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 ...

CHAP. II. OF MOTION.

SECT. I.

CErtainly, the Great Galilaeo did most judiciously and like himself,* 1.1 to lay the foundation of his incomparable En∣quiry into the most recondite myste∣ries of Nature, in the Consideratin of the Nature of MOTION, and severe Examination (that we may not say, subversion) of Aristotles Doctrine concerning it. Bec••use, Motion being the Heart, or rather the Vital Faculty of Nature, without which the Universe were yet but a meer Chaos; must also be the no∣blest part of Physiology: and consequently, the speculation thereof must be the most advantageous Introduction to the Anatomy of all other parts in the vast and symmetrical Body of this All, or Adspectable World. Again, if Motion and Quiet be the principal modes of Bodies Existing, as Des Cartes (in princip. philosoph. part. 2. sect. 27.) seems strongly to assert▪ if Generation, Corruption, Augmentation, D••minution, Alteration, be only certain species, or more properly the Effects of Motion, as our imme••••••te∣ly praecedent Ch••pter cleerly imports; and that we can have no other Cog∣nizance of the conditions or qualities of sensible objects, but what results from our perception of the Impulses made upon the organs of our senses, by their species thither transmitted: assuredly, the Physiologist is highly concerned to make the contemplation of Motion, its Causes, Kinds, and U∣niversal Laws, the First link in the chain of all his Natural Theorems. And, truly, this we our selves had not endeavoured, had not our firm resolution to avoid that ungrateful prolixity, which must arise from the frequent Re∣petitions of the same Notions, in the solution of various natural Apparen∣ces▪ and our design of insensibly praeparing the minde of our 〈…〉〈…〉 the gra••ual insinu••ti••n of all both C••uses and Effects o•• 〈…〉〈…〉, as they stood in relation to this or th••t particul••r sensible 〈◊〉〈◊〉, ••nd principally to Visibles, and the Grav••tation of Bodies: not only inc••••ed,

but by a necessity of Method almost constrained us, to make that the He••, or Fringe, which otherwise ought to have been the First Thread in this rawe and loosely contexed Web of our Philosophy.

Nor, indeed, can we yet praevent all Repetitions; for, our praesent Th••∣orem being Physicomathematical, and such as must borrow some light, by way of Reflection, from ••••ndry observables, occasionally diffused upon se∣veral of our Discourses praecedent: we need not despair of a Dispensation for our Recognition o•• a few remarkable passages, directly relating there∣unto, and especially of these Three Epicu••ean Postulates, or Principles.

* 1.2The FIRST, that 〈◊〉〈◊〉 Adam or Radical and Primary Cause of all mo∣tion competent to Concretions, i•• the inhaerent Gravity of their Materials, A∣••oms▪ whether the 〈◊〉〈◊〉 be moved spontaneously, or violently, i. e. by it self▪ or another. The Reason of its spontaneous or self-motion may be thus conceived. Whil•• Atom•• ••re, by their own inamissible propensity to motion, variously agitated and ••umultuous in any Concretion; if those which are more movea•••••• and agile then the rest, so conspire together in the course of their tendency, as to discharge their united forces upon one and the same quarter o•• 〈◊〉〈◊〉 body containing them, and so attempt to disen∣gage themselves towar•••••• ••t region: then do they propel the whole body to∣ward the same region, transferring the rest of their le••s active associates along with them. It being h••••hly consentaneous, that motion may be expressed first in the singular Atom•• themselves, then in the smallest masses, or ••nsen∣sible Combinations of Atoms; and successively in greater and greater, till the sensible parts of 〈◊〉〈◊〉, and at length the whole bodies ••hemselves par∣ticipate the motion, an•• undergo manifest agitation: as Lucretius (in lib. ••••) hath with lively Arguments asserted.

* 1.3And this, certainly, hath far a stronger claim to our assent, than that fun∣damental Position of A••istotle; that the First Princ••ple of motion in any thing, is the very Form•• of the thing moved. For, unless He shall give us leave, by the word 〈◊〉〈◊〉, to understand a certain tenuious Contexture ••f most subtile and most active Atoms, which being diffused through the body o•• mass consisting of other less subtile, and in respect of their greater com∣paction together, or 〈◊〉〈◊〉 close reciprocal revinction, less active Atoms; doth, by t••e impression 〈◊〉〈◊〉 its force or Virtue motive, upon the whole, or any sensible part thereof become the Principle of motion to the whole bo∣dy: we say, unless he 〈◊〉〈◊〉 be pleased to allow us this interpretation, we shall t••ke the liberty to 〈◊〉〈◊〉 ••hat it is absolutely incomprehensible. For, that the Forme of a thing, accepted according to His notion of a Forme, should be the Proto-cause or 〈◊〉〈◊〉 of its motion; is unconceivable; since, ac∣cording to the tenour 〈◊〉〈◊〉 Aristotles doctrine, the Forme must be educed out of the Matter, or power of the Matter, that constituteth or amasseth that thing: and consequently▪ 〈◊〉〈◊〉 the Forme must owe as well its very Entity or Be••ng, as 〈…〉〈…〉 onely to the matter it self; which yet He de∣scribe•• to be something 〈◊〉〈◊〉, nothing) meerly Passive, and devoi•• of 〈…〉〈…〉. How, therefore, can it appear other than a 〈…〉〈…〉 Contradiction to any man, whose intellect is not eclipsed, by rea∣so•• 〈…〉〈…〉 of its proper Organ; that that Matter, which in 〈…〉〈…〉 of Moving, should nevertheless be able 〈…〉〈…〉, and potent Activity, upon the Form, sup∣posed

to be absolutely distinct from matter? Doubtless, the Forme doth not derive that Motive Virtue from the Qualities inhaerent in the matter: forasmuch as those Qualities, as even the Aristoteleans themselves furiously contend, are but the meer Results of the Power of the matter. Nor from the Efficient; because ••hey account the Efficient to be a Cause meerly External, and to transfuse nothing of it self into the thing Generated; but only to display its Efficiency, or (to speak in their own dialect) to execute its Causality upon the matter. Again, it being necessary, that all that Vir∣tue of Moving, which is in the Efficient, should depend solely and wholly upon its Forme; and that Forme also ought, by equal reason, to be educed out of the matter: They lose themselves in a round of Petitions, and still reduce themselves to the same Difficulty, How it is possible, that the matter should give that Faculty of Mot••on to the Forme, which it self never had.

The SECOND; that in General there is no other but Local motion▪* 1.4 Wherein that we may plainly and briefly instruct you, how far Epicurus dif∣fers from Aristotle, Plato, and some other Philosophers; give us leave to commemorate unto you.

(1) That Aristotle putting a difference betwixt [〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉] Motion and Mutation, is not sufficiently constant in his doctrine: sometimes making Mutation to be the Genus, and Moti∣on onely a certain species thereof; and sometimes, by inversion of the tables, making Motion the Genus, and mutation a species there∣of. For, (in 5. physic. cap. 2.) stating Mutation betwixt two Terms, â quo, & ad quem, the from whence and to what; He assigns unto 4 distinct Modes, or Manners; the first, •• subjecto in subjectum; the second, ex non subjecto in non subjectum; the third, ex non subjecto in subjectum; the fourth ex subjecto in non subjectum: and thereupon infers, as of pure necessity, that since nothing can be changed according to the second mode, therefore must mutation according to the third, be Generation; according to the fourth, be Corruption; and according to the first, be Motion, which is always either from Quantity to Quantity, or from Quality to Quality, or from Place to Place. Whereas, in another place (viz. ••. Physic. 1.) He positive∣ly teacheth, that Motion is a certain Act, to which that p••sseth, which is in Power; and so makes the species thereof to be not only those motions, whose terms on either side are Positive, or (in his own phrase) Contrary, as are those which concern ••uantity, Quality, Place: but those also, whose each term is Privative, as are those which concern substance. And here∣upon He seems to have grounded that memorable Division of Motion (lib. de praedicam. cap. de motu.) into six species, viz. Generation, Corrupti∣on, Accretion, Diminution, Alteration, and Lation or Loco-motion: whereof the first two are according to substance; the second two, accor∣ding to Quantity; the fifth, according to Quality; and the Last, according to Place.

(2) That Plato seems constantly to accept Mutation for the Genus, and motion for one species thereof: subdividing motion into two species, La∣tion and Alteration. Forasmuch as in one place ••viz. in Polit.) He terms the Conversions of the Coelestial bodies, Mutations: and in another ••in Phaed.) he takes Alteration for mutation; saying most eloquently in the person of Socrate•• (in the••••.) Illu••••e ••overi appellas, du•• quidpi•••• locum

•• loco mutat, aut in ••ode•• ••onvertitur? Tho. ••quid••m. Socrat. illa ergo una sit species motus. A••▪ cum in eodem quidem p••rs••at; sed senescit tamen, aut ex albo fit nigrum, ex molli durum, aut alteratione quapiam alterum ••∣vadit▪ an non ••ideri 〈◊〉〈◊〉 motu•• spe••••em ne••esse est? Tho mihi quidem videtur. Socra••. 〈…〉〈…〉 id igitur; duas, inquam, esse motus species, Alterationem, & 〈◊〉〈◊〉, Circulationemve? &c.

(3) That most other ••hilosophers, insisting in the steps of Plato con∣stitute only two kinds o•• Motion; only in this they differ from Him, that what He calls [〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉], 〈◊〉〈◊〉, or Circumlation▪ They c••ll [〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉] Transition, or motion Transitive: and what ••e names [〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉] Alteration, They denominate [〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉] Mutation or [〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉] Motion Mutative▪ as Empiricus (2. advers. physic.) 〈…〉〈…〉 observed.

(4) That Epicuru•• (〈◊〉〈◊〉 the same Empiri••us, in the same place, attesteth) is chief of those Physio••••••ists, who accounted the Motion of Transition as the G••nus▪ and 〈◊〉〈◊〉 or Alteration as only the species thereof. And this upon 〈…〉〈…〉. Forasmuch as Alteration is nothing else but the consequen•• o•• 〈◊〉〈◊〉, whereby Atoms, or the insensible parti∣cles of Concretions 〈…〉〈…〉, decede, concur, complicate, and change their former positions, 〈…〉〈…〉 ••ender the sensible parts o•• whole of them other than they 〈…〉〈…〉. Which being considered, we are only to advertise farther▪ that 〈◊〉〈◊〉 Argument of our praesent Enquiry, is not Moti∣tion as it is proper to 〈◊〉〈◊〉, as they either concur to the first constitution of a body, or are 〈◊〉〈◊〉 at the dissolution thereof; in which respect it may comprehend 〈◊〉〈◊〉 and Corruption: nor as they concur to the Augmentation of a 〈…〉〈…〉 constituted, or flye off from it, and by their decedence 〈◊〉〈◊〉, in which respect it may comprehend Accreti∣on and Diminution: 〈…〉〈…〉 they are variously transported, and so conduce to affect the same bod•• 〈◊〉〈◊〉 divers Qualities; in which respect it may in∣clude Alteration. 〈◊〉〈◊〉 concerning Motion under all these Terms and relations, we have 〈◊〉〈◊〉 discoursed already, in places to which those considerations did 〈◊〉〈◊〉 refer themselves. But, our subject is Motion a•• proper to a body 〈◊〉〈◊〉 which sensibly changes the Place of its whole, or some sensible part. 〈…〉〈…〉 motion plainly distinguisheth it self from 〈◊〉〈◊〉 that in motio•• 〈◊〉〈◊〉 whole Body, V. G. of a man, or some sensible part thereof, as his 〈…〉〈…〉 ••oot is translated from one place to another: but in Mutation only 〈◊〉〈◊〉 insensible particles of a body, or any part thereof, change their positions 〈◊〉〈◊〉 places, though the whole, or sensible parts there∣of remain qu••et.

* 1.5Th•• THIRD▪ 〈◊〉〈◊〉 Motion or Loco motion (for, the common Notion, 〈…〉〈…〉, so soon as he hears the word motion 〈…〉〈…〉 more intelligibly and properly defined by Epicurus, 〈…〉〈…〉 the migration of a body from place 〈…〉〈…〉 be Actus entis potestate, quatenus est tale. For 〈…〉〈…〉 one; so nothing can be more 〈…〉〈…〉

〈…〉〈…〉 enough to furnish you with patience, 〈…〉〈…〉 of Aristotle, in that his aenig∣matical

Definition; we advise you to reflect upon the whole syntax of those conceptions, from whence He seems to have deduced it. Know, therefore, that He conceived, that there are some things, which always pos∣sess, and in••missibly retain the perfection due to their nature, [〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉] Perfec••i-habit••one, or (as his Expositors commonly render it) Act•• solum, in Act only: and others ••gain, which are not indeed, without some perfection, but such as they are c••pable of losing, and may at the same time acquire another; so that they may be said to be [〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉] both in Act and Power together. For, He admits nothing to be meerly in Power; because He would not allow, either that matter can exist withou•• Forme; or that any thing in nature can be altogether without some perfe∣ction. Now, those things, which are only in Act, must, according to His opinion, be no other but the Coelestial Bodies▪ insomuch as they alone seem constantly and in••missibly to posses•• their Forme, nor can their sub∣stan••e or m••tter ••e ••onceived, to h••ve a Capa••••ty of ••eceiving any other Forme wh••tever. But, those which are both in Act and Power at once, are all sub••un••ry Bodi••s, insomuch ••s their substance, or matter so stands possest of so••e one Forme in Act, ••s th••t it still remains in a Capacity of being d••vested of that ••orme, and in••••sted with a new one; and the whole Compositum ••o hath it•• certain Quantity, certain Quality, certain Place, and whatever other ••if there be any other) perfection requisite to its par∣ticular nature, as that it may notwithstanding be totally deprived thereof, and obtain another. Know also, that He useth the word, 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, sometimes for the perfection already acquired; sometimes for the very manner of its acquisition, in which ••ense it is a certain Action, and so comes to be called [〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉] an Energy; This being praesupposed; He infers, that Motion is [〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉] an Act, according to the posterior mode: understanding it to be as it were the Way, or manner, whereby the perfe∣ction is acquired, or the Acquisition it self: which is also a certain perfecti∣on, but competent to an Entity, or moveable, not as it hath a perfection, which it loseth; but as it hath a Power to that, which it receiveth. And hence is it, that He resolved to define Motion to be the Act of an Entity in Power, a•• it is such.

