Philosophy NATURAL Principles MATHEMATICS by Sir Isaac Newton
Philosophiae Naturalis Principia Mathematica by Sir Isaac Newton(translated from Latin below)
INexcellent menD. Isaac NewtonWORK HOCCE
Mathematics - PHYSICS
Age and race of our peerless beauty .
Here is your standard pole, and the size of the goddess of balance ,Calculator and Thursday , which , while beginnings of thingsBe made , BEARING violates the CreatorHe would not, of the eternal foundations set up by the work .Break into view intimate open air ,Would you like the things that the world rotates the other end nor longer hidden .The sun bids all things to himself, seated on a throneTend the descent , and do not the car in a straight lineStars Be allow the waste to be moved through the void ;But grabs fixed himself as center of the gyres .Now it appears what is the way with frightful stroll a comet ;No longer do we wonder bearded star phenomena .We learn from this, at which the cause of silver PhoebeInadequate mile walks , why , subject to anySo far astronomers refuse to curb the numbers :Then return node , curque enhance progress .And how much we learn BLOW BACK roaming Cynthia BlackForces , while the crushing waves the flagQuits, and the sailors suspected strips sands ;In alternate times, the last on the shores of knocking.Wise should she so often the minds of ancient torso ,Schools of things loud and vain contention harassObvious to see cloud pushing mathematics .Fog of uncertainty and no longer burdened with errorAnyone whose abodes of the gods and the heights of heavenDemons are allowed to climb high sharpness .Rise mortal, earthly caresHEAVEN-BORN and hence the strength of the mind dignosciteFrom far and wide the life of the animal and far-fetched.Check that the tables SlaughterTheft and adultery, accused of fraud and perjury ;Or who roamed the surrounding citiesAuthor was blessed gift Cererisve nations ;Or who cares, lessening the pressure of the grapes ;Or who showed Nile reedsAssociate sounds, voices and eyes to expose ;Human lot less emphasized , as fewLooking miserable life only advantages .Now, the gods allowed guests , highRights of the pole allowed to treat and now with dark secretsThe bars are open to the land of the changeless order of things ,And the things of the past ever aware of the world.Celebrate with me showing such muses,You who rejoice in the heavenly nectar to eat ,Unlocked the hidden treasuries closed NEWTONVM TruthNEWTONVM Muses dear , whose chest was pureApollo is here , the whole approach of the divine mind:It is wrong to close mortals reach the Gods.
EDM . Halley .
Def. I.The quantity of matter is the measure of the same, arising from its density andBulk conjointly.
Twice the space is four times denser than the air twice. Understand it from snowand dust by compression or melting of the condensate. And matchsystem of all the bodies, which causes whatsoever; various condensed.The medium, in the mean time, if there was any, freely pervadentis interstices of the parties, in this case noI have a. But that this is the amount of mass in the body or under the name ofI understand the following directions. It becomes known through the body of each weight. Forweight is proportional to the accuracy of pendulums found by experimentsinstitutions, will be taught to use it in future.
Def. 2.The quantity of motion is the measure of the same, arising from the velocity and quantity of matterconjointly.
Motion of the whole is the sum of the motions in the parts of the individual, and therefore in the body-DUPdescend with equal velocity is double the LO will be greater, and double, with four times the velocity.
Def. 3.Innate force of matter, is a power of resisting, by which every body, as much as in theit lies, continues in its state, either of rest or of moving uniformly in aline.
Thus it is always proportional to its body, nor; anything differs from the inertiaOf the masses, except in the way of conceiving. Through sloth comes to pass that the whole body of subject matter, of theits state of rest or of moving is difficult or disturbed. So even in a force-located name to be called a significant force of inertia. But this body exercisesonly by means of the force to change its condition in itself another force impressed upon it,estq; under different exercise his respect and enthusiasm by Resistance: Resistancethey are reluctant to force the body to maintain its state impressed ASSAULTfar as the body is the same, the resisting force as an obstacle difficult to give ground, trying to stand-then his change. Resistance at rest and moving mob attackattributes, but motion and rest, as commonly conceived, with respect to the distinct soil-they are from one another, nor ever really rest that commonly as at restviewed.
Def. 4.An impressed force is an action exerted upon a body, in order to change its state, either ofof rest, or of uniform motion in a straight line.This force consists in the action only, nor, after the action remains in the body.Continue as they were by the mere force of inertia for the body of a new all in the state of. But it isof different sources of impressed force, so that the result of an injury, the pressure from the, from the force of the centripetal.
