An entire body of philosophy according to the principles of the famous Renate Des Cartes in three books, (I) the institution ... (II) the history of nature ... (III) a dissertation of the want of sense and knowledge in brute animals ... / written originally in Latin by the learned Anthony Le Grand ; now carefully translated from the last corrections, alterations, and large additions of the author, never yet published ... by Richard Blome.

CHAP. XV. Of the Principle of Local Motion.

I. There are two Prin∣ciples of Motion. FOrasmuch as Matter hath no power to attribute any motion to it self, or to remove another Body out of its place (as shall be said in the fol∣lowing Chapter) we are to enquire here what is the Cause of motion in the Universe. In which en∣quiry, that we may follow the order we see in the World, we shall pitch upon two Principles of mo∣tion; the one General, on which all motions in the world do depend; and the other Particular or secundary, to which all singular motions are attri∣buted.

II. God is the first Cause of Motion. The First and Universal Cause is that which first put matter into Motion, and is no other but God a∣lone, who bestowed Motion upon the matter he had created, and preserves the same by the same Action by which he produc'd it at first; and because it is agreeable to Right Reason, and the Idea we have

of God, that he should conserve his Creatures in the most simple way; it seems more than probable that God continues the same Agitation in the Universe, which he imprest on it at first, yet so as that he can always whensoever it pleas∣eth him change these Laws, which he hath established.

III. The Second Cause is the meeting of other Bo∣dies. The Second or Particular Cause is the meeting of Bodies, by which means it happens, that this Divine Action, which preserves Motion, exerts it self sometimes in these, sometimes in other Bodies: Whence the difficulty which ariseth from the Communication of Motion may be easily solved; for tho' Motion, as being only the Mode of a Body, cannot remove from one Subject to another, which Regius unwarily asserts; yet the agitating force, being no Mode of a Body, may by remov∣ing shew it self sometimes in this, sometimes in the other Body.

IV. The Com∣munication of motion is performed according to the Laws at first set by God▪ Whensoever therefore DES CARTES speaks of the Communication of Motion, he is to be un∣derstood of that Power, which preserves Natural Things in the same condition wherein they were constituted at first, and all effects order'd accord∣ing to the Laws appointed for them, and suiting to their Natures.

V. Three Laws of Nature. There are three Laws of Nature, which are founded in that most simple Concourse, whereby God preserves all Bodies, which are very condu∣cive to understand the Nature of Motion.

VI. The First Law of Nature. The First is this; Every Natural thing, if it be simple and undivided, always inclines to con∣tinue in the same state wherein it is: So that no change can happen to it, but from some outward Principles. Thus a Round Body, always keeps its Round Figure, neither is the same destroy'd, but by some supervening foreign Agent. And supposing the same Body to be moved, it will still proceed further, except it meet with some impediment that puts a stop to its Motion. And according to this Rule, we say, that a Body once put into Motion, for example, a Ball struck by a Racket, doth not stop at the Wall from whence it is reflected; for should we suppose any interruption in its Motion, we should be at a loss to find the cause that excites a new Motion in it again. Wherefore we must con∣clude that that which is moved, is always moved, and that which rests, rests always. And for this cause it is that a Stone continues its Motion, after it is let go out of the hand of him that throws it.

VII. The Reason of the Fore∣going Rule. This Rule may easily be gather'd from what we shall say in the following Chapter: For seeing that a Body cannot move it self, it follows, that that which rests, must persevere so, except by some outward force it be driven out of its place. And in like manner, when a Body is once put into Motion, no reason can be assign'd why it should not con∣tinually proceed therein, with the same swiftness, as long as it meets with nothing that stops its career. For since nothing can be done without a Cause, the state of a Body cannot be changed without the Acti∣on of a Cause. Hence it is that a Leaden Bullet be∣ing let fall from the top of a Mast, notwithstand∣ing the swift course of the Ship, yet falls down straight to the bottom; for the Motion of the Bullet being a Compound of progressive and de∣scensory Motion, and both of them continuing in the same state, it is evident that the Bullet can fall no otherwise than it doth.

