qualicumque concipimus, eadem plane est cum idea substantiae corporeae.
XXI It is thus also demonstrated that the extension of the world is indefinite.
We further discover that this world or the whole (universitas) of corporeal substance, is extended without limit, for wherever we fix a limit, we still not only imagine beyond it spaces indefinitely extended, but perceive these to be truly imaginable, in other words, to be in reality such as we imagine them; so that they contain in them corporeal substance indefinitely extended, for, as has been already shown at length, the idea of extension which we conceive in any space whatever is plainly identical with the idea of corporeal substance.
XXIIItem unam et eandem esse materiam coeli et terrae; ac plures mundos esse non posse.II.22
Hincque etiam colligi facile potest, non aliam esse materiam coeli quam terrae; atque omnino, si mundi essent infiniti, non posse non illos omnes ex una et eadem materia constare; nec proinde plures, sed unum tantum, esse posse: quia perspicue intelligimus illam materiam, cuius natura in eo solo consistit quod sit substantia extensa, omnia omnino spatia imaginabilia, in quibus alii isti mundi esse deberent, iam occupare: nec ullius alterius materiae ideam in nobis reperimus.
XXII It also follows that the matter of the heavens and earth is the same, and that there cannot be a plurality of worlds.
And it may also be easily inferred from all this that the earth and heavens are made of the same matter; and that even although there were an infinity of worlds, they would all be composed of this matter; from which it follows that a plurality of worlds is impossible, because we clearly conceive that the matter whose nature consists only in its being an extended substance, already wholly occupies all the imaginable spaces where these other worlds could alone be, and we cannot find in ourselves the idea of any other matter.
XXIIIOmnem materiae uariationem, siue omnem eius formarum diuersitatem pendere a motu.II.23
Materia itaque in toto uniuerso una et eadem existit, utpote quae omnis per hoc unum tantum agnoscitur, quod sit extensa. Omnesque proprietates, quas in ea clare percipimus, ad hoc unum reducuntur, quod sit partibilis, et mobilis secundum partes, et proinde capax illarum omnium affectionum, quas ex eius partium motu sequi posse percipimus. Partitio enim, quae fit sola cogitatione, nihil mutat; sed omnis materiae uariatio, siue omnium eius formarum diuersitas, pendet a motu. Quod passim etiam a Philosophis uidetur fuisse animaduersum, quia dixerunt naturam esse principium motus et quietis. Tunc enim per naturam intellexerunt id, per quod res omnes corporeae tales euadunt, quales ipsas esse experimur.
XXIII That all the variety of matter, or the diversity of its forms, depends on motion.
There is therefore but one kind of matter in the whole universe, and this we know only by its being extended. All the properties we distinctly perceive to belong to it are reducible to its capacity of being divided and moved according to its parts; and accordingly it is capable of all those affections which we perceive can arise from the motion of its parts. For the partition of matter in thought makes no change in it; but all variation of it, or diversity of form, depends on motion. The philosophers even seem universally to have observed this, for they said that nature was the principle of motion and rest, and by nature they understood that by which all corporeal things become such as they are found in experience.
XXIVQuid sit motus iuxta uulgarem sensum.II.24
Motus autem (scilicet localis, neque enim ullus alius sub cogitationem meam cadit; nec ideo etiam ullum alium in rerum natura fingendum puto), motus, inquam, ut uulgo sumitur, nihil aliud est quam actio, qua corpus aliquod ex uno loco in alium migrat. Et idcirco, quemadmodum supra monuimus eandem rem eodem tempore dici posse locum mutare et non mutare, ita eadem etiam dici potest moueri et non moueri. Ut qui sedet in naui, dum ea soluit e portu, putat quidem se moueri, si respiciat ad littora eaque ut immota consideret; non autem, si ad ipsam nauim, inter cuius partes eundem semper situm seruat. Quin etiam, quatenus uulgo putamus in omni motu esse actionem, in quiete uero cessationem actionis, magis proprie tunc dicitur quiescere quam moueri, quia nullam in se actionem sentit.
XXIV What motion is, taking the term in its common use.
But motion (viz., local, for I can conceive no other kind of motion, and therefore I do not think we ought to suppose there is any other in nature), in the ordinary sense of the term, is nothing more than the action by which a body passes from one place to another. And just as we have remarked above that the same thing may be said to change and not to change place at the same time, so also we may say that the same thing is at the same time moved and not moved. Thus, for example, a person seated in a vessel which is setting sail, thinks he is in motion if he look to the shore that he has left, and consider it as fixed; but not if he regard the ship itself, among the parts of which he preserves always the same situation. Moreover, because we are accustomed to suppose that there is no motion without action, and that in rest there is the cessation of action, the person thus seated is more properly said to be at rest than in motion, seeing he is not conscious of being in action.
XXVQuid sit motus proprie sumptus.II.25
Sed si non tam ex uulgi usu, quam ex rei ueritate, consideremus quid per motum debeat intelligi, ut aliqua ei determinata natura tribuatur: dicere possumus esse translationem unius partis materiae, siue unius corporis, ex uicinia eorum corporum, quae illud immediate contingunt et tanquam quiescentia spectantur, in uiciniam aliorum. Ubi per unum corpus, siue unam partem materiae, intelligo id omne quod simul transfertur; etsi rursus hoc ipsum constare possit ex multis partibus, quae alios in se habeant motus. Et dico esse translationem, non uim uel actionem quae transfert, ut ostendam illum semper esse in mobili, non in mouente, quia haec duo non satis accurate solent distingui; ac esse duntaxat eius modum, non rem aliquam subsistentem, sicut figura est modus rei figuratae, ac quies rei quiescentis.
XXV What motion is properly so called.
But if, instead of occupying ourselves with that which has no foundation, unless in ordinary usage, we desire to know what ought to be understood by motion according to the truth of the thing, we may say, in order to give it a determinate nature, that it is THE TRANSPORTING OF ONE PART OF MATTER OR OF ONE BODY FROM THE VICINITY OF THOSE BODIES THAT ARE IN IMMEDIATE CONTACT WITH IT, OR WHICH WE REGARD AS AT REST, to the vicinity of other bodies. By a body as a part of matter, I understand all that which is transferred together, although it be perhaps composed of several parts, which in themselves have other motions; and I say that it is the transporting and not the force or action which transports, with the view of showing that motion is always in the movable thing, not in that which moves; for it seems to me that we are not accustomed to distinguish these two things with sufficient accuracy. Farther, I understand that it is a mode of the movable thing, and not a substance, just as figure is a property of the thing figured, and repose of that which is at rest.
