the Motion lasts also but when that ceaseth the Motion ceaseth likewise And 't is added That this Quality cannot last always being in its nature so imperfect that it cannot last long Besides it is Objected That Experience shews that all Motions do cease little by little as appeareth in a Wheel that hath been violently agitated in a Ball that hath been rolled on a Billiard-Table in a Ball suspended and vibrated and in other innumerable Bodies the Motions of which do by little and little diminish and at last are quite extinguish'd VII A Finite Cause may have an Effect that lasts always I Say it is very easie to Answer all these Objections and many such others If any one will maintain that Motion is an Infinite Effect because it lasts forever he must also say that Rest will be an Infinite Effect if it thus last eternally and that consequently a Finite Cause not being able to have an Infinite Effect it must be said that after a Man hath put a Body at Rest this Body cannot remain in that Rest forever but that Rest must at last cease and the Body begin to move which is not consonant to reason There is a great difference between an Infinite and an Ever-during Effect And if it be true that a Finite Cause cannot produce an Infinite Effect it is as true that a Cause how bounded soever it be may produce an Ever-subsisting Effect if it be not destroyed by some new Cause For if I make a square Figure upon Wax this Figure will last always if nothing survene to spoil it or to destroy the Wax it self So that 't is not incongruous at all to say that if Rest or Motion be once produced in a Body this Rest or Motion shall last without end if nothing come to destroy it VIII This Quality which is called Impetuosity lasts always AS to that Quality which is pretended to be produced in the Body by him that striketh it 't is all one to me whether it be believed to be so or not But this I say that if that Quality be necessary it will last forever after it hath been once produced and that it will never cease to be till some new Cause destroy it And herein the Sentiment of Vasquez 1. 2. d. 81. c. 2 3. is very remarkable when he teacheth generally of all Forms substantial and accidental and particularly of Motion and Impetuosity That if they can subsist one moment without needing the influence of their first Efficient Cause they will last always until they be destroyed by the production of a new contrary Form If Men will still persist in this Opinion and say That this Quality is so weak in its own nature that it destroys it self I do maintain that after this Quality shall have been destroy'd the Motion notwithstanding must continue for the reasons already deliver'd in regard that Motion cannot cease unless Rest be produced a new But there must always be a positive Cause to produce a new what Effect soever it be whereas there needs none such to make that subsist which is already in being And this is the true reason why a square Figure made in Wax would last eternally if God should keep all external Agents from destroying any thing in that Wax because this square Body of Wax could not lose this Figure unless another Figure were produced And as a Figure cannot begin to be a new unless there be some positive Cause to produce it and we also suppose that there is none such in this Case it must needs follow that this first Figure which is already produced keeps forever the possession of its existence 'T is the same thing with Motion And although this pretended Impetuosity ceaseth to be yet the Motion which is already produced is not therefore to cease also because there is no new Cause producing Rest and Motion cannot cease but Rest must be produced instead thereof IX The Bodies which we move do cease to move because they are impeded LAstly when we see that Bodies moved by us do in a little time cease to move that proveth nothing against us it being certain that those Bodies meet with impediments to their Motion Whence we see that the more or the less we remove of those impediments the more or less do those Motions continue Thus a Ball rolleth much longer over a very smooth Alley than in a rugged way A Wheel turns much better if its Axle-tree be slender and well turned than when 't is big and irregular A Stone is cast much farther in the Air than in Water But I shall endevour in the Sequel of this Discourse to explain how all these Impediments do by little and little make the Motion of Bodies to cease X. A Demand for the safety of the following Demonstrations ALl I have been just now deducing about the Nature and Perpetuity of Motion is in a manner necessary for the understanding what I pretend to demonstrate in this Discourse But as this Question can never be handled so clearly but that it will always be obnoxious to the Cavils of Disputants I foresee well enough that after all my reasonings it will doubtless so fall out that all will not be convinced of what I shall have undertaken to prove And besides not being willing to clash with any nor to leave ground to believe that I build my Discourse upon a doubtful Principle I declare that for the firmness of my Demonstrations I need not it should be thought that Motion would in effect be perpetual so it be but allow'd me which no Man can deny that Motion once begun lasts at least for some time and continues the more uniformly the less impediments there are to stop or diminish it Let this Continuance of Motion be explain'd by the production of an impressed Quality or by a simple Determination or by whatever you please 't is indifferent to me I only demand it may be allow'd me to take this as a Postulatum of Geometry That after a Body is