Which notwithstanding all the light this our most favourable Descant,* 1.6 or any other can cast upon it, is yet mu••h inferior in Perspicuity to tha•• most natural and familiar one of Epicurus; that Motion is the migration or Remove of a body from one place to another. Nevertheless, to verifie that unhappy proverb, that n•• Truth can be made so plain, as not to be impug∣ned; Empericus ••2. advers. physic.) hath charged it with sundry Imper••e∣ctions. As

(1) That it doth not comprehend the motion of a Globe, or wheel cir∣cumvolved upon its Axis▪ forasmuch as a wheel, when circumgyrated up∣on its Axe, is sensibly moved, but not removed from one place to another. But to this we may readily Answer; th••t though the whole wheel be no•• removed out of its who••e place, yet are the Parts of it sensibly transferred from place to place▪ the superior descending to inferior, while the inferior ascend to su••erio•• places, the right hand parts succeeding into the places of the left, as ••••st as the le••t ••••cceed into those of the r••ght, and all parts suc∣cessively ••hi••t••ng their particular places. And upon this distinction of Place into Tota•• and Part••••••▪ was 〈◊〉〈◊〉 that some Philosophers have Defined

motion to be Migrationem de loco in locum, vel totius corporis, vel partis ipsius; or as Chrysippus and Apollodorus (apud s••obaeum, in Eccl. phys.) Mutationem secundum locum, aut ex toto, aut ex parte. Nay, even Plato Himself seems to have had an eye upon the same Difference, when He said, that Local motion was conjunctly Lation, or Circum∣lation.

(2) That likewise the point of that arme of a Compass, which is fixed in the Centre, while the other is moved round, in the descripti∣on of a Circle; is moved, but not removed out of its place: as is also the Hinge of a door, while the door is opened or shut. But, this Objecti∣on must soon yeeld to the same Response, as the former: since tis ma∣nifest, that the parts of the point of the Compass, and Hinge change their Partial places.

(3) That there is a certain sort (He adds, Admirable) of motion, to which the importance of Epicurus Definition doth not extend; which is thus made. Let a man, in a ship under sail, walk, with a staff in his hand, from the for••••astle to the poup of the ship; and with just so much speed, as the ship is carried forward: so that in the same space of time, as the ship is moved a yard forward, the man and the staff in his hand may be moved a yard backward. This done (saith He) doubtless there must be a mo••ion both of the man and his staff; and yet neither of them shall be moved into new place, either as to their whole, or their parts: because both must remain in the same parts of the Aer, and Water, or in the same perpendicular line extended from the mans head to the bottom of the Sea; or, what is the same thing, they shall still possess the same Immoveable space. But, this so admirable Difficulty lies open to a double solution: for it may be Answered. (1) That in this case, the Thighs, Leggs, and feet of the man walking upon the deck of the ship, must be alternately moved into new places; because, as of∣ten as each of his feet is referred from the Anterior to the Posterior part thereof, it must be moved twice as swiftly, as the ship is moved from the Posterior toward the Anterior: since it is absolutely necessary, that the double velocity of one foot should compensate that space of time, in which the other foo•• resteth, while the ship is constantly carried for∣ward in one uniform tenour of motion. And, therefore, his ••eet may be conceived to be alt••rnately moved from place to place; after the same manner, as a man, sitting on a wooden, or standing Horse, doth move his leggs alternately forward and backward: the trunck and upper part of his body rema••ning unmoved, or still keeping the same Centre of Gravity. (2) That the Trunck of his body also must be moved from place to place; and also his ••ead, and the staff in his hand: because, at every step, all of them must be somewhat elevated, and again depressed, or let down. For, in progression, the feet of a man cannot be alternately moved forward, but at every time the one foot is set plainly upon the ground, the trunck and so the head and arms, must sink a little downward; in regard of the Disten∣sion of the muscles o•• ••hat thigh and leg: and again when the other leg is ad∣vanced, and the leg upon which the whole body resteth the while, is elevated upon the toes, to cas•• ••he body forward; the trunck, head and shoulders are lifted a little upward•• ••n respect of the bodies inclining to a new Centre of

Gravity. For, it is most true, what Galilaeo hath most subtly Demonstrated, that a man goes, because he falls: since he could not advance forward, while he kept his body a••quilibrated upon the same Centre of Gravity; but falling ••orward at each s••••p, he sustains himself with the fixing another foot upon •• new Centre of Gravity.

(4) That if we suppose an Individual, or smallest thing to be turned round in the same place; there will be motion, but no change of place, ei∣ther as to the whole, or any part thereof. And we Demand, whether by that Individual He means minimum mathematicum, or Physicum? If Ma∣thematical, the supposition is not to be admitted: because, what is meerly Imaginary is not capable of motion. But, if Physical; then admitting the supposition, we Answer; that the reason of the motion of an Individu∣al moved round in the same place, is the same with that of the motion of a Globe or wheel upon its Axis. For, such a body is not said to be Indivi∣dual, or smallest, because it hath no magnitude or parts designable by the minde; but because there is no force in nature, that can divide and resolve it into those par••s: and therefore, since it is not a meer point, but contains parts superior, inferior, &c. the whole cannot be moved, but some parts must succeed into the places deserted by others; and consequently there must be Loco-motion. Though this also be of the number of such Events, as can hardly be effected by the power of Nature; forasmuch as such a physi∣cal Individual being either permitted to its own liberty, would move spon∣ta••••ously in a direct line, not a circular; or impulsed by another, could not be so exactly circumvolved in a Circle, as not to deflect somewhat, more or less, to one side or other. And thus have we Resolved all the Difficul∣ties, by Emperi••us, objected to the Definition of Motion, given by Epi∣cu••u••.

But yet we have not ascertained our Reader, that there is such a thing as M••ti••n in the World and therefore,* 1.7 that we may not seem to be meerly ••••titionary, in begging that at the hand of another mans charitable Belief, which the stock of our own Reason is rich enough to afford us: we shall bri••fly touch upon that ••uaestion, An sit Motus, Whether there be any Motion in Nature: Especially, forasmuch as it is very well known, that a∣mong the Ancients there was a notable Controversie concerning it. For, some, as Heraclitus▪ Cratylus, Homer, ••mpedocles and Protagoras (as Plato [in theat.] notes at large) affirmed, that All things in the universe are in perpetual Motion: and others, of which number Parmenides, Melissus and Zeno were the Principal, (as Aristotle (1. physic.) particularly records) Ar∣gued, on the contrary, that All things are in perpetual Quiet, or that there is no motion at all.

Now as to the Former; our Quarrel against them is not so great, as that of Ar••stotle was: forasmuch as it carries the face of very great probability that They intended no more than this; that All sublunary Bodies are in perpetual Mutation of their Insensible Particles, not Loco-motion of their sensible Parts, or Whole; or, more plainly, that all Concretions uncessant∣ly suffer those irrequiet Agitations, or intestine Commotions of their insen∣sible particles, from which those sensible Changes, Alteration, Augmentati∣on, Diminution, Generation, and Corruption, are by slow and insensible degrees ••ntroduced upon them. And thus even Aristotle Himself inter∣prets

their opinion; saying (in 8. phys. 3.) they held, that All things are moved [〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉] verum id latere experientiam sensuum, that that motion falls not under the observation of the senses. Which is no more, than what Epicurus, or any man else, imbued with his excellent principles, might have asserted.

And as for the Latter S••ct; neither doth our Choler boyl up against them, to that height, as did Sextus Empericus his, when (in 2. advers. p••ysic.) H•• could not be content ••o nickname them [〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉] the standers; but so far obeys the impuls•• o•• his passion, as to fly out into opprobrious language, and brand them with the ignominious character of [〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉] Unnaturael Philosophers. And our Reasons, why we look not upon them w••th so oblique and 〈◊〉〈◊〉 an eye, as the Vulgar use to do; are these.

(1) Experience doth 〈◊〉〈◊〉 clearly Demonstrate, that there is motion; as that no man can deny 〈◊〉〈◊〉 he must, at the same instant, manifestly re••ute himsel•• with the motion of his tongue. And such is the constant verity of Epicurus his Logical Canon, concerning the Certitude of our senses, as to the information of our 〈◊〉〈◊〉; as that every Philosopher, nay every man ought to allow ••hem to be ju••g••s in cases of sensible Objects: and consequently to conclude, with Arist••••l••; ad mentis imbecillitatem debet referri si quis arbitretur omnia quiescer••, & dimisso sensu, rationem requirat. And, cer∣tainly, whoso seriousl•• impugnes, what the evidence of sense con∣firms; is so easie an Adversary, as to deserve our smiles, rather than our Anger.

(2) Divers have app••••hended, that those Philosophers, who seemed to impugn the being of Motion, did not oppose it in a serious, but purely Pa∣radoxical humor, and an ambition of shewing themselves so transcendently acute, as to be able to ••••dubitate Truths even of the most manifest Certi∣tude. Nor are They, indeed, to be understood in that gross sense, which is so generally passant ••mong Vulgar Authors; forasmuch as it is much mo••e probable, that P••rmenides and Melissus, when they laid down for a maxime Esse omnia unum Ens immobile, so intended Nature, or the All of things, as that they held it, or at least some certain Divine Virtue constantly dif••used through, and an••mating the vast mass of the Universe, to be God, or the Supreme Being; whose propriety it is to be Immoveable, as being Ubi∣quitary and All in All. And, that Zeno himself, the Prince of Antimo∣••••••ts, had some such 〈◊〉〈◊〉; may be naturally collected, as well from the Contents of that Book, commonly adscribed to Aristotle, concerning Xenophanes, Zeno and Gorgias: as from those very Arguments He allead∣ge•• against motion▪ t•••• ••mportance of them all declaring, that his suppo∣sition was, there could 〈◊〉〈◊〉 no motion, if as well motion it self, as Place and 〈◊〉〈◊〉 did consist of In••ectiles, or Indivisibles. Likewise, as for Diodorus, 〈◊〉〈◊〉 fervently addicted 〈◊〉〈◊〉 the Eristick, or Contentious Sect; manifest it is, that 〈◊〉〈◊〉 grand scope in his whole Discourse against motion, was only to evince, that a good W••t cou•••• not want Arguments wherewith to invade and s••••gger the 〈◊〉〈◊〉 of 〈◊〉〈◊〉 ••hing, than which nothing can be more certain. Lastly, as for t••e Pyr••honeans, or Scepticks; the design of all their stra••a∣•••••• against motion, 〈◊〉〈◊〉 to have been only this innocent one: to insi∣•••••••••• that no knowle••••e is exempted from Doubts; and tha•• the mind of

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doth detect the sophisme; for, since the word Esse, to Be, is, according to common signification, con••••nient as well to things Permanent, as Succes∣sive or Fluent; and according to a peculiarly accommodate signification, competent only to things Permanent: it is understood in the former sense, when the Quaestion is, 〈◊〉〈◊〉 where it is, or where it is not? and in the lat∣ter, when the subsumption is, But neither where it is, nor where it is not: according to which reason, ••ou Doubt, Whether a thing Be, while it is mo∣ving. Which considered, when it is Enquired, whether a moveable be moved in the place, where it is, or in that, wherein it is not: we are to Di∣stinguish thus; it is moved in the place, wherein it is Transiently, and mo∣ved in the place wherein 〈…〉〈…〉 not Permanently. And, to your Quaestion, Whether a thing be no•• in a place, when it passeth through a place? We Answer likewise, that it is in a place Transiently, not Permanently. Nor ought this Language to ••o••nd strange, since nothing ought to be concei∣ved to be in any other ma••••er, than what the Nature thereof doth prae∣scribe: and such is the N••ture of Motion, that is should be conceived to be [〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉] a Passing through, not [〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉] a Permansion, or stay∣ing in a place. Lastly, 〈…〉〈…〉 the Arguments of the Scepticks; they are all grounded upon the 〈◊〉〈◊〉 Difficulties as those of Zeno and D••odorus: and therefore must subm••t 〈◊〉〈◊〉 the same Resolutions.

SECT. II.

* 1.8BEing thus praepared 〈◊〉〈◊〉 Considerations of the most Genuine Noti∣on▪ most adaequate Definition, and Primary Cause of Motion in all Concretions▪ and an 〈…〉〈…〉 assurance, that there is such a thing as Mo∣t••on in the world▪ the 〈◊〉〈◊〉 degree to which our Enquiry is to advance, ••s the 〈◊〉〈◊〉 Gener••l and 〈◊〉〈◊〉 KINDS thereof▪ among which, the First we meet with, 〈…〉〈…〉 common Distinction of motion into Natural and Violent.

A Natural motion, 〈◊〉〈◊〉 Aristotle ••8. physic. 4.) is that, whose Princi∣ple is Internal; and a 〈◊〉〈◊〉, that, whose Principle is External: so that, accordingly▪ that Bo•••• 〈◊〉〈◊〉 be said to be moved Naturally, which is mo∣ved 〈…〉〈…〉, which is moved by another. But, for as much as Aristotle 〈…〉〈…〉 much amuse us, while he ever and anon 〈…〉〈…〉 be moved by another, and yet not be moved 〈…〉〈…〉 may be said to be Natural or Violent, in 〈…〉〈…〉 that some more easie and familiar Notion is 〈…〉〈…〉 of those Contrary Terms, Natural and 〈…〉〈…〉 more convenient for us, to understand a 〈…〉〈…〉 which is made either of Natures own accord, or with∣•••••• 〈…〉〈…〉 Violent to be that, which is made either Prae∣•••••• 〈…〉〈…〉 Repugnancy. Thus, the Progressive motion of 〈…〉〈…〉 made of Natures own accord; and yet if 〈…〉〈…〉 a steep hill, leap, or run, the motion

is to be accounted Violent, because though it proceed from an Internal Principle, the Soul of the Animal, yet is it not performed without some Repugnancy, either internal or external. On the contrary; when a Bul∣let is shot through the aer, the motion thereof is violent, because against the nature of the Bullet, and not performed without some repugnancy, either in∣ternal or external: and yet if the same Bullet be rowled upon a smooth plane, the motion thereof is Natural; because though it be caused by an External Principle, yet is it performed without any Repugnancy either in∣ternal or External.

