There is no Science which may fupply us with more Examples, to fhew the Ufefulnefs of thofe Rules, than Geometry., and efpecially Algebra, fince thefe two Sciences make a perpetual life of them. Geometry plainly difcovers the Neceffity always to begin with the moft fimple Things, and which include the leaft Number of Relations: It always examines thofe Relations by Meafures that are clearly known •, it takes off whatever is unferviceable to difcover them -, it divides into Parts Compound Queftions, dilpofes thofe Parts, and examines them in order. In fhort, The on- ly Fault to be found in this Science is, as I have obferv'd elfewhere, that it affords no conve- nient Means to abridge Ideas, and difcovefd Relations: So that though it regulates the Imagina- tion, and makes the Mind exacl; yet it increales not its Extent very much, neither does it give a Capacity to difcover very compound Truths.
But Algebra, continually teaching to abridge, and in the fhorteft Way imaginable, Ideas" and their Relations, extremely improves the Capacity of the Mind; for nothing fo compound can be conceiv'd in the Relations of Magnitudes, but the Mind may difcover it in time by the Means it affords, when we know the Way that ought to be taken.
The fifth Rule, and the following, which fpeak of the Method of abridging Ideas, concern on- ly that Science, for none elfe has a convenient Way of abridging them; fo that I (hall not infift upon their Explication. Thofe who have a great Inclination for TVlathematicks, and defire to give their Mind all the Force and Extent it is capable of, and to put themfelves into a State of difco- vering, without a Tutor, an infinite Number of new Truths, will perceive, if they earneftly ap- ply themfelves to Algebra, that the Ufefulnefs of that Science, as to the Enquiry after Truth, proceeds from its obferving the Rules we have prefcrib'd. But I muft advertife, that by Algebra^ I efpecially underftand that which des Cartes and fome others have made ufe of Before the Conclufion of this Book, I mail fet down an Example fomewhat at large, to fhew the Ufefulnefs of the whole Treatife: I mail reprefent by it the Advances of a Man who, in the Difcuffion of an important Queftion, endeavours to free himfelf from Prejudices -, I mall at firft make him fall into fome Faults, that they may excite the Remembrance of what has been faid elfe- where: But at laft, his Attention leading him to the Truth enquifd after, I induce him fpeaking pofitively, and as one who pretends to have folv'd the Queftion he examin'd.
CHAP. IX.
The laji Inflance to fherv the 'Ufefulnefs of thk Treatife, wherein the Caufe of the cVnioti of Tarts in Bodies y and withall^ the Rules of the Communica- tion of Motion ^ are exam in d.
BOdies are united together three different Ways, by Continuity, Contiguity, and in a third man- ner, that has no particular Name; becaufe" it feldom happens, I mall call it by the general Term of Union, Y By Bv Continuity, or by the Caufes of it, I underftand fomewhat or other which caufes the Parts ©f a Body to hold fo ftrongly together, that we mult ufe violence to feparate thern; for which Reafon they are look'd upon as a Whole.
3y. Contiguity I underftand that, whatever it is, which makes me judge that two" Bodies touch one another immediately, fo as that there is nothing-betwixt them •, though I judge not that they are ltrittly united, becaufe Imay eafily feparate them.
By the 'third Word, Union, I underftand fomething or other which makes two GlalTes, or two1 Marble-Scones, whofe furfaces are well tub'd and poliihed upon each other, to adhere together, lb as that though they can eafily be feparated, by making them glide over one another, yet we rind fome refittance when we endeavour to do it in another manner.'
Now thefe two united Glaffes, or Marble-ftones, cannot be faid to be continuous, becaufe they are not conceived as a Whole, fince they may eafily be feparated fome certain way. Neither, is this a Contiguity, though it be fomething very like it, becaufe thofe two pieces of Glafs, or Mar- ble, are ltrittly enough united, and even more than the Parts of foft and liquid Bodies, as'thoier of Butter and Water.