once mov'd it continues to move for some time and that this time is considerable when there is nothing without able to stop or lessen the Motion By the means of which Demand I hope that all the following Demonstrations will be found of full force XI A Body receiving successively many Determinations remains only affected with the last A Body not only persevereth in Rest or Motion according as it hath once begun to be in either but it persists also in the same kind of Motion and with the same degree of Celerity in which it hath been put For Example If it have begun to move in a straight Line Eastward with one degree of Celerity it continues to move with the same degree without ever receding a jot from the same Line Which is evident from the same reasons I alledged to prove the Motion to last always But it is to be Noted that when a Body hath successively received many different Determinations it remains
I could make out if I should write other Discourses of Motion XXXVIII The Conclusion THere would remain something to be said of the Motion of Heavy Bodies as well of those that fall or are projected in the Air as of those which roll on inclined Plains or which being suspended by a thred do vibrate to and fro Somewhat also should be spoken of the Motion of Liquors as well of their fall as their prosiliency as also of their Undulations and the like But all those particulars deserve so many particular Discourses And as I think I have found something new concerning these things I shall not scruple to publish my thoughts for examination if I find that this first Discourse hath not been judged altogether unworthy to be read by persons who take a delight in such matters AN ADVERTISEMENT TO THE READER THe Author of this Tract about Local Motion having been informed by a Friend that some persons who had read these papers as they were coming from the Press gave out that he followed altogether the Doctrine of Monsieur Des Cartes and that alâ—â—ough in some places he seemed 〈◊〉 oppose him without naming him yet he did establish all the Sentiments of that Philosopher concerning this Subject He hath thought himself obliged to undeceive those who should believe those persons upon their word by the following Notes which he thought fit to annex at the end of this Tract before it should appear in publick NOTES UPON THE DISCOURSE OF LOCAL MOTION WHen the Author of this Discourse insisted to prove that Motion is never destroyed but by a contrary determination survening a new he did sufficiently declare himself concerning the little addiction he had to this Sentiment But as those who have treated of this matter in Italy England Holland and France agree almost all in that particular he did not think he was to recede from so common a Doctrine Galilaeo Gassendi Hobbes Regius Magnan Digby Kircher Fabri and many others do all maintain in some manner this Perpetuity of Motion and they only differ in the way of proving it Of all the proofs alledged hitherto on its behalf the weakest doubtless is that of Monsieur Des-Cartes This Author pretends that if Motion or Rest once begun should cease God would be subject to change Which is a ratiocination that maketh those smile who have any tincture of Theology there being none that knoweth not that all these changes in the Creatures are made without any change in God Apud Deum non est transmutatio saith St Augustin ideo apud eum Cursus temporis diei noctisque alternatione nequaquam variatur And 't is manifest that the Cessation of Motion is no more repugnant to the Immutability of God than the Creation of the World or the actions of our Wills or the vicissitude of Days and Nights If this reason of Monsieur Des-Cartes were not so easie to answer it would be a dangerous one because it would prove that God should have made from Eternity all the Motion which is now found in the World As many in the choice of Opinions have a regard to the Sentiment of the Antients and of the Scholastick Doctors it may be added here that besides what Vasquez hath said who insists to prove at large this Perpetuity of Motion affirming that Motion once begun never ceaseth unless there survene some new Cause producing some positive form contrary to this Motion Besides that I say three of those great Disputations of Lyons held at several times affirm the same thing Moreover Aristotle is of the same mind See what he saith in his third Book of Meteors Chap. 2. If a Body that were without gravity or levity be moved it must needs be moved by some adventitious force and being once so moved it will move in infinitum 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 And in the fourth Book of his Physicks Text. 69. speaking of a Body that had moved in vacuo where 't is supposed that there is no kind of impediment he hath these words No Man can say why a Body that were thus moved in vacuo should stop any where For why should it rather stop here than there And therefore it will not stir at all or if it begin to stir it must move in infinitum if something stâ—onger doth not stop it 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Monsieur Des-Cartes maketh very ill use of the Principle that hath been explained in § 13. That a Body which is moved about a Center endevours to recede from it It can be made out that he hath mistaken in attempting thereby to explicate the Gravity of Bodies Neither do we mean to allow to this Principle all that Latitude which Monsieur Des-Cartes hath given it And we approve much of that restriction that hath been put by an Intelligent person viz. That that is true in Artificial Motions and that it cannot be so in the Natural What hath been