Physiologia Epicuro-Gassendo-Charltoniana, or, A fabrick of science natural, upon the hypothesis of atoms founded by Epicurus repaired [by] Petrus Gassendus ; augmented [by] Walter Charleton ...

SECT. II.

THe impossibility of Dividing a Physical Continuum into parts inter∣minably subdivisible, being thus amply Demonstrated; and the So∣phistry of the most specious Recesses, invented to assist the Contrary opi∣nion, clearly detected: the residue of this Chapter belongs to our Vindi∣cation of the same Thesis from the guilt of those Absurdities and In••on∣gruities, which the Dissenting Faction hath charged upon it.

* 1.1Empiricus, with great Virulency of language inveighing against the Pa∣trons of Atoms, accuseth them of subverting all Local Motion, by sup∣posing that not only Place and Time, but also Natural Quantity indivi∣sible beyond Insectile Parts. To make this the more credible, He Ob∣jects (1) That if we assume a Line, consisting of nine Insectils, and ima∣gine two insectile Bodies to be moved, with equal velocity, from the op∣posite extremes thereof toward the middle; it must be, to their mutual occurse, and convention in the middle, necessary that both possess the me∣dian part of the median, or Fifth Insectile place (there being no cause, why one should possess it more then the other) when yet both the Places and Bodies therein moved, are praesumed Insectile, i. e. without parts. (2) That all Bodies must be moved with equal celerity; for, the pace of the Sun and that of a Snail must be aequivelox, if both move through an insectile space, in an insectile Time. (3) That, if many Concentrical Cir∣cles be described by the circumduction of one Rule, defixed upon one of its extremes, as upon a Centre; since they are all delineated at one and the same time, and some are greater then others: it must follow, that un∣equal portions of Circles are described in the same individual point of Time, and consequently that an Insectile of an Interior Circle must be aequated to a sectile of an Exterior.

* 1.2To these our Modern Anti-Epicureans have superadded many other 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, or Inconcistencies, as dependent on the position of Insectility viz. (1) That a Line of unaequal Insectiles, suppose of 3.5.9. or 11. cannot be divided into two equal halfs: when yet, that any Line whatever may be exactly bipartited, is demonstrable to sense. (2) That a less line cannot be divided into so many parts, as a Greater: though the Contra∣ry be concordant to the maximes of Geometry. (3) That though lines drawn betwixt all the points of the Leggs of an Isoscelis Triangle, paral∣lel to its Base, are less then its Base; yet will they be found greater: be∣cause, supposing the Base to be of five points, and the Leggs of 10; it must follow, that the least Line, or the nearest to the Vertex, doth consist of only two points, the second of 3, the third of 4, the fourth of 5, the fifth of 6, the sixth of 7, the seventh of 8, and the greatest, or nearest to the Base, of 9; then which nothing can be more absurd. (4) That the Dia∣gone of a Quadrate would be commensurable in longitude with the side thereof: one and the same point being the measure common to both; though the Contrary is demonstrated by Euclid. (5) That the same Di∣agone of a Quadrate could not be greater then, but exactly adaequate to

the side thereof: because each of all its points must be possessed by just so many, nor more nor fewer lines, then may be drawn betwixt the points of the opposite sides; which is highly absurd. (6) That, with the danger of no less absurdity, would not a semicircle be greater then its Diametre; since to every point in the semicircle there would respond another in the Diametre, and there would be in both as many points, on which as many perpendicular Lines, deduced from them, might be incident. (7) That, according to the supposition of Insectility, of many Concentrick Circles the Exterior would not be greater then the Interior; insomuch as all the Lines drawn from all the points of it toward the Centre, must pass through as many points of the other. Many other Exceptions lye against our In∣sectility; but being they are of the same Nature with these, rather Ma∣thematical, then Physical, and that one common solution will serve them all: we may not abuse our leasure in their recitation.