But, that we may take the matter in a higher key,* 1.9 reflecting upon that so often inculcated Epicurean Principle, That all the motive Virtue of Con∣cretions is originally derived from the mobility inhaerent in, and inseparable from Atoms, which compose them; let us observe, that forasmuch as that essential mobility of Atoms doth neither cease, but is only impeded, when Concretions themselves begin to obtain a sensible Quiet; nor is produced anew, but only acquires more liberty, when Concretions begin to be mo∣ved: we may thence justly infer, that just so much motive Force is now, and ever will be in the World, while it is a world, as was in the first moment of its Creation. Which really is the same with that Rule of Des Cartes princip. philosoph. part. 2. art. ••6) Deum esse Primariam omnis motus Caus∣sam; & candem semper motus quantitatem in universo perseverare. And Hence may we extract these notable Conclusions. (1) That, because look how much one Atom, being impacted ag••inst another, doth impel it, just so much is it reciprocally impelled by it; and so the Force of motion ••oth neither increase, nor decrease, but in respect of the Compensation made, remains always the very same, while it 〈◊〉〈◊〉 executed through a free space, or without resistence: therefore, when Con••retions, likewise mutually occurring, do reciprocally impel each other; they are to be conceived, to act upon, or suf∣fer from each other, so, as that, if they encounter with equal forces, they re∣tain equal motions on each side, and if they encounter with unequal forces, such a Compensation of the tardity of one, is made by the supervelocity of the o∣ther, as that accepting both their motions together, or conjunctly the motion still continues the same. Which also is the same with that Third Law of Nature, registred by Des Cartes (princip. philosoph. part. 2. art. 4••.) Quod unum Corpus, alteri fortiori occurrendo, nihil amittat de suo motu: occurren∣do, vero minus forti, tantum amittere: quantum in illud transfert. (2) That forasmuch as Atoms constantly retain their motive Virtue even in the most compact and hard Concretions; therefore can there be no Absolute Qui••t in Nature: the Atoms uncessant striving for liberty, causing perpetual Com∣motions in all things, though those Commotions be intestine and insensible as we have often said. Which considered, Heraclitus seems to have been more reasonable, in his Denial of all Quiet, but to the dead (apud plutarch▪ 1. placit. 23.) than most have hitherto allowed: He understanding by the Dead, not only Animals deprived of life, and consequently of motion; but also all other things Dissolved, since then, and only then, the intestine Commotions of their Component Particles, or Atoms▪ cease. (3) That Motion is not only much more Natural than Quiet, in the G••••eral▪ but also always Natural, in respect of its Original, forasmuch as it proceeds from A∣toms▪ which are moved by their own Nature, or essentia Gravi••••▪ and ••ome∣times Violent, but ever so only at second hand, or from the nature of Concre∣tions, as they moved with a certain Repugnancy. And this Rule hath al∣so

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is moved per Accidens, because it is an Accident to him; and likewise his soul is moved by Accident, because it is only a Part of him. Again, when He teacheth, that whatever is moved, is moved by Another; that ought to be understood of that thing, which is moved per se: for, from hence it is, that when in the series of particular movents, He would have us to come at length to one First Movent, which is Immoveable, or which is not moved by any other; we are to understand that Primum Movens to be Immove∣able per se, since it may be moved per Accidens. Thus, when a stone is mo∣ved by a staff, the staff by the hand of a man, the mans hand by his Soul; the soul, indeed, is the First movent and Immoveable: but, understand it to be so, per se, because it is at the same moment moved per Accidens, i. e. when the hand, arme, and whole body, which contains it, is moved. More∣o••er, He declares, that whatever is moved per se, is moved juxta Naturam, according to Nature; such as he affirms that only to be, which is endowed with a soul: yet will He not admit, that what is moved by Another, should always be moved Praeter Naturam, Praeternaturally; but sometimes Un∣naturally (as a stone, when it is thrown upward) and sometimes Naturally (as a stone, when it falls Down again.) Now, if you hereupon Demand of Him, What that is, which makes a stone fall Down again; He shall An∣swer, that what moves it Downward, per se, is the Generant it self, or that which first Produced the stone: and that which moves it downward, per Accidens, is that which removes the impediment or obstacle to its descent, as the hand of a man, or other thing supporting the stone. And, if you again enquire of him, What is the Difference betwixt the Upward and Downward motion of a stone, how one should be Violent, and the other Natural, since, according to his own Assertion, both are Caused by ano∣ther: His Return will be, that the Difference lies in this, that the stone is not carried upward, of its own Nature, but Downward; as having the Principle of its Descent, inhaerent in it self, but not that of its Ascent. If you urge Him yet farther; since the stone hath in it self the Principle of its Motion, why therefore is it not moved only by it self, but wants Ano∣ther, or External Motor? His Answer will be: that there is a Twofold principle of motion, the one Active, the other Passive; and in the stone is only the Principle Passive, but in the External Motor is the Active. When yet it may be farther pressed; that since according to his own Do∣ctrine, the Passive principle is the matter, and the Active the Forme: as to the matter, that cannot be the principle of its motion Downward, no more than of its motion upward; and as for the Forme, if that be neither the Active principle, nor the Passive (as he will by no means admit) certainly there can be none. Which for Him to allow, were plainly to destroy his own great Definition of Nature, wherein He acknowledgeth it to be the Principle of Motion. But, alas! these are but light and venial Mistakes, in comparison of those gross Incongruities that follow.

When Aristotle comes to handle the Species,* 1.10 or sorts of Natural Moti∣on, you may remember, that He first Distinguisheth Natural motion in Di∣rect and Circular; and then subdistinguisheth the Direct into (1) that which is from the Circumference toward the Centre, or from the Extrems toward the middle of the world, which He calls Downward; and (2) that which is from the Centre toward the Circumference, which He calls Up∣ward: assigning the former, or Downward motion, only to Heavy things, to the Earth simply, to Water and mixt things, Secundum quid; and the Upward

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be. What then, must that External Principle be, as Aristotle contends, the very Generant of the thing moved? Certainly, thats highly Absurd; since the Generant is absent, and perhaps, long since ceased to be in rerum natura: and nothing either Absent, or Nonexistent, can be the Efficient of a Natural Action, such as motion is. If you will have, that to be moved by the Generant, signifies no more than to receive a Virtue or Power of moving it self, from the Generant▪ then while you endeavour to save Aristotle from the former Absurdity, you praecipitate him into a gross Contradiction of his own Doctrine: for, since the Generant it self ought to be moved by its Generant, and that again to be moved by its Generant, and so upward along the whole series of Generants, till you arrive at length at some First Gene∣rant, from whence that Virtue was first derived; you bring Aristotle to allow a First Generant, which impugns his fundamental supposition of the Eternity of the World. Nay, if you admit God to be the Author of the First Generant, it will then follow, that God must be the Cause of this par∣ticular motion, and not the First Generant, no more than the Last. Final∣ly, is that the Cause, which only removes the Impediment to a Heavy bo∣dies Descent? Neither is that Reasonable; for, as Aristotle himself con∣fesseth, such a Cause is only a C••use by Accident.

Seeing, therefore,* 1.11 that the Downward motion of a Heavy Body doth not proceed from any Intern••l Principle, nor from either its Generant, or that Accidental one, which removes the Impediment to its Descent, in the supposed Capacity of an External: let us proceed to enquire, Whether there be not some other External Cause, whereupon we may reasonably charge that Effect. Which that we may do with the more both of or∣der and plainness; it is requisite, that we first remember, how Philosophers constitute dive••s sorts of Violent, or Externally-caused motion. Emperi∣cus (••. advers. physicos.) makes 4 distinct species thereof, viz. Pulsion, Traction, Elation, Depression. And Aristotle sometimes superads a fifth, namely Collision; sometimes disallowing Empericus his Division, affirms that the species of motion, made by an External principle, are Traction, Pul∣sion, Vection, and Volutation: upon good reason reducing Elation and De∣pression to either Traction or Pulsion; forasmuch as a body may be eleva∣ted, or depressed by either ••raction or Pulsion. But, yet He hath left us rather a Confusion, than logical Discrimination of the species of Violent motion; for, Collision and Pulsion are one and the same thing; and Ve∣ction may be performed either by Pulsion or Traction, insomuch as the thing movent doth not forsake the thing pulsed, or drawn, but constantly adhaereth unto it: and as for Volutation; it is both Pulsion and Traction at once, as may be easily conceived by any man, who seriously considers the manner thereof. Nay, Traction it self may be justly reduced to Pulsion; forasmuch as the movent, which is said to Draw a thing, doth, indeed, no∣thing but Impel it, by frequently reiterated small strokes, either directly to∣ward it self, or to a lateral region: and yet notwithstanding, for pla••nness sake, and the cleerer Demonstration of our praesent thesis, we judge it con∣venient, to conserve the Common Notion, and to determine, that all Mo∣tion impressed upon one body by another, is performed, in the General ei∣ther when the movent Propels the moveable from it self, or Attracts it to∣ward it self. For, albeit the movent sometimes propels the thing moved from another body, or attracts it to another▪ yet can it not possibly do that▪ but it must, at the same time, either Avert it, in some measure, from, or Ad∣duce it toward it self. Nevertheless, it is not to be denied, but Pulsion is

always the Chie•• Species▪ ••nd for that consideration alone is it, that Pro∣••ection (which is only Impul••••on, or, as Aristotle emphatically calls it, a more Violent motion) is generall•• a••cepted as synonymous to Violent motion; and that Philosophers seldo•• or never Exemplifie Violent motion, but in Projectills, whether they be projected upward, or downward, ••••anve••sly, ob∣liquely▪ or any way whateve••▪

* 1.12These things considered•• 〈◊〉〈◊〉 follows of pure necessity, that the Down∣ward motion of Heavy Bo••••es, being caused (not by any Inte••nal, but) b•• an ••xternal Force impressed upon them▪ must be effected either by Im∣pulsion, or by Traction. B•• Impulsion it cannot; because, in the case of a stone throwneUpward, ther•• 〈◊〉〈◊〉 nothing External, that can be imagined to im∣pel 〈◊〉〈◊〉 Down again▪ 〈…〉〈…〉 attained the highest point of its mountee, unless 〈◊〉〈◊〉 should be the 〈◊〉〈◊〉 and i•• its Descent did proceed from the im∣pul••••▪ 〈…〉〈…〉 from below upon the upper part of the stone•• 〈…〉〈…〉 projection of the stone upward, during its Ascent, the motion thereo•• ••ould, in every degree of its remove from the pro••••cient▪ be Accelerated 〈…〉〈…〉 same proportion, as its Downward moti∣on is Accelerated▪ in ever•• ••••gree of its descent; but Experience testifies, ••hat ••ts upward motion 〈…〉〈…〉 and more Retarded, in every degree of its remo•••• from the projici•••••• and therefore it cannot be, that the Downward motion thereof should be ••••used, nay not so much as advanced by the Aer. Which thing ••as••endus 〈◊〉〈◊〉 Epist. de proport. qua Gravia decidentia a••∣celerantu•• 〈…〉〈…〉 ••••monstrated; and we our selves, out of him, 〈◊〉〈◊〉 the 9 Article of our 2 〈◊〉〈◊〉 concerning Gravity and Levity, in the 3. Book. praecedent. Wha••▪ 〈◊〉〈◊〉, can remain, but that it must be by AT∣TRACTION? 〈◊〉〈◊〉▪ because no other Attractive Force, which might begin and continu•• 〈◊〉〈◊〉 Downward motion of a stone, can be imagi∣ned▪ unless it be that Mag••••••••que Virtue of the Earth, whereby it Draws all Terrene Bodies to an 〈…〉〈…〉 it self, in order to their, and its own bet∣ter Conservation▪ 〈…〉〈…〉 Conclude, that the Cause of the Down∣war•• motion o•• all 〈…〉〈…〉, is the Magnetique Attraction of the Earth. Nor need we adferr other ••••guments, in this place, to confirm this Positi∣on•• in respect we have 〈◊〉〈◊〉 made it the chief subject of the 2 Sect. of our Chap. of Gravity 〈…〉〈…〉; whether we, therefore, remit our unsa∣tisfied Reader.

* 1.13From the Cause of 〈◊〉〈◊〉 Downward motion of Heavy bodies, let us ad∣vance to the Acceleration 〈◊〉〈◊〉 them, in every degree of space, through which 〈…〉〈…〉 reason, why we should at all enquire 〈…〉〈…〉 upward mo••ion of Light bodies, in every de∣gree 〈…〉〈…〉 as we know of no man, but Aristotle, that 〈…〉〈…〉 motion of Fire, and Aer is slower in the begin∣ning▪ and gradually 〈◊〉〈◊〉 and swifter in the progress. And so short was 〈…〉〈…〉 proving that his s••••gular conception, by Experiment, as he ought; 〈…〉〈…〉 assumed ••t upon 〈◊〉〈◊〉 credit of only one poor Argument, which is 〈◊〉〈◊〉.

〈…〉〈…〉 and other things of the like light and aspiring 〈…〉〈…〉 Caelo. cap. 8.) were Extruded and Impelled 〈…〉〈…〉 descending and crouding toward the 〈…〉〈…〉 force, as some have contended; and we••e 〈…〉〈…〉 spontaneous tendency of their own inhaerent 〈…〉〈…〉 moved more swiftly in the beginning, and mo••e slowly 〈…〉〈…〉 their motion▪ but Fire, and Aer are more 〈…〉〈…〉 beginning 〈…〉〈…〉 more and more swift in the progress of their

Assent; therefore are they not moved upward by the Extrusion and Im∣pulsion, but spontaneously, or by their own Levity.

And to Confirm his Minor proposition, that Fire and Aer are Accelerated in every degree of their Assent; without the suffrage of any Experiment, He subjoyns only, that as a Greater quantity of Earth is moved downward more swiftly, than a less; so is a Greater quantity of Fire moved upward more swiftly than a less: which could not be, if either of them were Impelled, or mo∣ved by an External Force.

But, this is, as the Former, meerly Petition∣ary; for, why should not a Greater quantity of Earth, or Fire be moved more swiftly than a less, both being moved (as we suppose) by External force, in ••••se the External force be proportionate to the quantity of each? Doubtless, the force of the ambient Aer, extruding and impelling flame up∣ward, is alway•• so much the greater, or more sensible, by how much more Copious the ••••re is; as may be evinced even from the greater Impetus and waving motion of the flame of a great fire: though it cannot yet be discerned, whether that Undulous or waving motion in a Great flame be (as He praesume•••• more swift and rapid, than that more calm and equal one observed in the flame of a Candle. Tha•• (youl say) is enough to detect the incircumspection of Aristotle, in assuming, upon so weak grounds, that the motion of Light things Ascending, is accelerated in the progress, and that in the same proportion, as that of Heavy things Descending is accele∣rated: but not enough to refute the Position it self; and therefore we think it expedient, to superad a Demonstrative Reason or two, toward the ple∣nary Refutation thereof. Seeing it is evident from Experience, that a Bladder blown up is so much the more hardly depressed in deep water, by how much neerer it com••s to the bottom▪ and a natural Consequent thereupon, that the bladder, in respect of the Aer included therein, begin∣ning its upward motion at the bottom of the Water, is moved toward the region of Aer so much the more slow••y, by how much the higher it riseth toward the surface of the Water, or lower part of the re∣gion of Aer incumbent thereupon; and that the Cause thereof is th••s, that so much the fewer parts of Water are incumbent upon the bladder and aer contained therein, and consequently so much the less must that force of Extrusion be, whereby the parts of Water bearing downward impel them upward: we may well infer hereupon, that if we imagine that any Flame should ascend through the region of Aer; till it arrived at the region of Fire, feigned to be immediately above the region of Aer; that Flame would always be moved so much the slower, by how much the higher it should ascend, or by how much the neerer it should arive at the region of Fire. Because Fire and Aer are conceived to be of the same aspiring na∣ture: and because the same Reason holds good, in proportion, for the de∣crease of Velocity in the ascension of Flame through the Aer, as for that of the decrease of velocity in the ascension of Aer, included in a bladder, through Water. And, as for Aristotles other relat••ve Assertion, that a Greater quantity of Earth is moved more swiftly Downward, than a Less; manifest 〈…〉〈…〉 without▪ nay 〈…〉〈…〉 E••perience doth 〈…〉〈…〉

inhaerent in bodies account•••• Heavy, and that every body must therefore ••all down so much the mor•• swiftly and violently, by how much the more of Gravity 〈◊〉〈◊〉 possesseth. H••ving thus totally subverted Aristotle•• errone∣ous Tenent▪ that the 〈◊〉〈◊〉 of L••ght bodies Ascending, is Accele••a••••d in every degree of their A••••••ntion: it follows, that we apply our selves to the consideration of the 〈◊〉〈◊〉 of t••e motion of Heavy bodies 〈◊〉〈◊〉 in every degree 〈…〉〈…〉 Descention. Whe••ein the First obs••••v••∣abl•• o••••urring, i•• the 〈…〉〈…〉, or that it is so, which is easily proved from hence, that in all ages 〈…〉〈…〉 been observed, that the motion of 〈◊〉〈◊〉 things Descendent▪ 〈…〉〈…〉 the beginning, and grows swifter and swi•••••••• 〈◊〉〈◊〉 toward th•• end▪ 〈…〉〈…〉 that in fine 〈◊〉〈◊〉 becomes highly rapid▪ 〈…〉〈…〉 that the 〈…〉〈…〉 or impression made upon the Earth▪ 〈…〉〈…〉 down from 〈◊〉〈◊〉 high, is always so much the greater or strong∣•••• by h••w much the 〈◊〉〈◊〉 ••he place is from which it ••ell.