Thefe Words being thus explained, we mult now enquire after the Caufe that unites Bodies, and the difference betwixt Continuity, Contiguity, and the Union of Bodies, taken in this particu-" lar Senfe: I iliall.firft feek the caufe of Continuity, or that, I don't know what, which unites the Parts of a Body, and links them fo ltrittly together, that violence mult be ufed to feparate them, and that they are look'd upon as making together but one Whole. I hope that this Caufe being found out,, it will prove no hard task to difcover the reft.
It feems now.neceffary to me, that this, I don't know what, which binds even the fmalleft Parrs ot that piece of Iron I hold in my Hands, fhould be fomething very powerful, fince I mult nfe a very great Force to break off a fmall Part of it. But am not I extremely miltaken, for may not thai difficulty I find in breaking the leaft piece of this Iron, come from my Weaknefs, and not from the Reiiftance of the Iron > And indeed, I remember, I have formerly ufed a greater vio- lence than I now do, to break a piece of Iron like this; and if I fell lick, it might happen that my utmoft endeavours could not perform it. I fee therefore that I mult not judge abfolutely of the firrnneis with which the Parts of Iron are joyned together, by the endeavours I make to dif-unite' them, but only judge that they flick very ltrittly to each other in relation to my little Strength, or that they hang more firmly together than the Parts of my Flelh; lince the Senfe of Pain I feel in ufing too much Force advertifes me, I lhall looner difunite the Parts of my Bo- dy, than thofe of the Iron.
Thence i conclude, That as I am not abfolutely ftrong nor weak, fo Iron and other Bodies are not abiolucely hard or flexible; but only in reference to the Caufe that atts upon them. And that • my Endeavours cannot be a Rule to meafure the Degrees of Force, that mult be ufed to overcome the Reliftance and Hardnels of Iron; fince Rules mult be unvariable; whereas thofe Endeavours vary, according to the Time, the plenty of Animal Spirits, and the Hardnefs of Flelh-, for, af- ter ail, I cannot always produce the fame EfFetts by the fame Endeavours.
This Coniideration frees me from a Prejudice, that made me imagine ftrong Bands to unite the Parts ot Bodies, which Bands perhaps are not in being, and I hope it will not be unprofitable hereafter: for I am wonderfully apt to judge of all things with relation to my felf, and to follow the Imprelhons of my Senles, of which I lhall more carefully beware. But let us proceed.
Having thought fome Time, and fearch'd with fome Application, the Caufe of this ftritt Union, without being able to dilcover it h I find my felf inelin'd. by my own natural Lazinels, to judge, as feveral others do, that it is the Form of Bodies that preferves the Unron betwixt their Parts, or the Friendlhip and Inclination they have for fuch as are alike to them: And to form other judge- ments of like nature; nothing being more convenient than fometimes to fuffer our felves to be le- due'd, and to become Learned on a fudden, with little Expence.
But I intend lo believe nothing but what I know, nor to fufter my felf to be call down by my own Laziijcis, nor to yield to bare Glimpfes. Let us therefore lay alide thofe Forms and Incli- nations, ol which we have no diftintt and particular, but only confufed and general Ideas, which rncthinks we only frame with reference to our Nature, and the Exiftence of which feveral Per- fons, and perhaps whole Nations, do not own. But methinks I fee the Caufe of this ftritt Union of the Parts which make up hard Bodies, without admitting any thing in it, but what all the World grants h or at leaft, what all the World diftinttly conceives to be poflible. For every one diftitittly conceives, that all Bodies are compofed, or may be compofed of fmall Parts: It may then be that ibrneihailbe crooked and branched, and be able,' as many little Fetters, ftrongly to hold others -, or that they lhall be fo iutricated amonglt each others Branches, that it will not be eafie to difuuite them.
Bodies, hold Im predion r the Reafon, . every one of thefe little Bands, hang together: For they cannot be united by other fmaller Bands •, fince I tup- le them to be lolid. Or if I lay they are united in that Manner, it will rcaibnably be ask'd, What unites thele others together? and ib in infinitum.