proved in § 16. and the following sheweth that Monsieur Des-Cartes hath been deceived in Six Rules of the * These Rules may be found in the second part of Des-Cartes 's Principles of Philosophy Sect. 46 47 48 49 50 51 52 in my Edition which is printed at Amsterdam A. 1656. Seven which he hath delivered about Motion In § 26. It is not at all pretended to favour the Opinion of the Motion of the Earth The Author of this Discourse is fully perswaded that although there were not the Holy Scriptures the Hypothesis which maketh the Earth moveless is preferable to all others He would only shew that that Argument of P. Ricciolo was not cogent There are others that are better especially that which hath been prevalent on very good occasions taken from the â—onique motion of the Load-stone The 29. § is against Monsieur Des-Cartes who hath not distinguished the Motion which is here called absolute from that which is called respective And when he saith that there is always an equal quantity of Motion before or after the percussion he means it of this absolute Motion or it is very apparent that he hath therein mistaken For in the figure 14. before the percussion the Motion of the two Balls A and B is A a and B b and all the Motion after the percussion reduced together in the sole Ball b is only b b the other Ball remaining moveless in a. When in § 21. mention is made of a substance more subtile than the Air the Reader is not to imagin that it is the subtile Matter of M. Des-Cartes All Men acknowledge that there are subtiler Bodies than the Air which we inspire And as Aristotle in his Constitution of the Universe hath placed the Sphere of the Air above the Water so hath he put the Fire above the Air and the Aether above the Fire which are all different substances which the more subtile they are the higher they are raised It is pretended in § 37. that M. Des-Cartes hath not proved the Refractions of Bodies and much less that of Light FINIS These Books are to be Sold by Moses Pitt at the White-Hart in Little-Britain Folio CAssandra the fam'd Romance 1667. Brigg's Logarithms Francisci Suarez Metaphysica Quarto Dr John Pells Introduction to Algebra Translated out of High-Duch into English by Thomas Branker M. A. Also a Table of odd Numbers less than 100000 shewing those that are Incomposits and resolving the rest into their Factors or Coefficients 1668. Nich. Mercatoris Logarithmo-Technia sive Methodus construendi Logarithmos 1668. Jacobi Gregorii Exercitationes Geometricae 1668. Dr. Joh. Wallis Opera Mechanica pars prima secunda 1670. Banister's Works of Chyrurgery Hugh Broughton's Consent of Scripture Snellii Typhis Batavus Lugd. Bat. 1624. Observat Hussiacae Petrus Paaw de ossibus Amstelreod 1633. A Letter from a Gentleman of the Lord Howard's Retinue to his Friend in London Dated at Fez Nov. 1669. Wherein he gives a full Relation of the most remarkeable passages in their Voyage thither and of the present State of the Countries under the power of Taffaletta Emperour of Morocco with a brief account of the Merchandizing Commodities of Africa as also the Manners and Customs of the People there Lex â—alionis sive Vindiciae Pharmacopoeorum Or A short Reply to Dr. Merret's Book and others written against the Apothecaries wherein may be discovered the Frauds and Abuses committed by Doctors professing and practising Pharmacy Octavo Biblia Hebraea Josephi Athias 1661. Gualteri Needham Disquisitio Anatomica de Formato Foetu 1667. Buxtorfius's Fpitomy of his Hebrew Grammar translated in English by John Davis 1658. Crow Scriptores in Scripturam Now in the Press The Fortunate Fool or the Life of the Dr. CenÌ„udo 1670. The Adventures of Mr. T S. an English Merchant taken Prisoner by the Turks of Argiers and carried into the Inland Countries of Africa with a Description of the Kingdom of Argiers and of all the Towns and Places thereabouts as also a Relation of the chief Commodities of the Countrey and of the Actions and Manners of the People Whereunto is annexed an Observation of the Tide and how to turn a Ship out of the Straights Mouth the wind being westerly 1670. Contemplations on Mortality 1669. A Discourse written to a learned Frier by M. Des Fourneillis shewing that the Systeme of M. Des Cartes and particularly his Opinion concerning Brutes does contain nothing dangerous and that all he hath written of both seems to have been taken out of the First Chapter of Genesis To which is annexed the Systeme general of the Cartesian Philosophy Basilius Valentinus of Natural and Supernatural Things also of the first Tincture Root and Spirit of Metals and Minerals how the same are Conceived Generated Brought forth Changed and Augmented To which is added Alex. van Suchten of the Secrets of Antimony 1670. Pharmacopoeia Lond. 24o. 1668.
are made in pleno as in vacuo pag. 56. XXXV When the Bodies are unequal the percussions are made in pleno otherwise than in vacuo pag. 57. XXXVI The Percussions of unequal Bodies cannot be reduced to one General Rule pag. 59. XXXVII Of Refraction pag. 61. XXXVIII The Conclusion pag. 62. An Appendix containing a Review of this Discourse made by the Author himself pag. 67. A DISCOURSE OF LOCAL MOTION I. A Body is in it self indifferent to Rest or Motion IF we should imagin that in the World there were nothing corporeal but one or two Balls and sever from the same whatever might cause any kind of secret Commerce whereby the one might attract or repel the other Or if we should consider such Balls free from all kind of particular Determination without Levity without Gravity in Vacuo or at least in a Space altogether uniform where nothing were that might carry