* 1.14The Second, 〈◊〉〈◊〉 the 〈◊〉〈◊〉 or Cause of that velocity Encreasing in 〈…〉〈…〉 which though enquired into by many of the Ancients, seem•• 〈…〉〈…〉 been 〈◊〉〈◊〉 by none of them. For (1) albeit Aristotle 〈◊〉〈◊〉 was so wary▪ as 〈…〉〈…〉 explicate his thoughts concerning it; y••t ••o••h hi•• great 〈◊〉〈◊〉 Simpli•••••••• tell us ••in Comment. 87.) that it was H••s opinion▪ that a 〈…〉〈…〉 other thing ••alling from on high, is Corrobo∣••••ted [〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉] a Totalitate propria, and hath its spe∣cies ma•••• mor•• and mo•••• 〈◊〉〈◊〉▪ as it comes neerer and neerer to its pro∣per 〈◊〉〈◊〉▪ and so 〈…〉〈…〉 degree of Gravity acceding to it in every ••egree of its 〈◊〉〈◊〉 to the Earth, it is accordingly carried more and more sw••ftly. But, 〈◊〉〈◊〉 that Simplicius hath not expounded, how the 〈◊〉〈◊〉 ston•• can 〈…〉〈…〉▪ how it can be Corroborated, or acquire more and more 〈…〉〈…〉 its species; or how that additament of fresh ••ravity should 〈…〉〈…〉 judge you, whether He hath done Aristotle 〈…〉〈…〉 Author of that Opinion, which instead of 〈◊〉〈◊〉 ••he 〈…〉〈…〉 much more obscure than afore. Besides, we have the 〈…〉〈…〉, that a descending body is not carried the more ••w••ftly▪ by re••so•• 〈◊〉〈◊〉 ••ny access or additament of Gravity: a stone 〈…〉〈…〉 ounce 〈…〉〈…〉 as speedily down, as one of an hundred poun••▪

* 1.15(2) Others 〈…〉〈…〉 as the same Simplicius commemorates) who 〈…〉〈…〉 the Cause 〈…〉〈…〉 the Decrease of the quantity of the Aer 〈◊〉〈◊〉 the s••o••••▪ 〈◊〉〈◊〉 that by how much the higher a stone is, by so 〈…〉〈…〉 and so much the greater Resistence to the motion 〈…〉〈…〉 much the greater quantity of the Aer resist∣ing 〈…〉〈…〉 consequently the resistence of the Aer grow∣ing 〈…〉〈…〉 of the stones descent, the velocity of its 〈…〉〈…〉 proportion thereunto. And this after 〈…〉〈…〉, sinking in deep water▪ more slowly 〈…〉〈…〉 neer the bottom. But, though we adm••t, 〈…〉〈…〉 stone Descending▪ yet we 〈…〉〈…〉 to m••ke ••ny sensible difference of 〈…〉〈…〉 And, would you have an Argument to 〈…〉〈…〉 one fathom; 〈…〉〈…〉 fall the same 〈…〉〈…〉

fathoms, observe again with what velocity it passeth the last, or tenth f••∣thom. This done, consider, sin••e in the latter case, the velocity shall be incompa••ably greater, than in the former; whether it be not necessary, that th••t great au••mentation of velocity in the stone, while it pervadeth the t••nth fathom of space, must not arise from some other, and more potent C••use, th••n the resistence of the inferio•• 〈◊〉〈◊〉? For, in both case••, the stone carries the same proportion of weight▪ and in the lowest f••thom there is the same quantity of Aer, and consequently the same measure o•• resistence. And, if you weigh the stone, fi••st in some very high place, ••n•• afterward in a low, or very neer the Earth; surely, you cannot expect to find•• ••t heavier in the low place in respect of the lesser quantity of A••r ••ub••ja••ent, than in the high, in respect of the greater quantity of Aer there 〈◊〉〈◊〉 it. Lastly, as for their Argument desumed from the slower sink••ing of weights in deep, than in sh••llow 〈…〉〈…〉 thereof 〈…〉〈…〉 same with th••t of the more diffi••ult depression of a 〈…〉〈…〉 Aer, neer the bottom, th••n neer the top of the 〈…〉〈…〉 explained.

(3) A third ••onceipt there 〈◊〉〈◊〉 (imputed to Hipparchu••,* 1.16 by the 〈◊〉〈◊〉 Simplicius) which comparing the Downward motion of a stone, 〈◊〉〈◊〉 by its own proper Gr••vity, with the Upward motion of the 〈…〉〈…〉, caused by an External ••orce impressed upon it by the 〈…〉〈…〉 infers, that as long as the force imprest praevails over the stones Gravity, 〈◊〉〈◊〉 long is the stone carried upward, and that more swiftly in the beginning, because the ••orce is then strongest, but afterward less and less swiftly, be∣cause the same f••rce imprest is gradually debilitated, until the stones pro∣per Gravity at length getting the upper hand of the force imprest, the stone begins it motion Downward; which is slower in the beginning, because the Gravity doth not y••t much praevail, but afterwards grows more and more sw••ft, because the Gravity more and more praevails. But this leaves us more than half way short of the Difficulty; for, though it be reasonable to assume, that a certain Compensation of Velocity is made in both 〈…〉〈…〉. that the Decrease of Velocity toward the end of the Upward motion, is made up again by the Encrease of Velocity toward the end of the Down∣ward, and that in proportion to the degrees of space: yet forasmuch as the motion of a stone falling down is constantly Accelerated, not only after it hath been projected Upward, but also when it is only dropt down from some high place, to which perhaps it was never elevated, but remained there from the beginning of the world, as it often happens in deep mines, the earth ••••∣derneath the stones neer the surface of it being 〈…〉〈…〉 cannot the stones Gravity, gradually praevailing over the Imprest Force, be, as Hipparchus concludes, the Cause of it•• 〈…〉〈…〉 of its Descent.

These Reasons thus deluding our Curiosity,* 1.17 let us have 〈…〉〈…〉 formerly asserted Position, that All terrene 〈…〉〈…〉 are Attracted by the magnetique Virtue of the Earth. 〈…〉〈…〉 that the magnetique Virtue of the Earth is 〈…〉〈…〉 afar off: and thereupon infer, that the 〈…〉〈…〉 therefore more rapid neer the earth, than far from 〈…〉〈…〉 took Virtue seems to be greater, and so the 〈…〉〈…〉 truth neerer the stone 〈…〉〈…〉

and plausible to our first thought: but insatisfactory to our second. For, if it were so, then ought the Celerity of the stones motion, in one fa∣thom neer the Earth, to be the same whether the stone be let fall from the altitude of only one fathom, or from that of 10, 20, an 100 fathoms, when we exactly measure the spa•••• of time, in which it pervades the one fathom neer the earth, in the former case, and compare it with that space of time, in which it pervades the same lowest fathom, in the latter. It may be farther observed, that, whether a stone be let fall from a small, or a great altitude, the motion thereof for the first fathom of its descent, is always of equal velocity, i. e. it is not more nor less swift for the first fathom of its descent from the altitude of an 1•••• fathoms, than from the altitude of only two fa∣thoms: when yet it ought to be more swift for the first fathom of the two, than for the first of the hundred, if the Attraction of the Earth be more vehement neer at hand, than far off; in a sensible proportion. We say, in a sensible proportion; because, forasmuch as the magnetique rays emit∣ted from it, are diffused in ••ound from all parts of the superfice thereof, and so must be so much the more dense, and consequently more potent, by how much less they are removed from it: therefore must the Attraction be some∣what more potent at little than at very great distance; but yet there is no tower or praecipice so high, as to accommodate us with convenience to ex∣periment, whether the power of the Earths magnetique rayes is Grea∣ter, to a sensible proportion, in a very low place, than in a very high.

And yet notwithstanding, nothing seems more reasonable than to con∣ceive, that since the magnetique Attraction of the Earth is the true Cause of a stones Downward motion, therefore it should be also the true Cause of the continual Increment of its Velocity, during that motion. But how it should be so; there's the Knot. Which that we may undo, let us first re∣sume our former supposition (in the 2. Sect. of our chap. of Gravity and Levity.) that a stone were situate in any of the Imaginary spaces; consi∣dering that in that case it could not of it self be moved at all: because, hold∣ing no Communion with the World (which you may suppose also to be Annihilated) there could be, in respect thereof, no inferior place or region, whereto it might be imagined to tend or fall; nor could it have any Re∣pugnancy to motion, because there would be no superior region, to which it might be conceived to aspire or mount. Then let us suppose it to be moved by simple Impulsion, or Attraction, toward any other part of the Empty, or Imaginary spaces; and without all doubt, it would be moved thitherward, with a motion altogether Equal or Uniform in all its parts: because there could be no Reason, why it should be more slow in some parts of its motion and more swift in others, there being no Centre, to which it might approach, or from which it might be removed. Suppose farther, that, as the stone is in th••t motion, another Impulse, equal in force to the former, whereby it was first moved, were impressed upon it; then, assured∣ly, would the stone be moved forward more swiftly than before, not by rea∣son of any Affection to tend to any Centre, but because the force of the 〈◊〉〈◊〉 impulse persevering▪ the force of the second impulse is superadded un∣to it, and the accession of that force must so corroborate the former, as to augment the Velocity of the stones motion. And hence comes it, that to move forward a bo•••• already in motion, doth not only prolong, but ac∣celerate the motion the••••of. Imagine moreover, that a third impulse were ••••••••ntinent••y superadded to the second▪ and then would the motion be yet

more swift than before; the Encrease of Velocity of necessity still respon∣ding to the multiplicity of Impulses made upon the body moved. This may be familiar to our conceptions, from the Example of a Globe set upon a plane; which may be emoved from its place with a very gentle impulse, and if many of those Impulses be repeated thickly upon it, as it moves, the motion thereof will be so accelerated, as at length to become superlatively rapid. Which also seems to be the Reason, why a clay Bullet is discharged by the breath of a man, from a Trunck, with so great force, as to kill a Pidgeon at 20, or 30 yards distance: the Impetus or force impelling the bullet, growing still greater and greater, because in the whole length of the trunck there is no one point, in which some of the particles of the mans breath successively flowing, do not impress fresh strokes, or impulses upon the hinder part of the bullet. The same also may be given, as the most probable Cause, why Long Guns carry or shot, or bullet farther than short; though yet there be a certain determinate proportion to be observed be∣twixt the diametre of the bore, and the length of the barrel or tube, as well in Truncks, as Guns: experience assuring, that a Gun of five foot, musket bore, will do as good execution upon Fowl, with shot, and kill as far, as one of ten foot, and the same bore; and consequently that those Gunners are mistaken, who desire to use Fowling pieces of above 5, or 6 foot long; These considerations premised, we may conceive, that when a stone first begins to move downward, it then hath newly received the first impulse of the magnetique rays emitted from the Earth: and that if after the impres∣sion of that first impulse, the Attraction of the Earth should instantly cease, and no nevv force be superadded thereunto from any Cause vvhate∣ver; in all probability, the stone vvould be carried on tovvard the Earth vvith a very slovv, but constantly equal and Uniform pace. But, because the Attraction of the Earth ceaseth not, but is renevved in the second mo∣ment by an impulse of equal force to that first, vvhich began the stones mo∣tion, and is again renevved in the third moment, in the 4, 5, 6, &c. as it vvas in the second, therefore is it necessary, that because the former impul∣ses, impressed are not destroyed by the subsequent, but so united as still to corroborate the first, and all combining together to make one great force; vve say, therefore is it necessary, that the motion of the stone, from the repeated impulses, and so continually multiplied Impetus or Force, should be more swift in the second moment, than in the first; in the third, than in the second; in the fourth, than the third, and so in the rest succes∣sively; and consequently, that the Celerity should be Augmented in one and the same tenour, or rate, from the beginning to the end of the mo∣tion.* 1.18

The Third thing considerable in this Downward motion of Bodies, is the PROPORTION, or Rate, in which their Celerity is encreased. Concerning this, we know of no Enquiry at all made by any one of the Ancients; only Hipparchus, as hath been said, thought that in the General, the increment of Velocity in things falling down, was made in the same re∣ciprocal proportion, as the Velocity of the same things projected upward. But, about 90 yeers past, one Michael Varro, an eminent Mathematician (in tract. de motu.) depending meerly upon Reason; would have the Problem to be thus solved. What is the Ration, or Proportion of space to space, the same is the Ration of Celerity to Celerity; so that if a stone falling down from the heigth of four fathoms, shall in the end of the first fathom acquire

one degree of Velocity, 〈…〉〈…〉 ••nd of the second two, in the end of the third three, in the end of 〈◊〉〈◊〉 fourth four: it will be moved twice as swift∣ly in the end of the second ••athom, as in the end of the first, thrice as swiftly in the end of the 〈◊〉〈◊〉, and four times as swiftly in the end of the fourth•• as of the first. 〈◊〉〈◊〉 this Proportion is deficient, first in this; that though the increment of ••••lerity, or of its equal degrees, may be com∣pared with the equal mo••••nts or parts of space: yet can it not be com∣pared also with the equal ••••ments o•• parts of Time, without which the myst••ry can never be 〈◊〉〈◊〉. And therefore Aristotle did excel∣lently well, in Defining 〈◊〉〈◊〉▪ and Slow, by Time▪ determining that to be swift, which 〈…〉〈…〉 deal of space in a little time; and on the contrary▪ that to be 〈…〉〈…〉 pervading a little of space in a great deal of time. Again, 〈…〉〈…〉 suppose the theorem to be explicable by e∣qual moments of times 〈…〉〈…〉 such as are the respites or intervals betwixt the pulses of our 〈…〉〈…〉 and that a stone falling down doth pervade the first fathom of 〈…〉〈…〉 the first moment: then, if it pervade the se∣cond fathom twice as 〈◊〉〈◊〉 as the first (as Varro conceives) it must ne∣cessarily follow, that 〈◊〉〈◊〉 second fathom must be pervaded in the half of a moment; if the 〈◊〉〈◊〉 ••hom he percurred thrice as swiftly as the first, it must be pervaded in 〈◊〉〈◊〉 third part of a moment; and if the fourth fathom be percurred four times 〈◊〉〈◊〉 swiftly as the first, it must be pervaded in the fourth part of a 〈◊〉〈◊〉 And, because, if you conjoyn the half, third, and fourth part of a mome•••• ••ou shall have a whole moment with one twelfth part of a moment; it 〈◊〉〈◊〉 necessary, that in the second moment, three fa∣thoms (very neer) must 〈◊〉〈◊〉 percurred: which indeed is very far from truth. For▪ because, if we 〈◊〉〈◊〉 after the same method, so that the fifth fathom be percurred in the 〈◊〉〈◊〉 part of a moment; the sixth in the sixth part of a moment, 〈◊〉〈◊〉 so successively; out of these fragments of time we shall not be 〈◊〉〈◊〉 to make up another whole moment, until it be after the stone hath 〈◊〉〈◊〉 the eleventh fathom, or thereabout; and so in the third moment 〈◊〉〈◊〉 fathoms shall be pervaded, nor shall we again be able to make up 〈…〉〈…〉 whole moment, until after the stone hath per∣vaded the 31 fathom 〈…〉〈…〉 so in the fourth moment, it shall pervade 20 fathoms, nor shall 〈◊〉〈◊〉 able to make up another complete moment, un∣t•••• after the stone 〈…〉〈…〉, neer upon, the 84 fathom, and so in the fifth moment, 53 fath••••s shall be percurred, &c. so that proceeding 〈…〉〈…〉, neer upon; you shall consequently, in a very short time, 〈…〉〈…〉 it up to Immensity: as is manifest from the short progress 〈…〉〈…〉 numbers, 1.2, 4, 11, 31, 84, &c. Which is impugned by easie 〈…〉〈…〉, and not defensible by any Reason whatever.