XXVINon plus actionis requiri ad motum quam ad quietem.II.26
Quippe notandum est, magno nos, in hoc, praeiudicio laborare, quod plus actionis ad motum requiri arbitremur, quam ad quietem. Hocque ideo nobis ab ineunte aetate persuasimus, quod corpus nostrum soleat moueri a nostra uoluntate, cuius intime conscii sumus, et quiescere ex hoc solo quod terrae adhaereat per grauitatem, cuius uim non sentimus. Et quidem quia ista grauitas, aliaeque plures causae, a nobis non animaduersae, motibus quos in membris nostris ciere uolumus resistunt, efficiuntque ut fatigemur, putamus maiore actione, siue maiore ui opus esse ad motum ciendum, quam ad illum sistendum: sumentes scilicet actionem pro conatu illo, quo utimur ad membra nostra et illorum ope alia corpora permouenda. Quod tamen praeiudicium facile exuemus, si consideremus, non modo conatu nobis opus esse ad mouenda corpora externa, sed saepe etiam ad eorum motus sistendos, cum a grauitate aliaue causa non sistuntur. Ut, exempli gratia, non maiori utimur actione ad nauigium in aqua stagnante quiescens impellendum, quam ad idem, cum mouetur, subito retinendum: uel certe non multo maiori; hinc enim demenda est aquae ab eo subleuatae grauitas, et eiusdem lentor, a quibus paulatim sisti posset.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.26.
XXVIIMotum et quietem esse tantum diuersos modos corporis moti.II.27
Cum autem hic non agatur de illa actione, quae intelligitur esse in mouente, uel in eo qui motum sistit, sed de sola translatione, ac translationis absentia, siue quiete: manifestum est hanc translationem extra corpus motum esse non posse, atque hoc corpus alio modo se habere, cum transfertur, et alio, cum non transfertur siue cum quiescit: adeo ut motus et quies nihil aliud in eo sint, quam duo diuersi modi.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.27.
XXVIIIMotum proprie sumtum non referri, nisi ad corpora contigua eius quod mouetur.II.28
Addidi praeterea, translationem fieri ex uicinia corporum contiguorum in uiciniam aliorum, non autem ex uno loco in alium: quia, ut supra explicui, loci acceptio uaria est, ac pendet a nostra cogitatione: sed cum per motum intelligimus eam translationem quae fit ex uicinia corporum contiguorum, quoniam una tantum corpora eodem temporis momento eiusdem mobilis contigua esse possunt, non possumus isti mobili plures motus eodem tempore tribuere, sed unum tantum.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.28.
XXIXNec referri nisi ad ea corpora contigua, quae tanquam quiescentia spectantur.II.29
Addidi denique, translationem illam fieri ex uicinia, non quorumlibet corporum contiguorum, sed eorum duntaxat, quae tanquam quiescentia spectantur. Ipsa enim translatio est reciproca, nec potest intelligi corpus AB transferri ex uicinia corporis CD, quin simul etiam intelligatur corpus CD transferri ex uicinia corporis AB: ac plane eadem uis et actio requiritur ex una parte atque ex altera. Quapropter si omnino propriam, et non ad aliud relatam, naturam motui tribuere uellemus, cum duo corpora contigua unum in unam, aliud in aliam partem transferuntur, sicque a se mutuo separantur, tantundem motus in uno quam in altero esse diceremus. Sed hoc a communi loquendi usu nimium abhorreret: cum enim assueti simus stare in terra, eamque ut quiescentem considerare, quamuis aliquas eius partes, aliis minoribus corporibus contiguas, ab eorum uicinia transferri uideamus, non tamen ipsam ideo moueri putamus.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.29.
XXXCur ex duobus corporibus contiguis quae separantur ab inuicem, unum potius quam aliud moueri dicatur.II.30
Huiusque rei praecipua ratio est, quod motus intelligatur esse totius corporis quod mouetur, nec possit ita intelligi esse totius terrae, ob translationem quarundam eius partium ex uicinia monorum corporum quibus contiguae sunt: quoniam saepe plures eiusmodi translationes, sibi mutuo contrarias, in ipsa licet aduertere. Ut si corpus EFGH sit terra, et supra ipsam eodem tempore corpus AB transferatur ab E uersus F, ac CD ab H uersus G, quamuis hoc ipso partes terrae corpori AB contiguae a B uersus A transferantur, neque minor uel alterius naturae actio in iis esse debeat, ad illam translationem, quam in corpore AB: non ideo intelligimus terram moueri a B uersus A, siue ab Occidente uersus Orientem, quia pari ratione ob id quod eius partes corpori CD contiguae transferantur a C uersus D, intelligendum esset eam etiam in aliam partem moueri, nempe ab Oriente in Occidentem; quae duo inter se pugnant. Ita ergo, ne nimium a communi usu loguendi recedamus, non hic dicemus terram moueri, sed sola corpora AB et CD; atque ita de reliquis. Sed interim recordabimur, id omne quod reale est ac positiuum in corporibus quae mouentur, propter quod moueri dicuntur, reperiri etiam in aliis ipsorum contiguis, quae tamen ut quiescentia tantum spectantur.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.30.
XXXIQuomodo in eodem corpore innumeri diuersi motus esse possint.II.31
Etsi autem unumquodque corpus habeat tantum unum motum sibi proprium, quoniam ab unis tantum corporibus sibi contiguis et quiescentibus recedere intelligitur, participare tamen etiam potest ex aliis innumeris, si nempe sit pars aliorum corporum alios motus habentium. Ut, si quis ambulans in naui horologium in pera gestet, eius horologii rotulae unico tantum motu sibi proprio mouebuntur, sed participabunt etiam ex alio, quatenus, adiunctae homini ambulanti, unam cum illo materiae partem component, et ex alio quatenus erunt adiunctae nauigio in mari fluctuanti, et ex alio quatenus adiunctae ipsi mari, et denique alio quatenus adiunctae ipsi terrae, si quidem tota terra moueatur. Omnesque hi motus reuera erunt in rotulis istis; sed quia non facile tam multi simul intelligi, nec etiam omnes agnosci possunt, sufficiet unicum illum, qui proprius est cuiusque corporis, in ipso considerare.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.31.