VIII. Every change pro∣ceeds from outward Causes. Wherefore we shall meet with no change in Bodies, as to Motion or Rest, Swiftness or Slow∣ness, Figure, Situation, Magnitude, &c. which do not proceed from without, the searching out of which Causes is the particular task of Natural Phi∣losophy. Water indeed doth by degrees lose its Heat, but then it is no simple, and undivided Body; for it derives its agitation from without, and re∣tains it as long as the agitating Cause continues; but forasmuch as the Cause ceaseth, and the more thin parts of the Water Evaporate, and communi∣cate their Motion to the Neighbouring Bodies, by this means the VVater becomes reduc'd to its former state of Coldness.

IX. Why a Stone after some time, falls down again to the ground. You'l say, a Stone cast up into the Air, doth after a short time fall down again to the ground, which would not be, if a Body once moved, were inclin'd to continue its Motion; for according to this Rule, it ought continually to proceed, tending upwards.

X. Answer. I answer, that a Stone falls down to the ground, not because it willingly desists from its Motion, but because it is hindred by the Bodies it meets with on its way from proceeding any further. For the Air and fluid Matter that is in it, do not without difficulty admit the entring of other Bodies; yea and besides do very much resist them, as is obvious to our sense of Feeling. For the subtil Matter, which thrusts Bodies downward, hinders the Stone from being carried up to Heaven. So that we our selves, when we leap up from the Earth, should still continue in the same Motion mounting upwards, if the subtil Matter which surrounds the whole Earth, did not drive us downwards.

XI. No body moves cir∣cularly but by the in∣tervening of outward force. What hath been said of a Stone falling to the Ground must likewise be understood in General of all other Bodies: Wherefore if we see a Body in its Motion describing the four sides of a Square Figure, we must conclude that at every one of the said An∣gles where it changeth its determination, it hath been forc'd to it by the meeting of some other Bodies, which have oppos'd its Motion and determination. And forasmuch as a Circle is Equivalent to a Figure of an infinite number of sides, it follows, that a Body which is circularly moved, must suffer a conti∣nual violence by meeting with several other Bodies, for without this it could never move in a round Line.

XII. Another reason why Bodies per∣severe in their mo∣tion. But the chief reason that moves us to assert, that a Stone, or any other Body would persevere in its Motion, if we were not hindred by other Bodies, is, because Rest is contrary to Motion, and nothing by its natural Propensity tends to its contrary, that is, to its own Destruction; and consequently a Body if once moved will move always, or if at rest, will always continue so. And in this Principle alone we place the Power of the Action and Resi∣stance of Bodies. For as a thing that is united, hath a Power to resist its being separated from that which rests, to oppose that which would put it into Motion; so that which is moved hath a Power to continue in its Motion with the same Swiftness, and towards the same place.

XIII. Why a Body ceaseth to move. Thus a weight hanging at the end of the Pack∣thread A B which by outward force is mov'd this way and that way, if it were transmitted to G, would fall down thence, and mount up to D, and always retain this Equality of Motion; neither would it ever, by slackning of its Motion, come * 1.1

down to E and F, but that the Air hinders it from continuing its begun Motion from G to D. Foras∣much as no reason can be assign'd, why that which is, should cease to be, except a more powerful thing do hinder and oppose its force.

XIV. The Second Law of Nature. The Sccond Law of Nature is this: Every Body in Motion, of it self tends to prosecute its Motion accord∣ing to a right line, and not according to a crooked line. Notwithstanding that, many Bodies are forc'd to turn aside by their meeting or justling against other Bodies, and that, as hath been said before, the whole circle of Bodies moves together in every Motion. This Rule is inferr'd from the Definition of Motion, because it affirms nothing concerning Motion, save only that it is a Translation of one Part of Matter, out of the Neighbourhood of those Bodies that do immediately touch it, &c. into the Neighbourhood of other Bodies. So that except this Translation be most simple, that is, by right lines, and not crooked, we have attributed some∣thing to Motion, which is not contained in the Essen∣tial Notion or Definition of it, and so consequently that which doth not belong to its Nature. For whatsoever is moved, in every moment of its Mo∣tion, is determin'd to continue its Motion to some part or other, in a Right Line. Forasmuch there∣fore as God preserves Motion in the most simple manner that may be, and every natural thing continues in the state wherein it is, the Body moved will always continue its Motion in a Right line, ex∣cept it be hindred from without.