That there have been hot and scarce ingenious Altercations among the gravest and leading Philosophers, in all ages;* 1.3 and even about those Ar∣guments, which wear the proper Characters of Truth fairly engraven on their Fronts: can be esteemed no wonder; because the general custom of men to speculate the Fabrick of Nature through the deceivable Glass of Authority, doth amply solve it. But, that so many Examples of Sa∣gacity and Disquisition, as have condemned the Hypothesis of Atoms, should think their Choler against the Patrons of it excusable only by the allegation of these light and impertinent Exceptions: cannot be denyed the reputation of a Wonder, and such a one as no plea, but an ambitious Affectation of extraordinary subtilty in the invention of Sophisms (where∣in Fallacy is so neatly disguised in the amiable habit of right Reason, as to be charming enough to impose upon the incircumspection of common Credulity, and cast disparagement upon the most noble and evident Fun∣damentals.) can palliate. For, certainly, They could not be ignorant, that they corrupted the state of the Quaestion; the Minimum, or Insectile of Atomists, being not Mathematicum, but Physicum, and of a far diffe∣rent nature from that Least of Quantity, which Geometricians imagining only, denominate a Point. And therefore, what Cicero (1. de finib.) said against Epicurus; Non esse ne illud quidem Physici, credere aliquid esse mini∣mum: may be justly converted into, Esse praesertim Physici, naturale quod∣dam minimum asserere; since Nature in her Exolutions cannot progress to infinity. We say, Physici; because it is the Naturalist, whose enquiries are confined to sensible objects, and such as are really Existent in Nature: nor is He at all concerned, to use those Abstractions (as they are termed) from Matter; the Mathematician being the only He, who cannot, with safety to his Principles, admit the Tenet of Insectility, or Term of Divi∣sibility. For to Him only is it requisite, to suppose and speculate Quan∣tity abstract from Corporiety; it being evident, that if He did allow any Magnitude divisible only into Individuals, or that the number of possible parts, or points in a Continuum, were definite: then could he not erect Geometrical, or exquisite Demonstrations. And hence only is it, that He supposeth an Infinitude of points in every the least Continuum, or (in his own phrase) that every Continuum is div••sible into parts infinitely subdi∣visible: not that He doth, or can really understand it so; but that many Convenient Conclusions, and no considerable Incongruities, follow upon the Concession thereof. This considered, we need no other evidence,

that all the former Objections, accumulated upon Epicurus by the maliti∣ous Sophistry of Empiricus and others, concern only the Mathematicians, not the Physiologist, who is a stranger to their supposition of interminable Divisibility.

* 1.4If this Response praevail not, and that we must yet sustain this seem∣ing Dilemma; Either the suppositions of the Mathematicians are True or False: if true, then doth their verity hold, when accommodated to Physical Theorems, by the assumption of any sensible Continuum, or real Magnitude; if false, then are not the Conclusions Necessary, that are deduced from them, but the contray is apparent in their de∣monstrations; Therefore, &c. Our Expedient is, that, though we should concede those suppositions to be False, yet may they afford true and necessary Conclusions: every Novice in Logick well knowing how to extract undeniable Conclusions out of most false propositions, only supposed true, as may be Instanced in this Syllogism. Omnes arbores sunt in coelo (that's false) sed omnia sydera sunt Arbores (that's false) Ergo, omnia sydera sunt in coelo (that's indisputable). Besides, 'tis evident, that of those many Hypotheses celebrated by Astronomers, ei∣ther no one is absolutely true, or all except one, are false: yet Ex∣perience assures, that from all, at least from most of them the Motions of Coelestial Bodies may be described, and respective Calculations insti∣tuted with equal Certude.

Digression.

* 1.5Here, because our Reader cannot but perceive us occasionally fallen into the mouth of that eminent Quaestion; An liceat in materiam physi∣cam, sive sensibilem, transferre Geometricas Demonstrationes? Whether it be convenient to transfer Geometrical Demonstrations to Physical or sensible Quantity? Since they, who accept the Negative, seem to ad∣nihilate the use of Geometry: we need not deprecate his impatience, though we digress so long, as to praesent him the summary of our thoughts concerning it.

First, we conceive it not justifiable, alwayes to expect the eviction of Physical Theorems; by Geometrical Demonstrations. This may be authorized from hence, that Geometricians themselves, when they fall upon the theory of those parts of the Mathematicks, which are Physicoma∣thematical, or of a mi••t and complex Consideration, are frequently neces∣sitated to convert to suppositions, not only different from, but directly and openly repugnant to their own proper and establisht maxims. Thus▪ in Opticks, Euclid concedes a Least Angle; and Vitellio admits a Least Light, such as being once understood to be divided, hath no longer the act of Light, i. e. wholly disappears: which is no less, then in Opticks to al∣low a Term, or point of Consistence to the Division of Quantity, which yet in Geometry they hold capable of an infinite process. We are pro∣vided of a most pertinent Example, for the illustration of the whole mat∣ter. The Geometrician Demonstrateth the Division of a Line into two equal segments, to be a thing not only possible, but most easie: and yet cannot the Physiologist be induced to swallow it, as really performable.