XXXIIQuomodo etiam motus proprie sumptus, qui in quoque corpore unicus est, pro pluribus sumi possit.II.32
Ac praeterea ille unicus cuiusque corporis motus, qui ei proprius est, instar plurium potest considerari: ut, cum in rotis curruum duos diuersos distinguimus, unum scilicet circularem circa ipsarum axem, et alium rectum secundum longitudinem uiae per quam feruntur. Sed quod ideo tales motus non sint reuera distincti, patet ex eo, quod unumquodque punctum corporis quod mouetur, unam tantum aliquam lineam describat. Nec refert, quod ista linea saepe sit ualde contorta, et ideo a pluribus diuersis motibus genita uideatur: quia possumus imaginari, eodem modo quamcumque lineam, etiam rectam, quae omnium simplicissima est, ex infinitis diuersis motibus ortam esse. Ut si linea AB feratur uersus CD, et eodem tempore punctum A feratur uersus B, linea recta AD, quam hoc punctum A describet, non minus pendebit a duobus motibus rectis, ab A in B et ab AB in CD, quam linea curua, quae a quouis rotae puncto describitur, pendet a motu recto et circulari. Ac proinde, quamuis saepe utile sit unum motum in plures partes hoc pacto distinguere, ad faciliorem eius perceptionem, absolute tamen loquendo, unus tantum in unoquoque corpore est numerandus.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.32.
XXXIIIQuomodo in omni motu integer circulus corporum simul moueatur.II.33
Ex hoc autem quod supra fuerit animaduersum, loca omnia corporibus plena esse, semperque easdem materiae partes aequalibus locis coaequari, sequitur nullum corpus moueri posse nisi per circulum, ita scilicet ut aliud aliquod corpus ex loco quem ingreditur expellat, hocque rursus aliud, et aliud, usque ad ultimum, quod in locum a primo derelictum, eodem temporis momento quo derelictus est, ingrediatur. Hocque facile intelligimus in circulo perfecto, quia uidemus nullum uacuum, nullamque rarefactionem aut condensationem requiri, ut pars circuli A moueatur uersus B, modo eodem tempore pars B moueatur uersus C, C uersus D, ac D uersus A. Sed idem intelligi etiam potest in circulo non perfecto, et quantumlibet irregulari, modo aduertatur, quo pacto omnes locorum inaequalitates inaequali motuum celeritate possint compensari. Sic tota materia contenta in spatio EFGH circulariter moueri potest absque ulla condensatione uel uacuo, et eodem tempore eius pars quae est uersus E, transire uersus G, ac ea quae est uersus G, transire uersus E: modo tantum, ut spatium in G supponitur esse quadruplo latius quam in E, ac duplo quam in F et H, ita etiam quadruplo celerius moueatur in E quam in G, ac duplo celerius quam in F uel H; atque ita reliquis omnibus in locis motus celeritas angustiam loci compenset. Hoc enim pacto, in quouis determinato tempore, tantundem materiae per unam istius circuli partem, quam per alteram transibit.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.33.
XXXIVHinc sequi diuisionem materiae in particulas reuera indefinitas, quamuis eae nobis sint incomprehensibiles.II.34
Fatendum tamen est in motu isto aliquid reperiri, quod mens quidem nostra percipit esse uerum, sed tamen, quo pacto fiat, non comprehendit: nempe diuisionem quarundam particularum materiae in infinitum, siue indefinitam, atque in tot partes, ut nullam cogitatione determinare possimus tam exiguam, quin intelligamus ipsam in alias adhuc minores reipsa esse diuisam. Fieri enim non potest, ut materia quae iam implet spatium G, successiue impleat omnia spatia innumeris gradibus minora, quae sunt inter G et E, nisi aliqua eius pars ad innumerabiles illorum spatiorum mensuras figuram suam accommodet: quod ut fiat, necesse est omnes imaginabiles eius particulas, quae sunt reuera innumerae, a se mutuo aliquantulum remoueri, et talis quantulacumque remotio uera diuisio est.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.34.
XXXVQuomodo fiat ista diuisio, et quod non sit dubitandum quin fiat, etsi non comprehendatur.II.35
Notandum autem me hic non logui de tota materia, sed tantum de aliqua eius parte. Quamuis enim supponamus duas aut tres eius partes esse in G tantae latitudinis quantae est spatium E, itemque etiam plures alias minores, quae maneant indiuisae: nihilominus intelligi potest eas moueri circulariter uersus E, modo quaedam aliae ipsis admistae sint, quae se quomodolibet inflectant, et figuras suas sic mutent, ut iunctae istis figuras suas non ita mutantibus, sed solam celeritatem motus ad rationem loci occupandi accommodantibus, omnes angulos quos istae aliae non occupabunt, accurate compleant. Et quamuis, quomodo fiat indefinita ista diuisio, cogitatione comprehendere nequeamus, non ideo tamen debemus dubitare quin fiat: quia clare percipimus illam necessario sequi ex natura materiae nobis euidentissime cognita, percipimusque etiam eam esse de genere eorum quae a mente nostra, utpote finita, capi non possunt.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.35.