them rather this than that way or hinder them to move freely if they should happen to be propelled towards a place Then should we conceive these Balls to be absolutely indifferent to touch one another or to be sever'd to be here or there forasmuch as they would find nothing more in one place than in another and consequently be equally indifferent for Rest or Motion II. If a Body be once at Rest it will ever remain therein ANd so if we further conceive that one of these Balls is at Rest having been put in that state by some Cause that hath power to stir or stop Bodies we at the same time conceive it will eternally remain at Rest if there be not some new Cause displacing it by putting it into Motion because this Ball being of it self indifferent to Rest or Motion and being once determined to Rest it is impossible it should of it self quit that Rest and fall to Motion Wherefore it must needs continue forever in that Rest if nothing happen to make it change that state III. And if it be once in Motion it continues also to move always BY the same Reason we must conceive that if one of these Balls be put in Motion by some Cause or other it will continue to move forever if no new Cause come to stop it Because this Ball being of it self indifferent to Motion and Rest and being once determined to Motion it is impossible it should determine it self to cease from that Motion to take Rest And so it must ever remain in this Motion if nothing else come to stop it IV. That Rest is not a meer Negation I Find that we are generally inclined to consider Rest as a Cessation of Action and to take Motion for a positive Action which we experiment in our selves when we move our selves or will move another Body Whereas we conceive a Body to be at Rest from the time that no Body touches it or that there is no other Cause which actually imprints in it this Quality or this Action necessary to Motion And so it seems that although a Body being once at Rest remains therein forever yet it should not follow that if it be once in Motion it should ever persist therein since that for to be mov'd there is required a positive Action but that Rest is nothing else but a Negation or a Ceasing from Action or Motion V. That there is as much positive Action in Rest as in Motion BUt if the Weight of our Bodies which we must bear the rigidness of our Limbs which we must bend the agitation of the Spirits which we must employ and many other things make us feel some resistance and oblige us to use some force to overcome these impediments We cannot draw from thence any Sequel against our Hypothesis in which we suppose there is no impediment neither of Gravity nor of particular Inclination nor of any Body resisting from without In this Case 't is manifest that there needs no more Action for Motion than for Rest and that for the Rest of a Body it is not less requisite it should be put at Rest than it is necessary for its Motion that it should be put into it And indeed if we consider well the nature of Rest and Motion we shall find that Motion may as well be called a Cessation of Rest as Rest a Cessation of Motion or rather we shall find that both are something positive in regard that Motion is a state by which a Body corresponds successively â—o many places or a passing Presence or a sequel of divers Presences in divers places As Rest is a state by which a Body always corresponds to one and the same place or one and the same Presence in one and the same place So that Rest as well as Motion is a State or a Presence but differing in this that Rest is a State of Consistency and a Constant Presence always kept to be the same whereas Motion is a Changing State and a Transitory Presence Now in what manner soever these constant or passing Presences be consider'd if there be any Action or any Power or any kind of Cause in the Body which is to produce this Consecution of divers Presences in Motion there is no less Action or Force necessary in Rest to preserve the same Presence in regard that to preserve a thing is to produce it continually It is therefore evident that after the Presence hath been produced by a Body in the first instant I speak in the sense of those who hold that there is a true production of these Presences it must needs be also produced a new in the instant following by the same Body to make it remain Quiescent But methinks there is in that as much Action and as much Power as there is for the producing in the second instant a new Presence instead of reproducing the first Nec minor est virtus quà m quaerere parta tueri So that whether there be to be produced every instant a new Presence for Motion or reproduced the same Presence for Rest it will always amount to the same and a Body will have no less work to preserve to it self this same Presence and to remain Quiescent than to produce new Presences and conserve it self in Motion Whence it is to be concluded that as a Body from the very time it hath been once determin'd to Rest is sufficiently determin'd always to keep it self in the same Presence so also from the very moment it hath been once determin'd to Motion it is sufficiently determin'd always to produce new Presences and so to move it self without ceasing VI. Objections I Shall not stay to answer all the cavilling Scruples that may be cast in upon this Subject seeing they are easie enough to resolve For instance 't is said That a Finite Cause cannot produce an Infinite Effect and that this Motion would be Infinite since it would last forever 'T is further alledged That whoever moveth a Body impresseth therein a certain Quality call'd Impetuosity and that as long as this Quality lasts