XV. Why every Motion tends to a Right Line. If you demand why every Motion tends to a Right Line, and not to a crooked? I answer, because all the least parts that are found in a Crooked Line, are right Lines; and since the circulating Body, ultimate∣ly exists in one of them, it follows according to the former Rule, that as soon as it is restor'd to its Liber∣ty, it perseveres in the same state, and continues its Motion in that Right Line which there toucheth the Circle. But if the least parts in the Circle were crooked, the moved Body being continually carried along them, and afterwards left to its Liberty, ac∣cording to the foregoing Rule, would pursue a crooked Motion, conform to the crooked particle of the Circle where it was last: But since this doth not happen, it is manifest that every Circle in Na∣ture is a Polygon, or a Body of many Angles.

XVI. Both these Laws de∣monstrated from the Di∣vine Im∣mutability. This Rule of Nature, as well as the foregoing, may be demonstrated from the consideration of the Divine Perfection, that is, from the immutability and simplicity of that operation whereby God con∣serves Motion in the Universe. For as God pre∣serves Motion in any Body, by making that Motion which now is, to continue to exist, without any regard had to the state wherein the Body was be∣fore; so he likewise continues to direct the Body moved to that Term, to which it is directed, at the present instant of time. But there is never any instant of time wherein it is not disposed to continue its Motion in a Right-Line, tho' before it was car∣ried in a crooked line, and accordingly will pursue its motion in a Right-Line. This is clearly made out by DES CARTES in the 2d part of his Principles, Artic. 39. by the example of a * 1.2Stone A, whirld about in a Sling AE, which tho' it be turn'd round in the Circle LABF, yet withal hath a tendency towards the Tangent Line ACG. For tho' the Stone first proceeds from L to A by a crooked line, yet nothing at all of that Obliquity can be understood to abide in it, whilst it is in the Point A. Because tho' the Stone be moved round, yet forasmuch as in every moment of time, parts may be assign'd that have no crook∣edness at all, it cannot be suppos'd to retain any obliquity, when the detaining force ceas∣eth.

XVII. The Circu∣lar▪Moti∣on of a Bo∣dy proceeds from a Cause Ex∣ternal. Hence it follows, that no Body of it self is moved in a Circular Motion, forasmuch as that always proceeds from an outward cause, which hinders the Body moved to pursue its Motion in a Right Line. Upon this account it is also that Wooden Bowls dashing against one another, are often whirld round; and so Water likewise, when it is hastily poured into any Vessel: Yea, in every motion there is a cir∣culation of Bodies, as shall be shewed here∣after.

XVIII. Every Body that's whirld round, en∣deavours 〈◊〉〈◊〉 recede fr••m its Center. Another Consectary is, that all Bodies circularly moved, do either actually recede, if they be not hindred; or endeavour to recede, if they be, from the Center of their Motion: Because, as soon as the detaining force ceaseth, they begin to move in a Right Line. This is the reason why the Wa∣ter doth not fall down out of a Bucket of Water as long as it is whirld round; and that it strives to recede from the Center, we may gather from hence, because upon making a Hole in it, the Water runs out immediately. This Rule is of very great use for explaining of the Heavenly Phaenomena. Now this strife of receding from the Center, is either greater or lesser, proportionable to the Agitation, as ony one may plainly perceive in the whirling about of a Sling.