XXXVIDeum esse primariam motus causam: et eandem semper motus quantitatem in uniuerso conseruare.II.36
Motus natura sic animaduersa, considerare oportet eius causam, eamque duplicem: primo scilicet uniuersalem et primariam, quae est causa generalis omnium motuum qui sunt in mundo; ac deinde particularem, a qua fit ut singulae materiae partes motus, quos prius non habuerunt, acquirant. Et generalem quod attinet, manifestum mihi uidetur illam non aliam esse, quam Deum ipsum, qui materiam simul cum motu et quiete in principio creauit, iamque, per solum suum concursum ordinarium, tantundem motus et quietis in ea tota quantum tunc posuit conseruat. Nam quamuis ille motus nihil aliud sit in materia mota quam eius modus; certam tamen et determinatam habet quantitatem, quam facile intelligimus eandem semper in tota rerum uniuersitate esse posse, quamuis in singulis eius partibus mutetur. Ita scilicet ut putemus, cum una pars materiae duplo celerius mouetur quam altera, et haec altera duplo maior est quam prior, tantundem motus esse in minore quam in maiore; ac quanto motus unius partis lentior fit, tanto motum alicuius alterius ipsi aequalis fieri celeriorem. Intelligimus etiam perfectionem esse in Deo, non solum quod in se ipso sit immutabilis, sed etiam quod modo quam maxime constanti et immutabili operetur: adeo ut, iis mutationibus exceptis, quas euidens experientia uel diuina reuelatio certas reddit, quasque sine ulla in creatore mutatione fieri percipimus aut credimus, nullas alias in eius operibus supponere debeamus, ne qua inde inconstantia in ipso arguatur. Unde sequitur quam maxime rationi esse consentaneum, ut putemus ex hoc solo, quod Deus diuersimode mouerit partes materiae, cum primum illas creauit, iamque totam istam materiam conseruet eodem plane modo eademque ratione qua prius creauit, eum etiam tantundem motus in ipsa semper conseruare.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.36.
XXXVIIPrima lex naturae: quod unaquaeque res, quantum in se est, semper in eodem statu perseueret; sicque quod semel mouetur, semper moueri pergat.II.37
Atque ex hac eadem immutabilitate Dei, regulae quaedam siue leges naturae cognosci possunt, quae sunt causae secundariae ac particulares diuersorum motuum, quos in singulis corporibus aduertimus. Harum prima est, unamquamque rem, quatenus est simplex et indiuisa, manere, quantum in se est, in eodem semper statu, nec unquam mutari nisi a causis externis. Ita, si pars aliqua materiae sit quadrata, facile nobis persuademus illam perpetuo mansuram esse quadratam, nisi quid aliunde adueniat quod eius figuram mutet. Si quiescat, non credimus illam unquam incepturam moueri, nisi ab aliqua causa ad id impellatur. Nec ulla maior ratio est, si moueatur, cur putemus ipsam unquam sua sponte, et a nullo alio impeditam, motum illum suum esse intermissuram. Atque ideo concludendum est, id quod mouetur, quantum in se est, semper moueri. Sed quia hic uersamur circa terram, cuius constitutio talis est, ut motus omnes qui prope illam fiunt, breui sistantur, et saepe ob causas quae sensus nostros latent: ideo ab ineunte aetate saepe iudicauimus eos motus, qui sic a causis nobis ignotis sistebantur, sua sponte desinere. Iamque procliues sumus ad illud de omnibus existimandum, [&] quod uidemur in multis esse experti: nempe illos ex natura sua cessare, siue tendere ad quietem. Quod profecto legibus naturae quam-maxime aduersatur: quies enim motui est contraria, nihilque ad suum contrarium, siue ad destructionem sui ipsius, ex propria natura ferri potest.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.37.
XXXVIIIDe motu proiectorum.II.38
Et uero quotidiana experientia, in iis quae proiiciuntur, regulam nostram omnino confirmat. Neque enim alia ratio est, cur proiecta perseuerent aliquandiu in motu, postquam a manu iaciente separata sunt, quam quia semel mota pergunt moueri, donec ab obuiis corporibus retardentur. Et manifestum est, ipsa solere ab aÎre, aliisue quibuslibet fluidis corporibus in quibus mouentur, paulatim retardari, atque ideo motum ipsorum diu durare non posse. AÎrem enim motibus aliorum corporum resistere, ipso sensu tactus possumus experiri, si flabello ipsum percutiamus; idemque uolatus auium confirmat. Et nullus alius est liquor, qui non manifestius adhuc, quam aÎr, motibus proiectorum resistat.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.38.
XXXIXAltera lex naturae: quod omnis motus ex se ipso sit rectus; et ideo quae circulariter mouentur, tendere semper ut recedant a centro circuli quem describunt.II.39
Altera lex naturae est: unamquamque partem materiae, seorsim spectatam, non tendere unquam ut secundum ullas lineas obliquas pergat moueri, sed tantummodo secundum rectas; etsi multae saepe cogantur deflectere propter occursum aliarum, atque, ut paulo ante dictum est, in quolibet motu fiat quodammodo circulus, ex omni materia simul mota. Causa huius regulae eadem est quae praecedentis, nempe immutabilitas et simplicitas operationis, per quam Deus motum in materia conseruat. Neque enim illum conseruat, nisi praecise qualis est eo ipso temporis momento quo conseruat, nulla habita ratione eius qui forte fuit paulo ante. Ac quamuis nullus motus fiat in instanti, manifestum tamen est omne id quod mouetur, in singulis instantibus quae possunt designari dum mouetur, determinatum esse ad motum suum continuandum uersus aliquam partem, secundum lineam rectam, non autem unquam secundum ullam lineam curuam. Ut, exempli causa, lapis A, in funda EA per circulum ABF rotatus, eo instanti, quo est in puncto A, determinatus quidem est ad motum uersus aliquam partem, nempe secundum lineam rectam uersus C, ita scilicet ut linea recta AC sit tangens circuli. Non autem fingi potest illum determinatum esse ad ullum motum curuum: etsi enim prius uenerit ex L ad A per lineam curuam, nihil tamen istius curuitatis intelligi potest in eo remanere, dum est in puncto A. Hocque etiam experientia confirmatur, quia si tunc e funda egrediatur, non perget moueri uersus B, sed uersus C.ex quo sequitur, omne corpus quod circulariter mouetur, perpetuo tendere ut recedat a centro circuli quem describit. Ut ipso manus sensu experimur in lapide, dum illum funda circumagimus. Et quia consideratione ista in sequentibus saepe utemur, diligenter erit aduertenda, fusiusque infra exponetur.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.39.