Chap. IX. The Search after Truth.. 87 So that the Difficulty of the Queftion now is, s^****3******^ how the Parrs of thole little Fetters, or of thole -r f S^ ) A branched Parts, can be fo {briefly united as they \^ ^^Vto.^«^ are -, A, for initance, with 5, which I fuppofe to be Parts of a little Band: Or, which is the fame thing, (Bodies being fo much the more hard, as they are the more folid and lels porous,) the Que- ftion at prefent is, to know how the. Parts of a Co- lumn being made of Matter without Pores, can be • A,,..,-,■„ _\ lb ftrongly joined together, and compole a very ~"~~*yC~ hard Body $ fince it cannot be laid that ■ the Parts y of this Column hang together by fmall Fetters; g j. ^V».<'i. - <2 for being without Pores, they have no particular Figure.
1 am again extremely apt to fay, that this Column is hard by its Nature ^ or that the fmall Fetters, of which hard Bodies are made up, are Attorns, the Parts of which cannot be divided •, as being the Eflential and laft Parts of Bodies, and eifentially crooked, branched, or of a perplex'd figure. But I freely own this is not folving the Difficulty, and that laying afide my Prejudices, and th illufions or my Senfes, I fhould be in the wrong, to have Recourfe to an abftracled form, and to lace a Phantafm of Logick, for the Caufe I enquire after. I mean, I fhould be in the wrong to onceive, as fome thing real and diftincf, the rambling or indefinite Idea of Nature or ElTence-, whi< h expre$es nothing but what is known to us 5 and fo to take an abftracfed univerfal Form foi the Phyficai Caule of a real Efrett: for there are Two things which I cannot too much mi- ftruft. Vatfu-Jl is, The Impreffion of my Senfes ^ and the other, My Readinefs to take abftracf- «f Natures, and general Ideas of Logtck, for real and particular, by which two Principles of Er- rour I remember to have been often feduc'd.
For to return to the Difficulty in hand j 'tis not poffible to conceive how thofe little Fetters fhould be indivifible by their own ElTence and Nature, nor confequently how they ihould be in- flexible-, lince, on the contrary, I conceive them moft divilible, nay, neceflarily divilible by their own ElTence and Nature. For the Part A is moft certainly a Subftance as well as Bh and confe- quently 'tis plain that A may exift without £, fince Subftances may exift without one another j otherwife they would be no Subftances.
It cannot be faid that A is no Subftance-, for 'tis plain that that is not a bare Mode, whereas every Being is either a Subftance, or the Mode of a Subftance. And therefore fince A is not a Mode, it is a Subftance, and may exift without B -, and much more the Part A exifts feparately fieri? £; fo that this fetter is divilible into A and B.
Moreover, if this Fetter were indivifible or crooked by its own Nature and Eilence, there would happen a thing quite contrary to what we fee by Experience; for not one Body could be broken. Let us fuppofe, as before, a Piece of Iron compofed of many Fetters perplexed within one ano- ther, and A a Bb to be two of them-, I fay it will not be poflible to difintangle them, and con- fequently to break the Iron. For to break it, the Fetters that make it up mult be bent, which however are fuppofed inflexible by their own Nature and EiTer ce.
If they be not fuppofed inflexible, but only indivifible by their own Nature, the Supposition would be unferviceable for folving the Queftion. For then the Difficulty will be, Why thofe little Fetters obey not the Force that is ufed to bend a Bar of Iron? Neither mult they be fup- pofed indivifible, if they be not fuppofed inflexible: For if the Parts of thofe Fetters could change their fituation in reference to one another, 'tis vifible that they might be feparated; fince there is no Reafon why, if one part may be fomewhat removed from the other, it could not be entirely re- moved. And therefore whether thefe little Fetters are fuppofed indivifible or inflexible, the Que- ftion cannot be folved by that means: for if they be only fuppofed indivifible, a Piece of Iron mult be broken without trouble; and if they be fuppofed inflexible, it will be impoffible to break it i fince the little Fetters that make up the Iron, being intricated within one another, it will be irapoTible to difintangle them. Let us therefore folve the Difficulty by clear and undeniable Principles, and find the Reafon why that little Band has two Parts A B fo firmly united to one another.