XIX. And that which it strongest doth the more 〈◊〉〈◊〉 from the Center. Forasmuch therefore as all Bodies moved round, strive to continue their Motion in Right Lines; it follows, that when many Bodies are so moved, every one of them must strive to move by the Tangent ACG of the Circle which it describes; and really move by the same Line, as soon as the causes that have hindred it be taken away. It is visible also that the most strongly moved Bodies, must at the same time describe longer Tangents than those that are more weakly moved, and consequently more withdraw themselves from the Center of their Motion, and by the same means force the weaker Bodies to approach to the Center.

XX. The Third Law of Na∣ture. Another Rule is; Whensoever the Moved Body, meets with another Body in Motion, if it have not as great a force to pursue its course by a Right Line, as there is in the other Body to hinder it, then it is turn'd out of its way, but yet continuing its Motion, loseth only the Determination of it. As it is evident in hard Bodies, which when they dash against another Body, do'nt therefore cease to move, but are reflected to the opposit part. But if one of them have a greater force than the other, then it pusheth it along, and as much of its own force as it imparts to this other Body, so much it loseth; as when a hard Body meeting with a soft, by com∣municating its own Motion unto it, ceaseth to move and lies still. Wherefore we are not to suppose that when a Ball is thrown into a Heap of Sand, that its Motion is lost, but that it is communicated first to the Particles of Sand, next to the Air, and other neighbouring Bodies, notwithstand∣ing the said communication be not visible to our Eyes.

XXI. The Rea∣son of the Third Rule. The Reason of this Rule is to be fetch'd from the First; for seeing every thing inclines to continue in the state wherein it is, it will follow that that which is weakest must be changed by the stronger, as experience teacheth.

XXII. From this Law arise those chan∣ges which happen to Bodies upon their meet∣ing one another. From this Third Law ariseth almost all the changes we find in Bodies, caused by the various resistance and occurrence of other Bodies; the effect of which occurrence will be different. First, according to the magnitude of those Bodies. Secondly, according to their Superficies, whereby they press upon each other. Thirdly, according to the swiftness and force of their Motion. Fourthly, according to the Rest and contact of Parts in that Body against which another dash∣eth, as shall be more amply shewed Part V.

XXIII. How to measure the Quantity of motion. The Quantity of Motion in a Body is known partly by the length of the Line which the Body moved runs through; partly from the quantity of its Bulk, which is transferr'd together with it. Thus a Square Body of one Foot, being moved the length of 10 Ells, is said to have a certain Quanti∣ty of Motion, which would be double, if an equal way, were added to the former length, which that Body shall run through. Again, if a Square Body of one Foot, should run through the space of 10 Ells, there would be a double portion of Motion in it, with respect to a Square Body of half a Foot. Whence it follows, that Bodies of different magni∣tudes, may have the same quantity of motion. Thus the Square Body of one Foot, and that of half a Foot would have the same quantity of motion, sup∣posing the former to run through a Line of five Feet, and the other a Line of ten Feet.

XXIV. Unequal Bodies may have an Equal quantity of motion. From hence it is evident, that to the end two Bodies of different magnitude may have an equal quantity of motion; it is necessary that the Lines they run through, be reciprocally taken according to their bigness. As supposing one Body to be thrice as big, as another, it is necessary that the Line it describes by its motion, be only the third part of the Line, the lesser Body runs through. And upon this ground we may build these four following Maxims.

XXV. The First Maxim. Two equal Bodies, have equal Quantities of motion, when in equal time, they describe equal Lines.

XXVI. Second Maxim. Two equal Bodies have unequal quantities of mo∣tion, when in equal time, they describe unequal Lines.

XXVII. The Third Maxim. Two unequal Bodies have equal quantity of motion, when in an equal space of time, they de∣scribe Lines, which are of a reciprocal Proportion to their magnitude.

XXVIII. The Fourth Maxim. Two unequal Bodies have unequal Quantity of motion, when in equal time they describe Lines which are not reciprocal to their Bulk.

Notes

• * 1.1

  Figure 5.
• * 1.2

  Figure 6.