XLTertia lex: quodunum corpus, alteri fortiori occurrendo, nihil amittat de suo motu; occurrendo uero minus forti, tantum amittat, quantum in illud transfert.II.40
Tertia lex naturae haec est: ubi corpus quod mouetur alteri occurrit, si minorem habeat uim ad pergendum secundum lineam rectam, quam hoc alterum ad ei resistendum, tunc deflectitur in aliam partem, et motum suum retinendo solam motus determinationem amittit; si uero habeat maiorem, tunc alterum corpus secum mouet, ac quantum ei dat de suo motu, tantundem perdit. Ita experimur dura quaelibet corpora proiecta, cum in aliud durum corpus impingunt, non ideo a motu cessare, sed uersus contrariam partem reflecti; contra uero, cum occurrunt corpori molli, quia facile in illud motum omnem suum transmittunt, ideo statim ad quietem reduci. Atque omnes causae particulares mutationum, quae corporibus accidunt, in hac tertia lege continentur, saltem eae quae ipsae corporeae sunt; an enim, et qualem, mentes humanae uel Angelicae uim habeant corpora mouendi, non iam inquirimus, sed ad tractationem de homine reseruamus.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.40.
XLIProbatio prioris partis huius regulae.II.41
Demonstratur autem prior pars huius legis, ex eo quod differentia sit inter motum in se spectatum et ipsius determinationem uersus certam partem, qua fit ut ista determinatio possit mutari, motu integro remanente. Cum enim, ut ante dictum est, unaquaeque res, non composita, sed simplex, qualis est motus, semper esse perseueret, quamdiu a nulla causa externa destruitur; et in occursu duri corporis, appareat quidem causa quae impediat, ne motus alterius corporis, cui occurrit, maneat determinatus uersus eandem partem; non autem ulla, quae motum ipsum tollat uel minuat, quia motus motui non est contrarius: hinc sequitur illum idcirco minui non debere.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.41.
XLIIProbatio posterioris partis.II.42
Demonstratur etiam pars altera ex immutabilitate operationis Dei, mundum eadem actione, qua olim creauit, continuo iam conseruantis. Cum enim omnia corporibus sint plena, et nihilominus uniuscuiusque corporis motus tendat in lineam rectam, perspicuum est Deum ab initio, mundum creando, non modo diuersas eius partes diuersimode mouisse, sed simul etiam effecisse, ut unae alias impellerent motusque suos in illas transferrent: adeo ut iam, ipsum conseruando eadem actione, ac cum iisdem legibus cum quibus creauit, motum, non iisdem materiae partibus semper infixum, sed ex unis in alias prout sibi mutuo occurrunt transeuntem, conseruet. Sicque haec ipsa creaturarum continua mutatio immutabilitatis Dei est argumentum.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.42.
XLIIIIn quo consistat uis cuiusque corporis ad agendum uel resistendum.II.43
Hic uero diligenter aduertendum est, in quo consistat uis cuiusque corporis ad agendum in aliud, uel ad actioni alterius resistendum: nempe in hoc uno, quod unaquaeque res tendat, quantum in se est, ad permanendum in eodem statu in quo est, iuxta legem primo loco positam. Hinc enim id quod alteri coniunctum est, uim habet nonnullam, ad impediendum ne disiungatur; id quod disiunctum est, ad manendum disiunctum; id quod quiescit, ad perseuerandum in sua quiete, atque ex consequenti ad resistendum iis omnibus quae illam possunt mutare; id quod mouetur, ad perseuerandum in suo motu, hoc est, in motu eiusdem celeritatis et uersus eandem partem. Visque illa debet aestimari tum a magnitudine corporis in quo est, et superficiei secundum quam istud corpus ab alio disiungitur; tum a celeritate motus, ac natura et contrarietate modi, quo diuersa corpora sibi mutuo occurrunt.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.43.
XLIVMotum non esse motui contrarium, sed quieti; et determinationem in unam partem, determinationi in partem oppositam.II.44
Atque notandum est, unum motum alteri motui aeque ueloci nullo modo esse contrarium, sed proprie tantum duplicem hic inueniri contrarietatem. Unam inter motum et quietem, uel etiam inter motus celeritatem et tarditatem, quatenus scilicet ista tarditas de quietis natura participat. Alteram inter determinationem motus uersus aliquam partem, et occursum corporis in illa parte quiescentis uel aliter moti; atque pro ratione partis in quam corpus alteri occurrens mouetur, haec contrarietas est maior uel minor.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.44.
XLVQuomodo possit determinari, quantum cuiusque corporis motus mutetur propter aliorum corporum occursum; idque per regulas sequentes.II.45
Ex quibus ut possimus determinare, quo pacto singula corpora motus suos augeant uel minuant, uel in alias partes conuertant, ob aliorum corporum occursus: oportet tantum calculo subducere, quantum in unoquoque sit uirium, siue ad mouendum, siue ad motui resistendum; ac pro certo statuere, illud semper, quod ualentius est, sortiri suum effectum. Hocque facile calculo subduci posset, si duo tantum corpora sibi mutuo occurrerent, eaque essent perfecte dura, et a reliquis omnibus sic diuisa, ut eorum motus a nullis aliis circumiacentibus impedirentur nec iuuarentur; ea enim regulas sequentes obseruarent.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.45.
XLVIPrima.II.46
Primo, si duo illa corpora, puta B et C, essent plane aequalia, et aeque uelociter mouerentur, B quidem a dextra uersus sinistram, et C illi in directum a sinistra uersus dextram, cum sibi mutuo occurrerent, reflecterentur, et postea pergerent moueri, B uersus dextram et C uersus sinistram, nulla parte suae celeritatis amissa.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.46.
XLVIISecunda.II.47
Secundo, si B esset tantillo maius quam C, caeteris positis ut prius, tunc solum C reflecteretur, et utrumque uersus sinistram eadem celeritate moueretur.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.47.
XLVIIITertia.II.48
Tertio, si mole essent aequalia, sed B tantillo celerius moueretur quam C, non tantum ambo pergerent moueri uersus sinistram, sed etiam transferretur ex B in C media pars celeritatis qua hoc ab illo excederetur: hoc est, si fuissent prius sex gradus celeritatis in B, et quatuor tantum in C, post mutuum occursum unumquodque tenderet uersus sinistram, cum quinque gradibus celeritatis.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.48.