* 1.19This the brave 〈◊〉〈◊〉 well considering, and long labouring his subtle and active 〈…〉〈…〉 explore a fully satisfactory Solution of this dark 〈…〉〈…〉 most happily to set up his rest in this. First, He defines Motion 〈◊〉〈◊〉 Accelerated to be that, which receding from qui∣et, doth acqu•••••• 〈…〉〈…〉 of Celerity, not in equal spaces, but equal 〈…〉〈…〉 upon Grounds partly Experimental, partly 〈…〉〈…〉 that the moments, or equal Degrees of Ce∣le••••ty 〈…〉〈…〉 or equal degrees of Time, or (more plain∣•••• 〈…〉〈…〉 the same proportions as the Times; so that 〈…〉〈…〉 of time pass during the motion, so many de∣grees 〈…〉〈…〉 by the thing moved. That the equal 〈…〉〈…〉 continently in single moments of time, do

encrease in each single moment, according to the progression not of U∣nities, but of Numbers unequal from an Unity: so that if in the first moment of time, the stone fall down one fathom, in the second moment, it must fall down three fathom, in the third five, in the fourth seven, in the fifth nine, in the sixth eleven, and so forward. And, because those Numbers, which they ••••ll Quadrate (viz. One is the quadrate of an U∣nity, Fower the quadrate of a Binary, Nine the quadrate of a Ternary, Sixteen of a Quaternary, and) are made up by the continual addition of unequal number•• (for, three added to one, make four; five added to four, make nine; seven, to nine▪ make sixteen▪ nine to sixteen, make twenty five; eleven to twenty five, make thirty six, &c.) thereupon He infers▪ that the Aggregates of the spaces percurred from the beginning to the end of the motion, are as the Quadrates of the times: i. e. assu∣ming any one particular moment of time, so many spaces are found per∣vaded in the end of that moment, as are indicated in the quadrate num∣ber of the same moment. For Example, when in the end of the first moment, one fathom of space is pervaded; in the end of the second mo∣ment, four fathom shall be pervaded▪ (viz. three being added to one) in the end of the third moment, nine fathom (five being added to four) in the end of the fourth moment, sixteen fathom (seven being added to nine) and so forward: so that, accordingly, the spaces pervaded from the beginning to the end of the motion, are among themselves in a Duplicate Ration of moments (as Geometricians speak) or equ••l Divisions of Time; or, all one as the Quadrates of moments are one to another.

Galilaeus, we said, herein relyed partly upon Experience,* 1.20 partly upon Reason. First, therefore, for his Experience; He affirms, that letting fall a Bullet, from the altitude of 100 Florentine Cubits (i. e. ac∣cording to exact comparation, 180 feet, Par••s measure, and thirty fathom of ours) He observed it to pervade the whole space, and arrive at the ground, in the space of five seconds, or ten sem••seconds▪ and accor∣ding to such a ration, as that in the first semisecond, it fell down one cubi••, in the second semisecond, four cubits; in the third semisecond, nine cubits, in the fourth sixteen; in the fifth twenty five; in the sixth 36; in the seventh, forty nine; in the eighth, sixty four; in the ninth, eighty and one; in the tenth the whole hundred. And though the good Mer∣sennus afterward found a bullet to pervade the same altitude in a much shorter time; nay, that in the space of five seconds, a bullet fell down through the space not onely of one hundred and eighty foot, but even of three hundred▪ i. e. of fifty fathom: yet doth He fully consent, that the Acceleration of its motion ariseth exactly according to Galilaeos progres∣sion by the Quadrates of unequal numbers. So as that if in the first se∣misecond, it descend one semi-fathom▪ in the second semisecond, it shall descend four semifathoms, in the third sem••second, nine semifathoms, &c. And Gassendu•• likewise, though he wanted the opportunity of experi∣menting the thing•• from a Tower of the like altitude; found notwith∣standing, from different heights, that the proportion was always the same; as Himself at large declares 〈…〉〈…〉 qua gravia decident. accelerantu•••• 〈…〉〈…〉 you doubt to find it so your self, if in a Glass Tube, neer upon two 〈◊〉〈◊〉 ••••ng, divided into an hundred degrees, or equal parts, 〈…〉〈…〉 either cut in, or inscribed

upon papers (after the manner of those usually starcht on to Weather-glasses, to denote the several degrees) and not perpendicularly erected, but somewhat inclining, you let fall a bullet, and exactly observe the manner of its descent, and rate of Acceleration. For, Heavy bodies are, indeed, moved more slowly in Tubes inclined, than in such as are perpendicularly erected; but yet still with the same proportion of Acce∣leration.

Secondly, for His Reason, it consists in this; that, if the Increment of Velocity be supposed to be Uniforme (and there is no reason, which can persuade to the contrary) certainly, no other proportion can be found out, but that newly exposed: since, with what Celerity, or Tardity soever you shall suppose the first fathom to be pervaded it is necessary that in the same proportion of time following, three fathoms should be pervaded; and in the same proportion of time following, five fathoms should be pervaded; &c. according to the progression of Quadrate Numbers. This, that Great man Ioh. Baptista Ballianus (whom Ricciolus often mentions (in Almagesto novo) but never without some honourable attribute) hath de∣monstrated divers ways in lib. 2. de Gravium motu.): but the most plain Demonstration of the verity thereof, yet excogitated, we conceive to be this, invented by Gassendus.

* 1.21

[illustration]

Understand the Lines LAB and ACI making a rectangular Trian∣gle, by their meeting at the point A, to be so divided, on each side, into equal parts, at the points DEFGHIKL: (being continued, they may be divided into many more) as that the Lines drawn both betwixt those points, and from them to the points MNO, divide the whole space KAL into Triangles perfect∣ly alike and equal each to other. This done, Assume the point o•• A∣pex A, for the beginning of Time, the beginning of space, and the be∣ginning of Velocity: All which are to be here considered in the motion, as beginning together with it. First, then we may account the equal parts of each Line, AB, AC. for the parts or equal moments of Time, flowing on from the beginning: so that AE may represent the first moment, EG the second, GI the third, IL the fourth. Secondly, we may account those equal Triangles, for the equal parts of the space, which are pervaded from the beginning: so that A∣nother perpendicular Line PQ. being drawn apart, and representing the fall of a stone, thro••gh sixteen fathom, the triangle ADE, may refer the first fathom P••, which is percurred in the first moment; the three next triangles may refer the three fathoms RS, which are percurred in the second moment; the five following triangles, the five fathoms ST, which are pervade•• in the third moment: and the seven following, the seven fathoms, which are pervaded in the fourth moment. Now from

hence it is manifest, that the Aggregate spaces carry the same pro∣portions,

[illustration]

as the Quadrates of Times: when, the Triangle ADE (or space PR.) is one, as the Quadrate of AE, that is of one Time, is one: and the Aggregate AFG (or PS) is four: as the Quadrate AG, of two, is fower: and the Aggregate AHI (or PT) is nine: as the Quadrate AI of three, is nine; and the Aggregate AKL (or PQ.) is sixteen, as the Qua∣drate AL of four, is sixteen.

Thirdly, we may account the Line DE for the first degree of Velocity acquired in the end of the first time; insomuch, as the first time AE is not individual, but may be divided into so many instants, or shorter times, as there are points, or particles in the line AE (or AD) so neither is the degree of Velocity indivi∣dual, or wholly acquired in one instant; but from the beginning encreaseth through the whole first time, and may be repraesented by so many Lines, as may be drawn parallel to the Line DE, be∣twixt the points of the Lines AD and AE: so that, as those Lines do continually encrease from the point A to the Line DE; so likewise doth the Velocity continually encrease from the begin∣ning of the motion, and being represented what it is in the inter∣cepted instants of the first time, by the intercepted Lines, it may be represented what it is in the last instant of the same first time, by the Line DE drawn betwixt the two last points of the Trian∣gle ADE. And because the Velocity, thenceforward conti∣nuing its Encrease, may be again signified, by Greater and Greater Lines continently drawn betwixt all the succeeding points of the remaining Lines, DB and EC; hence comes it, that the Line FG, doth represent the degree of Velocity acquired, in the end of the second moment: the Line HI. the Velocity acquired in the end of the third moment; and the Line KL. the velocity acquired in the end of the fourth moment. And evident it is from hence, how the velocities respond in proportions to the Times; since, by reason of the Triangles of a common angle, and parallel bases, it is well known, that as DE are to EA, so FG to GA: HI to IA, and KL to LA. Thus, keeping your eye upon the Figure, and your mind upon the Analogy; you shall fully comprehend, that in the first moment of Time, the falling stone doth ac∣quire one degree of Velocity, and pervades one degree of space; that in the second moment of Time, it acquires another degree of Velocity, which being conjoynd to the former, makes two, and in the mean while three spaces are pervaded; that in the third moment, it acquires another degree of Velocity, which conjoyned to the two former makes three, and in the mean while seven parts of space are pervaded; and so forward. You shall fully comprehend also, that the Celerities obtain the same Ra∣tion, as the moments of Time: and that the spaces pervaded from the beginning to the end of the motion, have the same Ration, as the Qua∣drates of the moments of Time; which we assumed to Demonstrate, out of Gassendus. But still it concerns you to remember, that we here dis∣course of that Motion, which is Equally, or Uniformly Accelerated; or whose velocity doth continually and uniformly encrease, nor is there any moment of the consequent time, in which the motion is not more swift, than it was in every antecedent moment, and in which it is not accelerated

according to the same Reason. For, the want of this Advertisement in chief, seems to have been the unhappy occasion of that great trouble the Learned Jesuit Petrus Cazraeus put Gassendus to, in his two Epistles, De Proportione, qua Gravia decidentia accelerantur.

* 1.22And this kindly conducts us to the Physical Reason of this Proportion, in which the velocity of bodies Descending is observed to encrease. For wholly excluding the supposition of the Aers assistance of the Downward motion of a stone, by recurring above, and so impelling it downward; and admitting the Magnetick Attraction of the Earth to be the sole Cause of its Descent; unto both which the considerations formerly alleadged seem to oblige us: it is familiar for us to conceive, that the Increment of its Celerity, according to the proportion assigned, ariseth from hence. While in the first moment, the earth attracts the stone, one degree of Ce∣lerity is acquired, and one degree of space is pervaded. In the second moment, the attraction of the Earth continuing, another degree of ce∣lerity is acquired, and three equal spaces are pervaded: one by reason of the degree of celerity in the mean while acquired, and two by reason of the degree of celerity formerly acquired, and still persevering, as that which is doubly ••equivalent to the new degree in the mean while ac∣quired; because it is Complete and entire from the very beginning of the 2^d moment, but the other is only acquiring, or in fieri, and so not complete till the end of the second moment. Then, according to the same Ration, in the third moment another degree of celerity is acquired, and five spaces (equal) are pervaded; one by reason of the new degree of celerity in the mean while acquired, and fower by reason of the two former persever∣ing, i. e. two in each moment praecedent, or one of a duplicate aequivalen∣cy to the new one not yet complete. Then, in the fourth moment another degree of celerity is acquired, and seven spaces are pervaded; one by reason of the fresh degree in the interim acquired, and six by reason of the three former per••••vering, i. e. two in each praecedent moment. And so of the rest through the whole motion, computing the degrees of en∣creasing Celerity, by the ration of Quadrate Numbers.

Now, many are the Physical Theorems, and of considerable impor∣tance,* 1.23 which might be genuinely deduced from this excellent and fruitful Physicomathematical speculation; and as many the admired Apparen∣ces in nature, that offer themselves to be solved by Reasons more than hinted in the same: but, such is the strictness of our method, and weari∣ness of our Pen, that we can, in the praesent, make no farther advantage of it, than only to infer from thence the most probable Reason of that so famous Phaenomenon, The equal velocity of two stones, or bullets, the one of 100 pound, the other of only one ounce weight, descending from the same altitude; experience constantly attesting, that being dropt down together, or turned off, in the same instant, from the top of a tower; the Lesser shall arrive at the ground, as soon as the Greater. For, this admirable Effect seems to have no other Cause but this; that the Lesser body, as it containeth fewer parts, so doth it require the Impulses or strokes of fewer Magnetical rays, by which the attraction is made: and such is the pro∣portion of the two forces, as that each moveable being considered with what Resistence you please, still is the force in the movent equally suffici∣ent to overcome that resistence, and a few magnetique rays suffice to the

attraction of a few parts, as well as many to the attraction of many parts. So that the space being equal, which both are to pervade; it fol∣lows, that it must be pervaded by both, in equal or the same time. Pro∣vided always, that the two bodies assumed, be of the same matter; for, in case they be of divers matters, as the one of Wood, the other of Iron or Lead, that may cause some small Difference in their Velocity. We say, some small Difference; because, if we take two Globes of different materials and weights, but of the same or equal diameters, as (V. G.) one of Lead, the other of Wax: we shall be very far from finding, that the Heavier will be carried down more swiftly than the Lighter, in a pro∣portion to the excess of its Gravity. For, if one be ten times heavier than the other; yet shall not the Heavier therefore, both being turned off, in the same instant, arrive at the ground ten times sooner than the Lighter: but, at the same time as the heavier, arrives at the ground, from the alti∣tude of 10 Fathoms; the lighter shall come within a foot of the earth; so far short doth the lighter come of being nine fathoms behind the Heavier. And the Cause, why the Lighter Globe of Wax, is carried so swiftly, is the same with that, why a bullet of Lead of only an ounce weight, is carried down as swiftly as another bullet of 100 pound. And, what though the Globe of Wax be as great in circumference, as the o∣ther of Lead, and somewhat greater; yet seeing still it hath fewer parts to be attracted, it therefore requires fewer magnetical rays to its attracti∣on with equal velocity to the heavier. But, the Cause why it is carried som∣what, though very little, slower than the heavier; is to be derived chiefly from the Aer resisting it underneath, the Aer being more copious in pro∣portion to the virtue Attrahent, in respect of the greatness of its Ambite, or Circumference: and thence is it, that Cork, Pith of Elder, straws, feathers, and the like less compact, and so more light bodies, fall down much more slowly.