For He considers (1) That the superfice of no body can be so exactly smooth and polite, as to be devoyd of all uneveness or asperity, every common Microscope discovering numerous inaequalities in the surface of even the best cut Diamonds, and the finest Chrystal, Bodies, whose Tra∣lucency sufficiently confesseth them to be exceeding polite: and conse∣quently, that there is assumable thereon no Line so perfectly uniform, as not to be made unequal by many Valleculae and Monticulae, small pits and protuberances frequently interjacent. (2) That the Edge of no Dissecting Instrument can be so acute, as not to draw a line of some Latitude. (3) That should the edge of the acutest Rasor be laid on the foot of a Handworm, which may be effected by the advantage of a good Magnify∣ing Glass, and a steady hand: yet is that composed of many Myriads of Atoms, or insensible particles of the First universal Matter. And thence Concludes that no real Line drawn upon the superfice of any the smoothest Body, can be practically divided into two Halfs, so exactly, as that the se∣ction shall be in that part, which is truly the median to both extremes. Since, that part, which appears, to the sense, to be the median, and is most exiguous; doth yet consist of so many Myriads of particles, as that though the edge of the Rasor be imposed by many Myriads of par∣ticles aside of that, which is truly in the middle, yet will it seem to the eye still to be one and the same. This duely perpended, we have no cause to fear the section of an Atome, though the edge of a knife were imposed directly upon it: Since the edge must be gross and blunt, if compared to the exility of an Atome: so that we may allow it to divide an Assembly, or Heap of Atoms, but never to cut a single one.

Secondly, We judge it expedient in some cases to accommodate sup∣positions Geometrical to Subjects merely Physical; but to this end only, that we may thereby acquire majorem 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, a greater degree of Acute∣ness, or advance our speculations to more Exactness. Thus the soul of the Mathematicks, Archimed, (de Arenarum num.) supposed the Diametre of a grain of Poppy seed to consist of 10000 particles; not that He conceived that any Art could really discern so vast a multitude of parts in a body of so minute circumscription: but that, by transferring the same reason to ano∣ther body of larger dimensions, He might attain the certitude of his Propo∣sition by so much the nearer, by how much the less he might have erred by neglecting one of those many particles. Thus also is it the custom of Geome∣tricians, in order to their exactness in Calculations, to imagine the Semi-diametre, or Radius of any Circle, divided into many Myriads of Parts; not that so many parts can be really distinguished in any Radius, but that, when comparation is made betwixt the Radius, and other right lines, which in parts Aliquotal, or such as are expressed by whole numbers, do not ex∣actly respond thereunto, particles may be found out so exile, as though one, or the fraction of one of them be neglected yet can no sensible Error ensue thereupon. And this (in a word) seems to be the true and only Cause, why Mathematicians constantly suppose every Continuum to consist of Infinite parts: not that they can, or ought to understand it to be Really so; but that they may conserve to themselves a liberty of insensible Latitude, by subdividing each division of Parts into so many as they please; For, they well know, that the Physiologist is in the right, when He admits no Infinity, but only an Innumerability of parts in natua∣ral Continuum. Lastly, if these Reasons appear not weighty enough to

counterpoise the Contrary Persuasion; we can aggravate them with a Grain of noble Authority. For, no meaner a man then Plato, who seems to have understood Geometry as well as the Aegyptian Theuth, the suppo∣sed Inventor thereof (vide Platon. in Phaedro) and to have honoured it much more in a solemn Panegyrick (9. dialog. de Rep.) sharply reprehends Eudoxus, Archytas, Menaechonus, &c. for their errour in endeavouring to adjust Geometrical speculations to sensible objects: subnecting in positive termes, that (〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉) thereby the good of Geometry was corrupted. (Lege Marsil. Ficin. in Compend▪ Timaei. cap. 19.)

Notes

• * 1.1

  Art. 1. The Absurdi∣ties, by Empi∣ricus, charged upon the sup∣position of on∣ly Finite parts in a Continu∣um.
• * 1.2

  Art. 2. The sundry Inc••ngruities & Inconsistenc••s, by the Modern Anti-Democri∣tans, imputed to the suppos••∣tion of Insecti∣lity.
• * 1.3

  Art. 3. The full Dero∣gation of the 〈◊〉〈◊〉 all together, by o••e single Resp••nse; that the minimum of Atomists is not Mathema∣tical, but Ph••∣sical, contrary to their prae∣sumption.
• * 1.4

  Art. 4. A seeming D••∣lemma of the Adversary, ex∣peditely eva∣ded.
• * 1.5

  Art. 5. A Digression, stating and determining that notable Quaestion, Whether Geo∣met••ical De∣m••nstrations may be conveni∣niently trans••f••••red to Physi∣cal or sensible Quantity?