XLIXQuarta.II.49
Quarto, si corpus C plane quiesceret, essetque paulo maius quam B, quacumque cum celeritate B moueretur uersus C, nunquam ipsum C moueret; sed ab eo repelleretur in contrariam partem: quia corpus quiescens magis resistit magnae celeritati quam paruae, idque pro ratione excessus unius supra alteram; et idcirco semper maior esset uis in C ad resistendum, quam in B ad impellendum.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.49.
LQuinta.II.50
Quinto, si corpus quiescens C esset minus quam B, tunc, quantumuis tarde B uersus C moueretur, illud secum moueret, partem scilicet sui motus ei talem transferendo, ut ambo postea aeque celeriter mouerentur: nempe, si B esset duplo maius quam C, transferret ipsi tertiam partem sui motus, quia una illa tertia pars tam celeriter moueret corpus C, quam duae aliae residuae corpus B duplo maius. Et ita, postquam B ipsi C occurrisset, una tertia parte tardius moueretur quam prius, hoc est, tantundem temporis requireret, ut moueretur per spatium duorum pedum, quam prius ut moueretur per spatium trium. Eodem modo, si B esset triplo maius quam C, transferret ipsi quartam partem sui motus; et sic de caeteris.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.50.
LISexta.II.51
Sexto, si corpus C quiescens esset accuratissime aequale corpori B uersus illud moto, partim ab ipso impelleretur, et partim ipsum in contrariam partem repelleret: nempe, si B ueniret uersus C cum quatuor gradibus celeritatis, communicaret ipsi C unum gradum, et cum tribus residuis reflecteretur uersus partem aduersam.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.51.
LIISeptima.II.52
Denique, si B et C uersus eandem partem mouerentur, C quidem tardius, B autem illud insequens celerius, ita ut ipsum tandem attingeret, essetque C maius quam B, sed excessus celeritatis in B esset maior, quam excessus magnitudinis in C: tunc B transferret tantum de suo motu in C, ut ambo postea aeque celeriter et in easdem partes mouerentur. Si autem e contra excessus celeritatis in B minor esset, quam excessus magnitudinis in C, B in contrariam partem reflecteretur, et motum omnem suum retineret. Atque hi excessus ita computantur: si C esset duplo maius quam B, et B non moueretur duplo celerius quam C, ipsum non pelleret, sed in contrariam partem reflecteretur; si uero magis quam duplo celerius moueretur, ipsum pelleret. Nempe, si C haberet tantum duos gradus celeritatis, et B haberet quinque, demerentur duo gradus ex B, qui translati in C unum tantum gradum efficerent, quia C est duplo maius quam B: quo fieret ut duo corpora B et C cum tribus gradibus celeritatis postea mouerentur; et ita de caeteris est iudicandum. Nec ista egent probatione, quia per se sunt manifesta.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.52.
LIIIHarum regularum usum esse difficilem, propterea quod unumquodque corpus a multis simul tangatur.II.53
Sed quia nulla in mundo corpora esse possunt a reliquis omnibus ita diuisa, et nulla circa nos esse solent plane dura, ideo multo difficilius iniri potest calculus, ad determinandum quantum cuiusque corporis motus ob aliorum occursum mutetur. Simul enim habenda est ratio eorum omnium, quae illud circumquaque contingunt, eaque, quantum ad hoc, ualde diuersos habent effectus, prout sunt dura uel fluida: quorum ideo diuersitas in quo consistat, hic est quaerendum.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.53.
LIVQuae sint corpora dura, quae fluida.II.54
Nempe, sensu teste, non aliam agnoscimus, quam quod fluidorum partes facile recedant ex locis suis, atque ideo manibus nostris uersus illa se mouentibus non resistant; contra autem durorum partes ita sibi mutuo cohaereant, ut non sine ui, quae sufficiat ad istam illorum cohaerentiam superandam, seiungi possint. Et ulterius inuestigantes qui fiat ut quaedam corpora sine ulla difficultate loca sua corporibus aliis relinquant, alia non item: facile aduertimus ea quae iam sunt in motu, non impedire ne loca quae sponte deserunt ab aliis occupentur; sed ea quae quiescunt, non sine aliqua ui ex locis suis extrudi posse. Unde licet colligere, corpora diuisa in multas exiguas particulas, motibus a se mutuo diuersis agitatas, esse fluida; ea uero, quorum omnes particulae iuxta se mutuo quiescunt, esse dura.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.54.
LVDurorum partes nullo alio glutino simul iungi, quam earum quiete.II.55
Neque profecto ullum glutinum possumus excogitare, quod particulas durorum corporum firmius inter se coniungat, quam ipsarum quies. Quid enim esse posset glutinum istud? Non substantia: quia, cum particulae istae sint substantiae, nulla ratio est cur per aliam substantiam potius quam per se ipsas iungerentur. Non etiam est modus ullus diuersus a quiete: nullus enim alius magis aduersari potest motui, per quem istae particulae separentur, quam ipsarum quies. Atque praeter substantias et earum modos, nullum aliud genus rerum agnoscimus.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.55.