From this Experiment, and the Reason of it,* 1.24 we have an opportuni∣ty of observing and easily understanding the Distinction of Gravity in∣to Simple and Adjectitious: the Former being that, which is competent to a body though unmoved, and whose quantity may be exactly determi∣ned by the balance suspending the body in the aer; the Latter being proper only to a body moved, and vanisheth as soon as the body attaineth quiet, and whose measure is to be explored both from the quantity of the simple gravity which the body bears during its quiet, and the Altitude from which it falls. Thus, assuming two Bullets, the one of an ounce, the o∣ther of 100 pound, Simple Gravity, according to the Scales; the Ad∣jectitious Gravity of the Lesser bullet, acquired by the increment of its velocity during its descent, must be less proportionably to its simple gra∣vity, than the Adjectitious gravity of the Greater bullet, acquired by the increment of its Velocity during its Descent, in the same time, and from the same altitude: because, the space and time of the descent of both being equal, the proportion of the acquired gravity of each must be respondent to the proportion of the simple gravity of each. So that if in the end of the fall of the Lesser bullet of an ounce weight, the Ad∣jectitious Gravity of it shall amount to 10 ounces: the Adjectitious gra∣vity of the Greater of 100 pound weight, shall, in the end of its fall, amount to a thousand pound; nor can the Acquired Gravity of the Les∣ser ever equal that of the Greater, unless it fall from a far greater Alti∣tude.

* 1.25Here, perhaps, you'l Demand our opinion, concerning that admirable because superlative Velocity, which Galilaeo and other Mathematicians conceive that a bullet would acquire in case it should fall to the ••arth from those vast (we might have said Immense) heights of the Moon, Sun, and region of the Fixed starrs. Of this, therefore, we say in short; (1) That, in this case, Mathematicians are wont to suppose, that there are the same Causes of Gravity and Velocity in those sublime places, as are observed here with us below, or neer the surface of the Earth: and if they be not, certainly our Description and Computation must be altoge∣ther vain and fruitless. For, if the Cause of Gravity, and consequent∣ly of the Velocity be the Attraction made by the magnetique rays trans∣mitted from the Earth; forasmuch as those magnetique rays must become more Rare, and fewer of them arrive at a body, by how much farther it is removed from the Earth: though, perchance, a bullet might be attra∣cted down from the region of the Moon (and if so, the motion of the bullet would be very slow, for a good while, in respect of the very few magnetique rays, that could arrive to that great height) yet from that far greater height of th•• region of the Fixt stars, a bullet could not be attra∣cted at all, it being impossible that any magnetique ray should be transmit∣ted so far as half way thither. (2) But, supposing that the magnetique Virtue of the Earth did extend thither; and that a bullet, from whence soever falling, should begin its motion with that speed, and proceed ac∣cording to the same degrees of Acceleration, which we observe in a stone, or bullet falling from a very high tower: then must it of necessity acquire that incredible Velocity, which our Mathematicians describe. To Par∣ticular; conceding the Distances or Intervals betwixt the Earth and each of those Caelestial Orbs, which our modern and best Astronomers gene∣rally assign; a bullet would fall from the body, or rather the Limbus of the Moon, to the Earth, in two hours and an half; from the Limbus of the Sun, in eleven hours and a quarter: from the region of the Fixt stars, in 39 hours and a quarter. And so, if we imagine the Earth to be per∣forated to the Centre, since a bullet would fall from the superfice thereof down to the Centre, in 20 minutes, or the third part of an hour: the same bullet coming from the moon, would pervade the same space from the su∣perfice of the Earth to the Centre of it, in one minute and twenty se∣conds, or the third part of a minute: coming from the Sun, it would per∣vade the same semidiametral space of the Earth, in seventeen seconds: and coming from the region of the Fixt stars, it would percur the same semi∣diametral space of the Earth, in five seconds. So incredibly great would be the Velocity of a bullet falling from such vast Altitudes. And this we think sufficient▪ concerning the Downward motion of Bodies, accoun∣ted Heavy.

SECT. III.

THe Remnant of our praesent Province consists only in the conside∣ration of the Upward motion of Heavy Bodies PROJECTED: concerning which the principal Enquiries among Philosophers are (1) VVhat and whence is that Force, or Virtue motive, whereby bodies pro∣jected are carried on, after they are separated from the Projicient? (2) What are the Laws of their motion. Direct, and Reflex?

Concerning the FIRST, therefore, we observe,* 1.26 that Aristotle (in 8. physic. cap. ult.) and most of his Sectators confidently affirm, that a stone thrown out of a sling, an arrow shot from a bow, a bullet discharged from a Gun, &c. is moved only by the Aer, from the time of its separation from the sling, bow, or Gun: and the manner of that mo••ive activity of the Aer upon the thing projected, They thus explicate. The Aer (say they) which is first moved by the Projicient, together with the moveable, doth, at the same time, both propel the moveable, and impel the Aer im∣mediately beyond it, which being likewise moved, doth in the same man∣ner propel the moveable, and impel the aer immediately beyond it; and that aer being thus moved, doth again impel both the moveable and the aer next beyond it: and so consequently the next aer impels both the moveable and the next aer beyond it, until the propulsion and promo∣tion being gradually debilitated, and at length wholly overcome, partly by the Gravity of the thing moved, partly by the Resistence of the occurring Aer, the motion wholly ceaseth, and the thing projected attain∣eth quiet.

And that Others contend, that the Body Projected is carryed forward by a Force (as They call it) Imprest; which they account to be a Qua∣lity so communicated unto the body projected, from the Projicient, as that not being indelible, it must gradually decay in the progress thereof, and at length wholly perish, whereupon the motion also must by degrees remit its violence, and at length absolutely vanish, and the thing project∣ed again recover its native quiet. But, lest we trifle away our praecious moments, in confutin•• each of these weak Opinions, against which the Reason of every man is ready to object many great absurdities, especially such as the praecedent theory will soon advertise him of: let us praesently recur to the more solid speculations of our master Gassendus in his Epi∣stles (de motu impresso a motore translato) and praesenting you the sum∣mary thereof, without further delay satisfie your Curiosity, and our own Debt of assisting it.

First we are to determine, that nothing, remaining it self unmoved, can move another. For, since our Discourse concerns not the First Cause of all motion, God, whose Power is infinite, who is in all places, who can, on∣ly by the force of his Will, create, move, and destroy all things; mani∣fest it is, that nothing Finite, especially Corporeal (and such only hath

an interest in our praesent consideration) can move another thing, unless it self be also moved at the same time: as Plato well observed in his say∣ing, Neque est Dissicile modo, sed etiam plane impossibile, ut quidpiam mo∣tum imprimere, sine quapiam sui commotione, valeat: (in Timaeo.) And the Reason is this; whatever doth move, doth act; and e converso, what∣ever doth act, doth move; Action and Passion (as Aristotle, 3. physic. 3) being the same with motion. Again, the movent and Moveable ought to be together, or to touch each other, because, whether the movent im∣pel, attract, carry, or ••owle the moveable: necessary it is, that still it should impress some certain Force upon it: and force it can impress none there∣upon, unless by touching it. And though it doth touch it, yet if it dis∣charge no force of motion upon it, i. e. remain unmoved it self: there shall be only a meer Contact reciprocal, but no motion, and as the one, so shall the other remain unmoved. Therefore, that the one may move the other: it ought to have that vigour or motion first in it self, which it doth impress upon the other: since if it have none, it can give none. Even sense demonstrates, that by how much more vehement motion the mo∣vent it self is in, at the instant it toucheth the moveable, by so much the farther doth it always propel the same: and thence our Reason may ne∣cessarily infer, that the movent must it self be in some small motion, in the same instant it gives a small motion to another. Moreover, though Aristotle (in 8. Physic cap 5.) subtly Distinguisheth three Things in mo∣tion, viz. the 〈◊〉〈◊〉 ut quod, as (V. G.) a man, the Movens ut quo, as a staff: and the Mobile, as a stone: and thereupon magisterially teach∣eth, that the stone is moved, and doth not move; that the staff is mo∣ved, and doth move: that the man doth move, and is not mo∣ved: yet is it not ••••ident, how far short He comes, of thereby De∣monstrating the immobility of the First Movent, to which He praetended. For whereas He urgeth, that otherwise we must proceed to In∣finity; that binds not at all: because the movens ut quod, the man is mo∣ved by Himself: and sense declares, that the man must move his Arm, or Hand together with the staff, which if you suppose not to be the movens ut quo, (the stone b••••ng not moved thereby) but the mobile it self: is not the movent it self ••••so moved? Suppose also, that the mans Arme, or Hand is the move•••• 〈◊〉〈◊〉 quo, nay if you please, that his whole Body, or the Muscles, or Nerve, or Spirits, are the movens ut quo, and deriving the motion from his very Soul, suppose that to be the movens ut quod: yet truely can you not ••••••ceive, that the Soul, it self remaining Immote, doth move the Arm, o•• ••and. Nor is the Soul it self then moved onely by Accident (as whe•• •• marriner is carried by the motion of his ship) but also per se, as w•••••• the mariner moves himself, that he may move the Oar, that it may move the ship, in which himself is carried. For, as a ship, in a calm sea, ••ould not be moved it self, nor the mariner be moved with it, by Accid••••••▪ in case the mariner himself wanted motion, where∣by to impel his ship•• so neither would the body be moved, nor the Soul be moved therew•••••• by Accident, unless the soul be first agitated within, with a motion wh••••••by the body is moved. Conclude, therefore that nothing can be 〈◊〉〈◊〉, but the Projicient must not only Touch it, ei∣ther immediately, ••••mediately by some Instrument; but also Propel it with the same 〈◊〉〈◊〉, wh••••••with it self is, in the same instant, moved.

It is moreover ••••••••ssary, that the movent be moved, not only in a point,

or so far as that point of space, in which it first toucheth the moveable: but also that a while cohaering unto the moveable, it be moved along with it: so as we may well conceive them to be made, by that Cohaesion, as it were one and the same body, or one entire moveable, pro tempore; and consequently, that the motion of both the movent and moveable is one intire motion. For, what motion is in the moveable, so long as it remains conjoyned to the movent, is in a manner a certain Tyrocinium, in which the moveable is as it were taught to progress foreward in that way, which the movent hath begun, upward, downward, transverse, ob∣lique, circular, and that either slowly, or swiftly, and according as the mo∣vent shall guide and direct it, before its manumission or dismission.

Thus, when a man throws a stone with his hand, you may plainly per∣ceive, how the motion thereof begins together with that of his hand: and after it is discharged from his hand, you cannot say, that a new moti∣on is impressed upon the stone, but only that the same motion begun in the hand is continued. And, therefore, it seems also very unnecessary to require the impression of any new and distinct Force upon the stone projected, by the projicient, which should be the Cause of its motion af∣ter its Dismission: seeing nothing else is impressed, but the very motion to be continued through a certain space; so that we are not to enquire, what motive Virtue that is, which makes the Persevering motion, but what hath made the motion, that is to persever. In the moveable, cer∣tainly, there is none but a Passive Force to motion; nor can the Active Force be required in any thing but the movent: and should we, with the Vulgar, say, that there is an Imprest Force remaining, for some time, in the thing moved, or projected; we could thereby understand no other than the Impetus, or motion it self.

Here might we opportunely insist upon this,* 1.27 that motion is impressed upon a thing moved, only in respect, that the thing moved hath less force of Resistence, than the movent hath of Impulsion: so that the movent, forcing it self into the place of the moveable, compels it to recede, or give way, and go into another place. But it is more material for us to observe; that when a thing projected is impelled, it is first touch∣ed by the projicient only in those parts, which are in its superfice or outside and that those outward parts, being pressed by the impulse, do drive in∣ward or press upon the parts next to them; and those again impel the parts next to them, and those again the next to them; till the impulse be by succession propagated quite through the body of the thing projected, to the superficial parts in the opposite side, and then begins the motion of the whole, the parts reciprocally cohaering: as hath been formerly explain∣ed, in the example of a long pole, or beam of wood. Which being per∣cussed, but with a very gentle or softly stroke, that one end hath all its parts so commoved successively, as that the stroke may be plainly percei∣ved by a man, that lays his ear close to the other end: which could not be if the impulse were not propagated from parts to parts successively, through the whole substance of the beam. To which it is requisite, that we superad this observable also; that by reason of the force made by Contact, and that short Cohaesion of the moveable to the movent, there is created a certain Tension, or stress of all the parts of it, towards the opposite region: and of that by that means, all the parts of the thing

projected, are disposed or conformed as it were into certain Fibers, or di∣rect Files; of all which the most strong and powerful is that, which being trajected through the Centre of Gravity in the thing projected, becomes as it were the Axis to all the circumstant ones. Our eys ascertain, that unless the Centre of Gravity be in the middle of the thing projected, or directly obverted to the mark, at which the thing is thrown; the thing instantly turns it self about, and that part, wherein the Centre of Gravi∣ty is, always goes foremost, and as it were carries the rest of the parts, as that which is the most Direct and most Tense of all the Fibres. And this cannot be effected, but with some (more or less) Deflection from the mark, at which the force, according to the Centre and Axis of Gravity, was directed; forasmuch as the Centre of Gravity, wherein many Fibres concur, makes some Resistence, and detorting the Fibres, inflecteth them another way, and so a new Axis is made pro tempore, according to which the Direction of all the parts in their motion afterward is determined. Hence is it, that, if you would hit a mark, either with a sling, or stone∣bow, you must choose a stone, or bullet of an uniform matter and com∣position: or, at least, turn the heavier part of the body to be thrown, for∣ward; because otherwise, it will Deflect more or less, to one side or other according to the position and inclination of its Centre of Gravity. More∣over, whether soever the thing projected doth tend, all the Fibers constant∣ly follow the Direction of the Axis, or are made parallels thereunto; so that as often as the Centre is changed, so often doth the Axis, so often do all the Fibres change their position, and follow the Centre. Which we insert chiefly in respect of the motion of Convolution, or Turning of a thing projected immediately after its Dismission; and of the Curvity of that Line, which is thereby described, whether ascending, or descending. But these are onely Transient Touches, or Hints; that we might easily intimate, why a motion once imprest, is continued rather this way, than that: and why Feathers, Sponges, and the like Light and Porous bodies, are incapable of having quick and vehement motions imprest upon them; because they consist of interrupted Fibres, and such as are not Dirigi∣ble with the Centre of Gravity.