Tis needful, I perceive, to divide the Subject of my Meditation into Parts, that I may examine it the, more exactly, and with lefs Intention of Thought; fince I could not at firft, at a fingle view, and with the whole Attention I am capable of, difcover what I enquired after. This I might have done at the beginning; for when the Subjects of our Meditation ate fomewhat abftrufe,. 'tis al- ways the belt way to confider them by parts, and not fruitlefsly weary our felves with the vain Hopes of meeting happily with the Truth.
Wliat I enquire after is,. The Caufe of the ftrict. Union betwixt the minute Parts, that make uo the little fetter A B. Now I conceive only diltin£tly three Things that can be the Caufe fought for, viz. The very Pans of that little Fetter, or the Will of the Author of Nature, or laftly invifi- bie Bodies funonnding fuch little Bands. I might yet ailedge,. as the Caufe of thefe things, the form of Bodies, the Qualities of Hardnefs, or ibme occult Quality, the Sympathy betwixt Parts of the lame Species, &c. but fince I have no diftinct Idea of thofe 'fine things, I neither mult nor can ground my Keaionings thereupon: fo that if I find not the Caufe I fearch after, in thole things - • of wiilcti I have diitinct Ideas, I will not fruitlefsly trouble my felf with the Contemplation of fuch F: Maleb-ranche Concerning BookVL fuch rambling and general Notions of Logick^ and fhall forbear fpeaking of what I urrderftand not. But let us examine xhzfirft of thefe tilings, that may be the Caufe, why the Parts of that ifnall Band are fo firmly joined -, viz. the very Parts of which it is made up.
When I only confider the Parts of which hard Bodies are compofed, I am inclined to believe, *M. Des "\hcit no ^ Cement, which unites the Farts of that Fetter, can be imagind befides themfclves and ^yes--i their own Reft: for of what Nature could it be? It cannot be a thing fubfi fling of it- J elf fince all Art. /<i ' thofe minute Farts being Subftances, for what Reafon fhould they be united by other Subftances but Part. II. the mf elves? Neither can it be a Vitality different from Reft $ becaufe there is no Quality more con- trary to Motion, that mayfeparatc thoje Parts, but their own Reft: but befides Subftances and their ^■unities, we know not any other forts of things'.
'Tis'true, that the Parts of hard Bodies remain united, as long as they are inReft one by another -, and that when they are once in Reft, they remain of themfelves in the fame ftate, as long as they can; but this is not what I enquire after, and I know not how too I came to miftake the Subject. I en- deavour here to difcover, why the, Parts of hard Bodies have lb great a ftrength, to remain in Reft One by another, that they withftand the Force that is ufed to move them. *Jitt. 43. * I might however anfwer my felf, that every Body has truly Force of continuing fix'd in its pre- ibid. fent ftate, and that this Force is equal whether in Motion- or Reft: But that the Reafon why the -\-/ri. 63; parts of hard Bodies remain in Reft by one another, and that we can t difficultly move and fepa- rate them, is our not imploying fufficient Motion to overpower the Reft. This is probable, but I am feeking Certainty, if it be to be found, and not bare Probability. And how can I know with Certainty, and Evidence, that each Body has this Force to continue in the ftate it's in, and that this Force is equal both as to Motion and Reft, fince Matter on the contrary, feems indifferently pailive to either, and altogether deftitute of Force. Let us have recouife then with M. des Cartes to the Will of the Creatour, which is, it may be, that Force which Bodies feem to have in them- felves, which is the fecond thing above mention'd, fuppos'd capable of preierving the Parts of this little Fetter we fpeak of, fo clofely link'd to one another.