LVIFluidorum particulas aequali ui uersus omnes partes moueri. Et corpus durum in fluido existens, a minima ui posse determinari ad motum.II.56
Quantum autem ad fluida, etsi sensu non aduertamus ipsorum particulas moueri, quia sunt nimis exiguae, facile tamen ex effectibus id colligitur, praecipue in aÎre et aqua, ex eo quod alia multa corpora corrumpant. Neque enim actio ulla corporea, qualis ista corruptio est, sine motu locali esse potest; et causae ipsorum motus infra dicentur. Sed in eo est difficultas, quod istae fluidorum particulae non possint omnes eodem tempore in unamquamque partem ferri; quod tamen requiri uidetur, ut non impediant motum corporum ex qualibet parte uenientium, quemadmodum uidemus illas eum non impedire. Nam si, exempli causa, corpus durum B moueatur uersus C, ac quaedam ex partibus fluidi intermedii D ferantur in contrarium a C uersus B, hae motum eius non iuuabunt, sed contra magis impedient, quam si plane essent sine motu. Quae difficultas ut soluatur, recordandum est, non motum, sed quietem esse motui contrariam; et motus determinationem uersus unam partem esse contrariam eiusdem determinationi uersus partem oppositam, ut iam dictum est; itemque omne id quod mouetur, tendere semper ut pergat moueri secundum lineam rectam. Ex his enim patet: primo, corpus durum B, dum quiescit, magis opponi, sua illa quiete, motibus particularum corporis fluidi D simul spectatis, quam iisdem opponeretur suo motu, si moueretur. Ac deinde, quantum ad determinationem, uerum quidem est tot esse ex particulis ipsius D, quae mouentur a C uersus B, quot sunt quae mouentur in contrarium: quippe eaedem sunt quae, uenientes a C, impingunt in superficiem corporis B, ac deinde retorquentur uersus C. Et quidem singulae ex istis seorsim spectatae, impingentes in B, pellunt ipsum uersus F, atque ita magis impediunt, ne moueatur uersus C, quam si essent sine motu; sed, quia totidem etiam ab F tendunt in B, illudque pellunt uersus C, idcirco, quantum ad hoc attinet, B non magis pellitur uersus unam partem quam uersus alteram, et ideo, nisi quid aliud accedat, manet immotum. Cuiuscumque enim figurae ipsum esse supponamus, semper accurate a totidem particulis fluidi ex una parte pelletur quam ex altera; modo ne fluidum ipsum in ullam partem magis feratur quam in reliquas. Et supponere debemus B omni ex parte a fluido DF circumdari; atque si forte non tanta sit istius fluidi quantitas in F quam in D, nihil refert: quia non agit in B se toto, sed duntaxat iis suis partibus quae superficiem eius attingunt. Hactenus uero spectauimus B ut immotum; iam si ponamus ipsum ab aliqua ui, aliunde adueniente, impelli uersus C, haec uis (quantumuis exigua) sufficiet, non quidem ad ipsum se sola mouendum, sed ad concurrendum cum particulis corporis fluidi FD, ipsasque determinandas ad illud etiam pellendum uersus C, eique partem sui motus communicandam.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.56.
LVIIEiusdem rei demonstratio.II.57
Quod ut clarius intelligatur, fingamus primo, corpus durum B nondum esse in fluido FD, sed huius fluidi particulas aeioa, dispositas in modum annuli, moueri circulariter secundum ordinem notarum aei; aliasque ouyao moueri eodem modo secundum ordinem notarum ouy. Ut enim corpus aliquod sit fluidum, debent eius particulae moueri pluribus modis, ut iam dictum est. Quiescat deinde corpus durum B in hoc fluido FD inter a et o: quid fiet? Nempe particulae aeio impedientur ab ipso, ne possint transire ab o uersus a, ut absoluant circulum sui motus; itemque particulae ouya impedientur ne pergant ab a uersus o; ac uenientes ab i uersus o, pellent B uersus C; itemque uenientes ab y uersus a, ipsum tantundem repellent uersus F: ideoque nullam solae habebunt uim ad illud mouendum, sed reflectentur ab o uersus u, et ab a uersus e, fietque una circulatio ex duabus, secundum ordinem notarum aeiouya. Et ita, propter occursum corporis B, non quidem sistetur ullo modo ipsarum motus, sed mutabitur tantum determinatio, nec incedent per lineas tam rectas, uel tam prope accedentes ad rectam, quam si in B non impingerent. Tandem denique accedat noua aliqua uis, pellens B uersus C, haec uis, quantumuis exigua, iuncta ei qua particulae fluidi, uenientes ab i uersus o, ipsum etiam pellunt uersus C, superabit eam qua uenientes ab y uersus a illud in contrariam partem repellunt; atque ideo sufficiet ad ipsarum determinationem mutandam, et efficiendum ut ferantur secundum ordinem notarum ayuo, in quantum hoc requiritur ad motum corporis B non impediendum: quia, cum duo corpora determinantur ad motum uersus partes plane contrarias et sibi mutuo oppositas, illud in quo maior est uis, alterius determinationem debet mutare. Atque quod hic dico de particulis aeiouy, de omnibus etiam aliis fluidi FD, quae in B impingunt, est intelligendum: quod nempe singulae ex iis quae illud pellunt uersus C, oppositae sint totidem aliis, id ipsum in contrariam partem pellentibus; quodque perexigua uis, illis adiuncta, sufficiat ad harum determinationem mutandam; quodque, quamuis nullae forte describant tales circulos, quales hic repraesentantur aeio et ouya, haud dubie tamen omnes circulariter, et aliquibus modis huic aequipollentibus, moueantur.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.57.
LVIIISi quae fluidi particulae tardius moueantur, quam corpus durum in eo existens, illud hac in parte fluidi rationem non habere.II.58
Ita ergo mutata determinatione particularum fluidi, quae impediebant ne corpus B moueretur uersus C, hoc corpus B omnino incipiet moueri, et quidem eadem cum celeritate, qua uis a fluido diuersa illud pellit, si supponamus in isto fluido nullas esse particulas, quae non celerius, uel saltem aeque celeriter moueantur. Nam, si quae tardius agantur, quatenus ex illis constat, rationem fluidi non habet, neque tunc sufficit minima quaeque uis ad corpus durum in hoc fluido existens mouendum; sed tanta requiritur, ut superet resistentiam quae oritur ab istarum fluidi particularum tarditate. Ac ideo saepe uidemus aÎrem, aquam et alia fluida, multum resistere corporibus, quae in ipsis ualde celeriter aguntur, iisdemque sine ulla difficultate cedere, cum lentius procedunt.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.58.
LIXCorpus durum ab alio duro impulsum, non omnem suum motum ab eo mutuari, sed partim etiam a fluido circumiacente.II.59
Cum autem corpus B sic mouetur uersus C, non putandum est, illud accipere suum motum a sola ui externa ipsum impellente, sed maxima ex parte a fluidi particulis; ita scilicet, ut eae quae componunt circulos aeio et ayuo, tantum amittant de suo motu, quantum acquirent eae particulae corporis duri B quae sunt inter o et a: quippe quae iam facient partem motuum circularium aeioa et ayuoa: quamuis, prout ulterius procedent uersus C, nouis semper fluidi particulis iungantur.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.59.