* 1.28Here we ask leave, once more to have recourse to that useful suppositi∣on of a stone situate in the immensity of the Imaginary spaces. We lately said, as you may remember, that if a stone placed in the empty Ex∣tramundane spaces, should be impelled any way, the motion there∣of would be continued the same way, and that uniformly or equally, and with tardity or celerity proportionate to the smartness or gentleness of the Impulse, and perpetually in the same line; because in those empty spaces it could meet with no cause, which by Diversion might either accelerate, or retard its motion. Nor ought it to be Objected, that nothing Violent can be Perpetual; because, in this case, there could be no Repugnancy or Resistence, but a pure indifferency in the stone to all regions, there being no Centre, in relation whereunto it may be conceived to be Heavy or Light. And, therefore, the condition of the stone would be the very same, as to Uniformity and Perpetuity of motion, with that of the Cae∣lestial Orbs; which being obnoxious to no Retardation, or Acceleration, but free from all Repugnancy internal, and Resistence External, constant∣ly and inde••inently maintain that Circular motion, which was, in the first moment of their Creation, imprest uopon them, by the Will of the Cre∣ator;

and that toward one part, rather than any other. Let us now far∣ther consider; seeing that if upon some large horizontal plane you should place a smooth Globe, and then gently impel it; you would observe it to be moved therupon equally and indefinently, till it came to the end there∣of: why may you not lawfully conjecture, that if the Terrestrial Globe were of a superfice exquisitely polite, or smooth as the finest Venice Glass; and another small Globe as polite were placed in any part of its superfice, and but gently impelled any way, it would be moved with constant Uni∣formity quite round the Earth, according to the line of its first direction; and having rowled once round the Earth, it would, without intermission again begin, or rather continue another Circuit, and so maintain a perpe∣tual Circulation upon the surface of the Earth? Especially, since there is no Difficulty 〈◊〉〈◊〉 discourage that conjecture; forasmuch as look how many parts of the small Globe, during the motion thereof, tend toward the Centre of the Earth, just so many are, at the same time, elevated from it: so that a full Compensation being made in all points of the motion, the same cannot but perpetually continue, and in the same equal tenour, there being no Declivity, whereby it should be Accelerated, no Acclivity, wher∣by it should be Retarded, no Cavity, whereby after many accurses and recurses, or reciprocations, it should be brought at length to acquiesce. Moreover, in order to our grand scope, let us suppose, that the space, through which a stone should be Projected, were absolute Inane, or such as the Imaginary spaces; and then we must acknowledge, that it would be carried in a direct and invariate line, through the same space, and with an Uniforme and Perpetual motion, until it should meet with some other space, full of magnetique rayes, Aer, or some other resisting sub∣stance. But, here with us, in the Atmosphere, because no space is Inane (sensibly) but replete as well with Aer, as with millions of mag∣netique rayes transmitted from the Earth; and so a stone Projected must encounter them in every point of space through which it moves: therefore is it, that it cannot be moved either in a direct Line, or equally, or long. For, since multitudes of magnetique Rayes must necessarily invade and attach it, as soon as it is discharged from the Projicient; though at first setting forth it break through them, and so is scarce at all Deflected: yet because more and more magnetique rayes freshly lay hold of it in every part of space, renew the Attra∣ction, and so more and more infringe and weaken the force of its motion; hence comes it, that in the progress it doth by little and little Deflect from the Line of Direction, moves slower and slower, and at length sinking down to the Earth, thereon attains its quiet. Hereupon, when men shall Demand, what is that Cause, which weakens and at last quite destroys the Virtue Impressed upon a thing Pro∣jected; rightly understanding, by the Virtue Imprest, the motion be∣gun by the Projicient, and continued by the Projectum: the Answer is manifest; viz. That it is the Attraction of the Earth, which first op∣poseth, after gradually refracteth, and in fine wholly overcometh the motion imprest, and so determineth the Projectum to Quiet. Hence also may we learn, that All motion once impressed, is of it self Indelible, and cannot be Diminished, or Determined, but by some External Cause, that is of power to repress it.

* 1.29This considered, you may please to observe, that through the Atmo∣sphere, or spaces circumvironing the Terrestrial Globe, being so pos∣sessed by the Aer and swarms of Magnetique Rayes, no body can be pro∣jected in an absolute Direct: or perfectly streight Line, unless perpendi∣cularly upward or downward. For, if the projection be made either obliquely, or parallel to the Horizon; the projectum suddain∣ly begins to Deflect from the mark at which it was aimed, and so describes not a streight, but crooked line. Not that the Deflection or Curvity is sensible, at a small distance, especially if the motion be vehement, such as that of an Arrow shot from a Bowe, or Bullet discharged from a Gun: but, that in every point of space, and time, the thing Proje∣cted is attracted somewhat Downward; and there is the same Reason for its Deflection in the first, as there is for its Deflection in the second, third, fourth, or any following point of space, and instant of time, though the greater opposition of the Force imprest makes that Deflection less at the first. Nor ought it to incline us to the contrary, that Archers and Gunners frequently hit the mark, at which they levelled, to some certain distance: because, that Distance is commonly such, as that the Deflecti∣on therein is not sensible, though it be sometimes an hairs-breadth, two, three, or four, sometimes an inch below the mark.

* 1.30Further you may observe, that when a stone is projected, or a bullet shot upward, yet not p••••pendicularly, but obliquely; the motion there∣of is to be considered, not as simply perpendicular, or simply Horizontal, but as mixed, or composed of an Horizontal and Perpendicular toge∣ther: of a Perpendicular, forasmuch as the Altitude thereof may be measured by a Perpendicular line; of an Horizontal, forasmuch as it is made according to the Horizon, and the Latitude thereof may be taken by the plane of the Horizon. But, because by how much the more it hath of the perpendicular, so much the less it hath of the Horizontal; so that the Altitude of it may amount to fifty feet, and the Latitude not exceed one foot: therefore is it manifest, that the crooked Line described by this Compass motion, cannot be Circular; and Galilaeo (Dialog. 4.) hath demonstrated that the Line is Parabolical, or such as Geometricians describe in the ambite of a Cone, when they so intersect it obliquely from one side at the base, that the motion of the intersection is made parallel to the other side left whole, for the Area of each resegment is the Geometricians Para∣bola: and the crooked ambite of the Area, is a Parabolical Line, and frequently taken for the Parabola it self. We remember also, how Galilaeo, upon consequence, and among other remarkables doth observe; that of all Projections, made by the same force, the Longest, and in that respect the most Efficacious, is that, which is made to an half-right Angle, or by aiming at the forty fifth de∣gree of Altitude; in respect of the more prolix Parabola which is described by the Pr••jectum, aimed at that altitude: since at all other altitudes the Parabola must be shorter; the superior Altitudes being less, and the inferior more open than is requisite.

Now this Composition of a Perpendicular and Horizontal moti∣on may be most conveniently Demonstrated unto you, thus.* 1.31 Be∣ing in a ship, under sayl, if you hold a Ball in your hand; the mo∣tion of the ball will be onely Horizontal, viz. That, whereby the ship doth carry you, your hand, and the ball in it. If the ship stand still, and you throw the ball directly upward; the motion of the ball will be onely Perpendicular: but if the ship be moved, at the same instant you throw the ball upward; then will the moti∣on thereof be Compound, partly Perpendicular, partly Horizon∣tal. For, the ball shall be carried obliquely, and describe a Para∣bolical line, in which it ascends and again falls down again; and in the mean time, it shall be promoved Horizontally. The Per∣pendicular alone, your self may discern with your own eye: because, the horizontal is common both to the ball and your eye, and when as well the ball, as your eye is promoved, therefore doth it always appear imminent over your eye, and in the same perpendicular: but, for the Horizontal, He onely can deprehend it, who stands still on the shoare, or another ship not carryed on at the same rate, as that where∣in you are.

Herein there occur Two things, not unworthy our admiration.* 1.32 The One is, that though there be two divers Forces or motions impressed upon the Ball, at the same time: the one from the Vibration of your Arm, the other from the horizontal Translation of the ship: yet doth neither destroy the other, but each attains its proper scope as fully, as if they were impressed apart. For, the Ball ascends as high, when the ship is moved forward, as when it stands still: and whether it describe a Direct, or a semiparabolical: and again, it is as much promoved Horizontally, when you divert it upward by projection, as when you hold it still in your hand and so it be carried onely by the motion of the ship: and consequently whether the motion there∣of describe a Direct line, or a whole Parabola. Onely this you are to note: that a greater Force is required to the projection of a Ball from the foot to the top of the Mast, when the ship moves for∣ward, than when it lies at anchor: because that semiparabolical line, which the Ball must describe in the former case, is shorter than that perpendicular one, which it must describe in the latter: and how∣ever the vibration or swing of your arme may seem to you to be e∣qual in both cases, yet is that vibration or force, whereby the ball is carried upward to the top of the Mast, when the ship is in motion, really greater than that, whereby the same ball is carried to the same height, when the ship lies quiet: because, in the former case, there is superadded to the force of your arme, the force which is impressed both upon you and your arme (without your apprehension) by the motion of the ship. This you shall plainly perceive, if you onely drop down a ball from the top of the Mast, without any swing or motion of your arme at all. For, seeing that the ball doth always fall at the foot of the mast, in the same distance from it, as it was in the instant of its dimission from the top; whether the ship be mo∣ved, or quiet: necessary it is, that some force be imprest upon

the ball by the motion of the ship, or the the same motion, where∣by both the Mast it self, and your hand are affected, at the instant of its dimission; since it must describe a semiparabolical line, longer than that Direct one, which it would describe, if it fell down the ship being quiet. And hence comes it, that if you project a ball from the Poop to the Fore Castle of a ship, under sayl, and back again from the Fore-Castl•• to the Poop; you shall impress a greater force upon it, in throwing it from the Poop to the Fore-Castle, than back again from the Fore-Castle to the Poop: because, in the former case, the force or seconding impulse of the ship must be superadded to the force of your arme in projection, and so make it the stronger; and, in the latter case, the contrary force of the ship doth as much detract from the force of your arme, and so make it the weaker. And though the ball be carried over equal spaces of the Deck of the ship, in both cases: yet shall it not be carried through equal spaces in the Aer.

* 1.33Hence may it be Demonstrated, that the space of Time which the ball is Ascending from the foot to the top of the Mast, is Equal to that in which it is Descending again from the top to the foot. For, were it not so, when the ball is projected in a line perpendicular and parallel to the Mast, the ball would not ascend and descend always at the same distance from the Mast, but would either desert it, or be deserted by it, the ship being in motion. Whence it follows also, that in what proportion the velocity of the ball Ascending doth de∣crease; in the same proportion doth the velocity of the ball again Descending encrease•• so that the motion of the ball must be of equal velocity, when it is removed from the plane of the ship, one fathom ascending, or descending, and likewise at the altitude of one foot, ascending or descending. Again, forasmuch as the force of your arme, projecting the ball, is still equal; but the force superadded thereunto by the motion of the ship, may be more or less vehement, according as the s••••p is carried with greater or less speed: thence it follows, that the ••arabolical lines described by the ball, are respe∣ctively Greater or Less, and the motions of it through the Aer more or less swift. 〈◊〉〈◊〉, yet all are performed in Equal Time; be∣cause the times of them all are equal to the same time, which is due to the simple Assent and Descent, and with the same proportion of parts.

* 1.34The Other, which deserves our admiration, is this; that not∣withstanding, of the twofold motion composing the Oblique one, that which is Perpendicular, is Unequal, the Velocity there∣of being as well diminished in the assent, as augmented in the de∣scent, so that; in equal moments of time, less spaces are pervaded in the assent, and greater in the descent: yet is that motion, which is Horizontal, plainly Equal in all its parts, or of equal velocity throughout; so that equal spaces of the Horizon are pervaded in e∣qual times. The truth of this is constant from hence; that if (the ship being equally moved on, and the ball being projected in a line parallel to the Mast) the foot of the Mast shall pervade twenty

paces, or an hundred foot of horizontal space: the ball shall be horizontally (i. e. toward that region, to which the ship tends) pro∣moved, not more swiftly or slowly in one pace or foot, than in a∣nother, but equally in all: for, otherwise, it could not be al∣ways imminent over the same part of the ship neer the Mast: nor therefore consist in the same line, or distance from the Mast: which yet it constantly observes. But this easily deceives, that at the end of the balls ascent, or beginning of its descent, the motion is slowest: but then are we to observe, that the Devexity, or Con∣formity of it to the Horizon is the Greater, as when it comes low∣er, where the motion is more rapid, the Devexity is less, and its conformity to the Perpendicular greater: so that the whole Inaequa∣bility doth consist in the Assent and Descent, or Perpendicular moti∣on of the ball: while in the mean time there is a perfect Aequability in its Horizontal advance, or promotion. From hence we collect: that since a thing Projected is moved unequally, insomuch as it tends upward or downward: and not as it progresseth parallel to the Hori∣zon, or Ambite of the Earth: therefore is it, that the upward and downward motions are both to be accounted Violent: but the Hori∣zontal, or Circular, Natural: Equality, or Uniformity being the inseparable Character of Natural, and Inequality of Violent motion.

Thus far have we treated of that Returning or Reflex motion of Bodies, whereby, being violently projected upward,* 1.35 they re∣vert or fall down again, by reason of the magnetique Attraction of the Earth: and it now remains onely, that we consider the Rea∣sons of that other species of motion Reflex or Rebounding, whereby Bodies, being also violently moved or projected any way, are im∣peded in their course and Diverted from the line of their Direction, by other bodies encountring them. Concerning this Theorem, therefore, be pleased to know, that among all Reflexions, by way of Rebound or Resilition, that is the Chiefest, when a body projected, and impinged against another body, is returned from thence directly, or in the same line toward the place, from whence it was projected: which always happens, when the Projection is made to right Angles, or in regular line, such as that in which a Heavy body descends upon an horizontal plane. And all other Reflections are in dignity inferior thereunto, as such whereby the thing projected doth not rebound in a direct line toward the same point from whence it was projected, but to some other region by o∣ther lines: according as it is projected in lines more or less oblique. Because, with what inclination a body falls upon a plane, with the very same inclination doth it rebound from the plane (especially a Globe, and such as is of an uniform matter, and consequently hath the Centre of magnitude and that of Gravity coincident in the same point) so that by how much the more oblique the projection is, and how much the less is the Angle made of its line with the line of the plane, (called the Angle of Incidence) so much the more ob∣lique is the reflexion made, and so much the less the Angle made of its line, with the line of the plane continued (called the Angle of Re∣flexion)

and that so long, as till the line of projection shall become pa∣rallel to the plane, and so, no body occurring to or encountring the pro∣jectum, no reflexion at all be made.