Certainly, 'tis poiTible that God may will every Body fhould remain in its prefent ftate, and that his Will mould be the Force which unites their Parts to one another, as I otherwife know his Will to be the Moving Force which puts Bodies in Motion: For fince Matter is incapable of moving it felf, I have Reafon, methinks, to conclude it is a Spirit, and even the Author of Nature, which puts it and preferves it in Motion, by preferving it fuccefhvely in different places by his bare Will -, in as much as an Almighty Being aas not with Initruments, and his Will is necelTarily folio w'd by Effefts. * A\ t. 33. - * I acknowledge then, it's poffible that God may will that every thing remain in its prefent ftate, Part. 11. whether it be Motion or Reft, and that his Will may be the natural Power, which Bodies have of rem:.i ii:ng in the ftate they once have obtain'd. And if fo, we muft like M. des Cartes, meafure that Power, conclude what ought to be the Effects of it, and give Rules for the Force and Communica- tion of Motions upon the Collifion of different Bodies, in proportion to their Magnitude; fince we have no other way of coming to the knowledge of that general and immutable Will of God, who makes the different Power thefe Bodies have of afting upon, and refilling one another, confift in their different Magnitude and Swiftnefs.
But however, I have no infallible proof that God wills by a pofitive Will, that Bodies remain in Reft, and one would think it fufficient for God to will the Exiftence of Matter, not only tor caufe it to exift, but to exift in Reft.
The cafe is not the lame with Motion, fince the Idea of a Matter mov'd, certainly includes two Powers to which it is related, viz. that which created, and alfo that which mov'd it. But the I- dea of a Matter in Reft, includes only the Idea of a Power which has created it, whilft there is no neceffity of any other Power to put it in Reft, fince if we barely conceive Matter, without think- ing on any Power, we fhall necelTarily conceive it in Reft. Thus it is I conceive things: fori am " to judge by my Ideas • and my Ideas tell me, Reft is but the privation of Motion. For God need- but ceafe to will the Motion of a Body -, to make its Motion ceafe, and to caufe it to Reft.
But I remember I have heard from many very ingenious Perfons, that Motion feem'd to them as much the privation of Reft, as Reft the privation of Motion. And fome will not doubt to af- firm, lor Reafons I cant comprehend, that Mot/on feems rather a privation than reft. I do not diitin&ly call, to Mind the Reafons they alledge: however this ought to make me fufpicious, left iry ideas fhould be falfe. For though moft Men fay what they pleafe upon Subjefts that feem or little moment, yet I have Reafon to believe the Perfons I fpeak of, were pleas'd to fpeak what they thbilght': wherefore I muft ftill examine my Ideas more carefully. . inc To me it feems a thing of undoubted Certainty, and the Gentlemen before mention'd wont deny here <*i!j is tnat '"s tne Will of God which moves Bodies. The Force then which that Bowl I fee in Mo- ,, my tipn has, is the Will of God that moves it; what now is God requir'd to do to ftop it? Muft he felt; and Will, by a pofitive Will, that it fhould Reft? or is it fufficient to ceafe to will its Motion? 'Tijr BowI' plain, that if God but ceafe to will the Motion of this Bowl, the celfation of its Motion, and con'feq.ue'ntly Reft will fiicceed the cefiation of the Will of God. For the Will of God, which was tin. Force that moved the Bowl, debiting, that Force defifts, and the Bowl will be no longer mov1d. Therefore the celiation of the moving Force produces Reft: Reft then has no Force to caufe it} but is a bare privation that fuppoies no pofithe Will in God. Thus we fhould admit in God 4, pofitive Will without any Reafon or Neceflity, if we alcriUed to Bodies any Force to remain in Reft.