LXNon posse tamen ab isto fluido maiorem celeritatem acquirere, quam habeat a duro, a quo impulsum est.II.60
Superest tantum hic explicadum, cur paulo ante non dixerim, mutari absolute determinationem particularum ayuo, sed mutari in quantum hoc requiritur, ad motum corporis B non impediendum. Quippe hoc corpus B non potest celerius moueri, quam a ui aduentitia impulsum est, quamuis saepe omnes particulae fluidi FD multo plus habeant agitationis. Hocque unum est ex iis, quae nobis inter philosophandum praecipue sunt obseruanda, ut ne cui causae ullum effectum tribuamus, qui potentiam eius excedat. Ita ponentes corpus durum B, in medio fluidi FD prius immotum, nunc ab externa aliqua ui, exempli causa, a manu mea, tardo motu impelli: cum haec sola impulsio meae manus sit causa cur moueatur, credi non debet ipsum celerius moueri quam impellitur; et quamuis omnes fluidi particulae multo celerius moueantur, non putandum est eas determinari ad motus circulares aeioa et ayuoa et similes, quae sint celeriores hac impulsione, sed ipsas, quatenus celerius aguntur, in quaslibet alias partes, ut prius, ferri.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.60.
LXICum corpus fluidum totum simul uersus aliquam partem fertur, necessario secum deferre corpus durum quod in se continet.II.61
Atque ex his clare percipitur, corpus durum undique fluido cinctum, et in illo quiescens, ibi tanquam in aequilibrio consistere; ac quantumuis sit magnum, semper tamen a minima ui posse in hanc uel illam partem impelli: siue illa uis aliunde adueniat, siue in hoc sit sita, quod fluidum istud, totum simul, uersus aliquem locum feratur, ut flumina feruntur uersus mare, ac totus aÎr, Euro flante, fertur uersus Occidentem. Quod ubi contingit, omnino necesse est, corpus durum, in tali fluido existens, simul cum ipso deferri; nec obstat regula illa quarta, iuxta quam, ut paullo ante dictum est, corpus quiescens a nullo alio se minori, quantumuis celeriter acto, potest ad motum impelli.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.61.
LXIICum corpus durum a fluido sic defertur, non idcirco moueri.II.62
Quinimo, si ad ueram et absolutam motus naturam attendamus, quae consistit in translatione corporis moti ex uicinia corporum aliorum sibi contiguorum, et in utroque ex corporibus, quae se mutuo contingunt, est aequalis, quamuis non eodem modo soleat nominari: plane agnoscemus, non tam proprie moueri corpus durum, cum sic a fluido ipsum continente defertur, quam si non ab eo deferretur, quia tunc nempe a uicinis istius fluidi particulis minus recedit.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.62.
LXIIICur quaedam corpora tam dura sint, ut, quamuis parua, non facile manibus nostris diuidantur.II.63
Unum autem adhuc est, in quo experientia regulis motus, paullo ante traditis, ualde uidetur aduersari: nempe quod uideamus multa corpora, manibus nostris longe minora, tam firmiter sibi mutuo adhaerere, ut nulla earum ui seiungi possint. Si enim illorum partes nullo alio glutino sibi inuicem adhaereant, quam quod singulae iuxta uicinas quiescant, et omne corpus quod quiescit, ab alio se maiori quod mouetur, possit ad motum impelli: non apparet prima fronte ratio, cur (exempli causa) clauus ferreus, uel aliud quodlibet, non magnum, sed ualde durum corpus, sola ui manuum nostrarum in duas partes diuidi non possit. Licet enim unamquamque mediam partem istius claui pro uno corpore numerare; cumque ista media pars manu nostra sit minor, uidetur eius ui debere posse moueri, atque sic ab alia media parte diuelli. Sed notandum est manus nostras esse admodum molles, siue ad naturam corporum fluidorum magis quam durorum accedentes; ideoque non totas simul agere solere in corpus ab iis mouendum, sed eam tantum ipsarum partem, quae, corpus istud tangens, tota simul in illud incumbit. Quippe, sicuti media pars claui ferrei, quatenus ab alia eius media parte est diuidenda, rationem habet unius corporis: sic pars manus nostrae proxime illam tangens, et ipsa minor, quatenus a reliquis eiusdem manus partibus seiungi potest, habet rationem alterius corporis. Et quia facilius a reliqua manu potest separari quam pars claui a reliquo clauo, et ista separatio sine doloris sensu fieri nequit, ideo clauum ferreum sola manu frangere non possumus; sed si illam malleo, lima, forfice, alioue instrumento muniamus, ut ita eius uis ad partem corporis diuidendi, minorem corpore quo utitur, ad illud diuidendum applicetur, quamlibet eius duritiem poterit superare.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.63.
LXIVNon alia principia in Physica, quam in Geometria, uel in Mathesi abstracta, a me admitti, nec optari, quia sic omnia naturae phaenomend explicantur, et certae de iis demonstrationes dari possunt.II.64
Nihil hic addam de figuris, nec quomodo ex earum infinita uarietate motuum quoque uarietates innumerae consequantur, quia satis ista per se patebunt, ubicumque usus ueniet ut de ipsis agamus. Et suppono meos lectores uel prima elementa Geometriae iam nouisse, uel saltem ingenium satis aptum habere ad Mathematicas demonstrationes intelligendas. Nam plane profiteor me nullam aliam rerum corporearum materiam agnoscere, quam illam omnimode diuisibilem, figurabilem et mobilem, quam Geometrae quantitatem uocant, et pro obiecto suarum demonstrationum assumunt; ac nihil plane in ipsa considerare, praeter istas diuisiones, figuras et motus; nihilque de ipsis ut uerum admittere, quod non ex communibus illis notionibus, de quarum ueritate non possumus dubitare, tam euidenter deducatur, ut pro Mathematica demonstratione sit habendum. Et quia sic omnia Naturae Phaenomena possunt explicari, ut in sequentibus apparebit, nulla alia Physicae principia puto esse admittenda, nec alia etiam optanda.
John Veitch's translation (Edinburgh: Sutherland and Knox, 1850) has no passage at II.64.