* 1.36Know moreover, that betwixt No Reflexion at all, and the Least Reflexion that is possible, there may be assigned as it were a certain Medium; and that is the Emersion or Rising up again of a weight appensed to a thread or Lutestring, when performing a vibration or swing from one side to the other, it ascends from the perpen∣dicular Line, to which by descending it had reduced it self. For, in that case, no ••••••lecting body doth occur, a simple Arch is described; and y•••• ••here is as a certain Procidence or falling down to the lowest point of the Arch, so also a certain Resilition or ri∣sing up again from ••he lowest point of the Arch, toward the con∣trary side. Again▪ having conceived a direct line touching the lowest point of the Arch, so as that the weight suspended by a string, may, in its vibration, glance upon it with its lowest extreme, and onely in a point touch the horizontal line; you shall have on each side an Angle mad•• from the Arch and the line touching it, which is therefore called the Angle of Contingence: and because Geome∣tricians demonstrate•• that the Angle of Contingence, which truly differs from a right line, is less than any Rectilinear Angle, how∣ever acute; therefore may each of those Angles be said to be Medi∣an betwixt the right line, and the Angle either of Incidence•• or of Reflexion, how small soever it be; and consequently, the E∣mersion of the weight in Vibration may as justly be said to be Me∣dian betwixt the smallest Reflexion and none at all. However, this Emersion seems to 〈◊〉〈◊〉 the Rule of all Reflection whatever; for, as in the Vibration of a weight appensed to a string, and describing a simple Arch, the A••gle of its Emersion is always equal to the An∣gle of its Prociden••••: so in Projection describing an Angular line, the Angle of Reflection is always (quantum ex se est) equal to the Angle of Incidence▪ We say, quantum ex se est; for otherwise, whether it be sensible, or not, because so long as the Projectum is transferred, it is a••ways somewhat depressed toward the earth, for the reason formerly alleadged; thence comes it, that the Refle∣xion can neither be so strong or smart as the Incidence, nor make as great an angle, 〈◊〉〈◊〉 arise to as great an altitude. Which we in∣sinuate, that we might not insist upon this advertisement; that the Aequality of the Angle of the Reflexion to that of the Incidence, may be so much th•• less, by how much the less the projected body comes to a spherical figure, or doth consist of matter the less uniform.

* 1.37For, to attain to that Aequality of the Angels of Incidence and Reflexion, necessary it is, that the body projected be exactly sphe∣rical, and of Uni••orm matter, and so having the Centre of Gra∣vity, and the Centre of magnitude coincident in one and the same point; as we have formerly intimated: it being as well against Reason, as Experience, that bodies wanting those conditions should arise to that aequali•••• which that we may the better understan••, let us consider, that 〈◊〉〈◊〉 in a Globe, or Ball Falling down, we regard onely that Gravity▪ which it acquires in its descent, from the mag∣netique

Attraction of the Earth: so in a Globe, or Ball Projected, we are to regard onely that Impetus or Force, which being imprest upon it by the Projicient, supplies the place of Gravity, and in re∣spect whereof the Centre of its Gravity may be conceived to be one with that of its magnitude. Let a Ball, therefore, be projected Directly or to right Angles, upon a plane; and, because, in that case, that Fibre must be the Axis of its Gravity, whose extreme going foremost is impinged against the plane: thence is it mani∣fest, that the Repression must be made, in a direct line, along that Axis; the parallel Fibres in equal number on each part invi∣roning that Axis, and so not swaying or diverting the ball more to one part than to another, by reason of any the least dispro∣portion of quantity on either side. Then, l••t the same Ball be projected Obliquely against the same plane; and because, in this case, not that middle Fibre, which constituteth the Axis of Gravity, but some one or other of the Fibres circumstant about it, must with one of its extreams strike against the plane: there∣fore is it necessary, that that same Fibre be repressed by that im∣pulse, and by that repression compelled to give backward toward its contrary extream, and thereby in some measure to oppose the motion begun, which it wholly overcome, and so the ball would rebound from the plane, the same way it came, if the Fibres on that side the Axis of Gravity, which is neerest to the plane, were equal in number to that are on the farther, or contrary side of it: but, because those Fibres, that are on the farther side, or on the part of the Centre and Axis, are far more in number, and so the••e is a greater quantity of matter, and consequently a greater force imprest, than on the side neerer to the plane; therefore doth the begun motion persever, as praevailing upon the repression and renitency of the Fibre impinged against the plane, and since it can∣not be continued in a direct line, because of the impediment arise∣ing from the parts cohaerent, it is continued by that way it can, i. e. by the open and free obliquity of the plane. But, this, of necessity, must be done with some certain Evolution of the Ball, and with the contact of the Fibres posited in order both toward the Axis and beyond it; and while this is in doing, every Fibre strives to give back, but, because the farther part doth yet praevail over the neerer, therefore doth the neerer part still follow the sway, and conform to the inclination and conduct of the farther, and all the toucht Fibres change their situation, nor are they any longer capa∣ble of returning by the same way they came, because they no long∣er respect that part from whence they came. We say, with the Contact of the plane by the Fibres posited toward the Axis and be∣yond it; because, since in that Evolution or Turn of the Ball, the extream of the Axis toucheth the plane, yet nevertheless no Resi∣lition, or Rebound is therefore caused, in that instant; and if there were a resilition, at that time, it would be to a perpendicu∣lar, as well the Axis, as all the circumstant Fibres being erected perpendicularly upon the face of the plane: but the Resilition there must be beyond it, because the force of the farther part of the Fi∣bres doth yet praevail over that of the neerer. For, the Force of

the farther part doth yet continue direct and intire; but, that of the neerer is reflected, and by the repression somewhat debilitated: and therefore, the Resilition cannot be made, until so much of Repression and Debilitation be made in the further part, as was made at first in the neerer. And that must of necessity be done, so soon as ever the plane is touched by some one Fibre, which is distant from the Axis as much beyond, as that Fibre, which first touched the plane, is distant from the Axis on this side: for, then do the two forces become equal, and so one part of the Fibres having no reason any longer to praevail over the other, by counter inclination, the Ball instantly ceaseth to touch the plane, and flies off from it, toward that region, to which the Axis and all the cir∣cumstant Fibres are then, i. e. after the Evolution, directed. Now, because the Ball is, after this manner, reflected from the plane, with the same inclination, or obliquity, with which it was impin∣ged against it; it is an evident consequence, that the Angle of its Reflexion must be commensurable by the Angle of its Incidence: and that each of them must be so much the more Obtuse, by how much less the line of projection doth recede from a perpendicular; and contrariwise, so much the more Acute, by how much more the line of projection doth recede from a perpendicular, or how much neerer it approacheth to a parallel with the plane.

* 1.38From these Considerations we may infer Two Observables. The One, that the oblique projection of a Globe against a plane, is com∣posed of a double Parallel, the one with the Perpendicular, the other with the plane: for, the Globe at one and the same time, tends both to the plane, and to that part toward which the plane runs out for∣ward. The Other, that Nature loseth nothing of her right, by the Reflexion of bodies; forasmuch as she may nevertheless be allowed still to affect and pursue the shortest, or neerest way: for, because the Angle of Reflexion above the plane, is equal to that Angle, which would have been below the plane, in case the plane had not hinderd the progress of the line of projection beyond it, by reason of the Angles Equal at the Vertex, as Geometricians speak; therefore, is the Reflex way equal to the Direct, and consequently to the shortest, in which the ball projected could have tended from this to that place.

* 1.39Here, to bring up the rear of this Section, we might advance, a discourse, concerning the Aptitude and Ineptitude of Bodies to Reflexion; but, the dulness of our Pen with long writing, as well as the Confidence we have of our Readers Collective Abili∣ties, inclining us to all possible brevity, we judge it sufficient onely to advertise, that what we have formerly said, concerning the Aptitude and Ineptitude of Bodies to Projection, hath anticipated that Disquisition. For, certain it is, in the General, that such Bodies, which are More Compact, Cohaerent, and Hard, as they may be, with more vehemence, and to greater distance, Projected: so may they, with more vehemence, and to greater distance Rebound, or be Reflected; provided, they be impinged against other bodies

of requisite Compactness, Cohaerence, and Hardness. And, the Reason, why a Tennis-ball doth make a far greater Rebound, than a Globe of Brass, of the same magnitude, and thrown with equal force; is onely this, that there is not a proportion be∣twixt the Force imprest by the Projicient, and the Gravity of each of them; or betwixt the Gravity of each, and the Resistence of the Plane. Which holds true also concerning other bodies, of dif∣ferent Contextures.

Notes

• * 1.1

  Art. 1. Why th•• Na∣ture of ••otion which d••s••rved to have been the subject of the first specu∣lati••••▪ was re∣s••rved to b•• the Argum••nt of t••e Last, in this Ph••siology.
• * 1.2

  Art. 2 An Epicurean Principle▪ of ••un••amental concern to mo••ion.
• * 1.3

  Art. 3. 〈…〉〈…〉.
• * 1.4

  Art. 〈…〉〈…〉
• * 1.5

  〈1 paragraph〉〈1 paragraph〉
• * 1.6

  Art. 6. Emperi•••••• his ••••••ections against that D••finition of Epic••rus: and 〈…〉〈…〉 of each
• * 1.7

  Art. 7. That t••ere is motion; con∣trary ••o th•• Sop••••sms of Parmenides, Mel••ssus, Zeno, D••••do••us. and the Sce••ticks.
• * 1.8

  Art. 1. 〈…〉〈…〉
• * 1.9

  Art. 2 The 〈◊〉〈◊〉 de∣duced from the 〈◊〉〈◊〉 Epi∣curean P••••••ci∣p••e of mo••••on, 〈◊〉〈◊〉▪ and 〈◊〉〈◊〉 consid••∣ra••le Conclusi∣ons extracted from the••ce.
• * 1.10

  Art. 4. 〈◊〉〈◊〉 or Aequanility, ••he 〈◊〉〈◊〉 ••haracter of a Natural moti∣on•• and 〈◊〉〈◊〉 want of uni∣••ormity, of a 〈◊〉〈◊〉.
• * 1.11

  Art. 5. ••he D••wn∣w••rd motion 〈◊〉〈◊〉 Inanimates, derived from ••n External Principle, contrary to A¦ristotle
• * 1.12

  〈1 paragraph〉〈1 paragraph〉
• * 1.13

  〈1 paragraph〉〈1 paragraph〉
• * 1.14

  〈1 paragraph〉〈1 paragraph〉
• * 1.15

  〈1 paragraph〉〈1 paragraph〉
• * 1.16

  Art. 〈1 paragraph〉〈1 paragraph〉
• * 1.17

  〈1 paragraph〉〈1 paragraph〉
• * 1.18

  Art. 12. That the Pro∣portion, or Ration of Ce∣lerity to Cele∣rity, encreasing in the descent of Heavy things; is not the same as the Proporti∣on, or Ration of Space to Space, which they pervade contrary to Michael Var•• the Mathema∣tician▪
• * 1.19

  〈1 paragraph〉〈1 paragraph〉
• * 1.20

  Art. 14 〈…〉〈…〉
• * 1.21

  Art. 15. The same De∣monstrated.
• * 1.22

  Art. 16. The Physical Reason of that Proportion.
• * 1.23

  Art. 17. The Reason of the E••ual Veloc••ty of B••∣dies of very d••ffe••••n•• weig••ts, fal∣ling from the same altitude; inferred from the same The∣••••y.
• * 1.24

  Art. 18. Gravity Di∣stinguish't in∣to Simple, and Adjectitious.
• * 1.25

  Art. 19. The R••••e of that superla∣tive velocity, with which a Bullet would be carried, in case it should fall from the Moon, Sun, or region of the ••ixed stars, to the Earth: and 〈◊〉〈◊〉 each of those vast heights, to the 〈◊〉〈◊〉 of the 〈◊〉〈◊〉.
• * 1.26

  Art. 1. What, and whence is that Force, or Vir∣tue Motive, whereby Bo∣dies Projected are carried on after their Dismission from the Pro∣jicient.
• * 1.27

  Art. 2. The Manner of the Impression of that Force▪
• * 1.28

  Art. 3. That all Moti∣on, in a free or Empty space, must be Vniform, and Perpetual: and that the chief Cause of the Inequality and Brevity of the motion of things project∣ed through the Atmosphere, is the magne∣tique Attracti∣on of the Earth.
• * 1.29

  Art. 4. That, in the Atmosphere, no body can be projected in a Direct line; unless perpendicu∣larly Upward, o•• Downward: and why.
• * 1.30

  Art. 5. That the Mo∣tion of a stone pro••ected up∣wards ob∣liquely, is Composed of an H••••iz••••tal and Perpendi∣••ular together.
• * 1.31

  Art. 6. Demonstrati∣on of that Composition.
• * 1.32

  Art. 7. That of the two different Forces, impres∣sed upon a ball, thrown upward from the hand of a man standing in a ship, that is under sayl; the one doth not destroy the other▪ but each attain•• its proper scope.
• * 1.33

  Art. 8. T••at the space of time, in w••i••h the ••all is A••cending f••om the F 〈…〉〈…〉 the Top of the M••st; is equal to that, in which it is again Descend∣ing from the top to the ••oot.
• * 1.34

  Art. 9. 〈…〉〈…〉.
• * 1.35

  Art. 10. The Reason and Manner of the Reflexion or Rebounding motion of Bo∣dies, diverted from the line of their di∣rection by o∣thers encoun∣tring them.
• * 1.36

  Art. 11. That the ••mer∣si••n of a weight appen••••d to a 〈…〉〈…〉 the perpendicular, 〈◊〉〈◊〉 which it had ••••duced it self, in Vibration; 〈◊〉〈◊〉 a R••flexion 〈◊〉〈◊〉 betwixt 〈◊〉〈◊〉 Reflexion at all, and the Least Reflexion assignable; and the R••le of all other Reflexion whatever.
• * 1.37

  Art. 12. ••he ••ea••••n of the Ae••ualit•• of the Angles of In••iden••e and R••••l••xi••n.
• * 1.38

  Art. 13. Two Inferen∣ces from the praea••ses▪ viz. (1) That the oblique Proje∣ction of a Globe against a plane, is composed of a double Paral∣lel: and (2) That Nature suffers no di∣minution of her right to the shortest way, by Refle∣xion.
• * 1.39

  Art. 14. Wherein the Aptitude or In∣e••••itude of bo∣dies to Re∣fle••ion doth consist.