But Chap. IX. The Search after Truth. * $9 .- But to overthrow this Argument if poflible, Let us now fuppofea Bowl at Reft, as before we iuppos'd it in Motion, what muit God do in order to agitate it? Is it enough that he ceafes to will its repofe? if lb, I have hitherto made no advance; for that Motion will be equally the privation of Reft, as Reft of Motion. I fuppofe then that God defiits to will the Reft of this Bowl; tut fuppofing it, I fee it not put in Motion; and if any others do, I defire. them to inform me with what degree of Motion it is carried. Certainly 'tis impoflible it fhould be mov'd, or have any degree of Motion: and 'tis impoflible to conceive any degree of Motion in if, barely irorn bur conceiving that God ceafes to will it fhould be at Reft; becaufe it goes not with Motion as it dees with Rett. Motions are infinitely various, and are iufceptible oi' more and fejb; but Reft being na- 'thing, one cannot differ from another. One and the lame Bowl which moves twice as fait at one time as at another, has twice as much Force, or Motion, at one time as at another. But it can- not be laid that the fame Bowl has Reft double at one time to its Reft at another.
There mult therefore be a pofitive Will in God, to put a Bowl in Motion, or to give it fuch a Force as it may move it felf with: But lie need only ceafe to will it Ihould be mov'd, to caufe its Motion to defift; that is, to make it Reft. Jult as to the creating a World, it is not enough that God ceafe to will its non-exiftence, unlefs he likewiie pofitively will the manner it 'fhall exiil in. But in order to annihilate it, there is no need of God's willing it fhould notexift, fince God cannot will Nothingnefs by a pofitive Will, but barely, that he ceafe to will its Being.
I confider not here Motion and Reft, according to their relative Capacity; ( for 'tis manifeft that retting Bodies have as real Relations to thole about them, as Bodies in Motion ) I only conceive that Bodies mov'd have a moving Force, and that others at Reft have no Force at all to perfevere in it; becaufe the Relations of mov'd to the circumambient Bodies, perpetually changing, they need a continual Force to produce thefe Changes; it being indeed nothing but thefe Changes, that caufe all that Novelty we obferve in Nature; but there is no need of Force to do nothing. When the Relation of a Body to thofe furrounding it is conftantly the fame, there is nothing done; and the Continuance of that Relation, I mean the A£tion of the Will of God, which preferves it, is not different from that which preferves the Body it felf Ifitbetrue, as I conceive, That Reft is but the Privation of Motion, the leaft Motion, or that of the leaft Body mov'd, will include a greater Force or power than the Reft of the greateft Body; and fo the leaft Force, and the leaft Body, fuppos'd to be mov'd * in a Vacuum, againft *EvaEo_ another never fo great and bulky, will be capable of moving it; fince the largeft Body at Reft will dy hi a Va- have no power of refitting the leaft Body that fhall ftrike againft it. Therefore the Refiftance which w, i«n- is made by the Parts of hard Bodies, to hinder their Separation, neceffarily proceeds from fome- derfl?n'! thing elfe than their Repofe. ™ le" from othere, whether hard or liquid, as that there is none either to aid or hinder the Communication of Motions.
But 'tis neceflary to demonftrate by fenfible Experiments, what we have been proving by abftra£t- ed Reafonings, to lee whether our Ideas comport with the Senfations we receive from Effects. For it often happens that fuch Reafonings deceive us, at leaft will not convince others, and efpecially fuch as are prejudiced to the contrary. M. Des Cartes's Authority has fuch an influence upon fome Mens Reafon, that unlefs we prove all imaginable ways, that great Man in an Errour, we cannot difabufe them. What I have faid will be readily admitted by fuch as are not prepoflefs'd with a contrary Opinion; and I perceive that I fhall even be blam'd by them, for proving things which feem to them indifputable: However, the Cartefians well deierve our endeavours to content them. The others may pals over this Diicourfe, if they think it tedious.
Here then are fome Experiments which fenfibly demonftrate that Reft has no power to refill Motion, and which confequently evince, that the Will of the Author of Nature, which conftitutes the Power and Force every Body has to continue in its prefent ftate, refpe&s not Reft, but Mo- tion only; fince Bodies confider'd in themfelves have no Force at all.