Def. 5.Centripetal force is that by which the body towards a point as to the center ofis drawn or impelled, or any way tend.This is the case of gravity, towards the center of the land of which the body is: Do you want to Magnetica, by which he asks for the iron center of the magnet, and that force is, quæcunq, is, in what the planets,perpetually drawn back from rectilinear motions, and they are compelled to revolve in a curved line.But there is a centripetal force, the quantity of three-in-law, the absolute, and the acceleration due tomotor.
Def. 6.The centripetal force is the measure of the absolute quantity of the same, proportional to thefrom the center of the efficacy of the cause that propagates it throughout the regions round about.To use the magnet in one greater than the virtue of the magnet, while the minor in the other.
Def. 7.Centripetal force, the magnitude of the acceleration is a measure of the velocityproportional to, which it generates in a given time.
Greater use of the power of a magnet in a shorter distance, less than in the larger, orgravitans a major force in the valley, the minor peaks in the lofty mountains (aspendulums is evident by experience) render this Discourse was still less than (that from now on will be made clear) in the the ma-joribus distances from Earth, at equal distances, the same undiq thereforeThe bodies of all the setting (heavy or light, great or small) was lifted Airresistance, accelerated equally.
Def. 8.Centripetal force, the size of the dimensions of the motor is proportional to the motion, whichgiven time.
Greater use in the greater body weight, less in smaller, inq, same bodyclose to the ground is greater than, is less than in heaven. This force is the centripetal force of the whole bodyor in the center of the propensity and (so to speak) weight, and is made known to it by the force is alwaysopposition in an equal, by which the descent of the body may be impeded.Brevity forces these quantities may call absolute forces,accelerating the motor, and the distinction of gratitude to the bodies, the bodiesof the places, and to the center of forces, for sure the moving force to the body, as it were,and the tendency of the whole effort of the center, from the inclinations of all the match-the components of the composite, and the accelerating force to the body, as the effectivenessanalysis, since the center of the diffused round about you in several places, to move the body-play the role of the things that are in them, the force of an absolute, however, to the center, as if it were the cause of somecontinence, and without which the moving forces are propagated through the country, not in the circuit, oris a body that cause some central (such as it is the magnetic force of the magnet in the center ofor you want to land in the center of gravitantis) or any other things that is not obvious.
Math-This is at least a dogmatic concept. The causes and physical strength for the seat no morespend.There is, therefore, that the speed of the moving force to the acceleration of the force to the movement. Risesfor the magnitude of the quantities of material drawn into the movement for the speed, and the motive force is increasedfrom the force of the acceleration multiplied by the quantity of matter of the same. For most high-actionum force accelerating the individual particles is the motive force of the whole body. Whenceaccording to the face of the earth, where the acceleration due to gravity, or the force on the bodies of gravitansis the same for all, the heaviness of the weight of motor is or as a solid, but if the regions in themounts where the acceleration due to gravity is less, as well as weight reduction, eritq;always that the body in gravity accelerations. So in areas whereacceleration due to gravity is less than a factor of two, the weight of the body, two or three times of lesswill be a four-or six times less.The same sense accelerations and motor impulses and attractions mentionedno. Of words in the attraction, impulse, or tendency of any in the center-he went on, without distinction, and for each other indiscriminately acquire, these forces are not physicallybut considering only mathematically. Hence, the reader should be cautious of suchI think the voices of the character's physical appearance or manner of action or causamvein some places be defined, or the centers (which are mathematical points) the forces truly and physicallyattribute, it may be the centers of, or to pull, or I shall have said to be the strength of the centers.
Note.So far we have the voices of the less well known, in the sense of which are to be accepted in the following pages,explain it. In fact, the time, space, place, and that in all their not-the motion of themost do not define. I will say, however, that the common people, those quantities under no other wayconceives from the relation they bear to sensible objects. And thence arise certain prejudices,the removing of which belongs to distinguish them into absolute and relative, true and apparent,Mathematical and common.I. The time of absolute truth and they Mathematician, and of itself, and without any of its own nature;relation to anything external, flows uniformly, otherwise, it is said, the name of the duration;the apparent and common time, is some sensible and external relative duration by the meansthe motion of the measure, (whether accurate or unequable) instead of true time, which is commonlymakes use of, as an hour, a day, a month, a year.2. Space absolute of its own nature without any relation to anything external teamwork-by means of similar and remains immobile, or the measure of the relative dimension of this space iseuery one of which is mobile, and our senses, which have been defined by its position to bodies,And is commonly used for stationary space, use the space dimension of the underground, aerialor defined by its position to the heavenly land. Are the same absolute spaceAnd relative, though its appearance and size, but they do not remain always numerically the same.In fact, if the earth, for instance, moves, a space of our air, which relatively and in the re-sight of the earth remains always the same, now it will be one part of the absolute space into whichThe air passes over, now the other part of him, and so he would absolutely be changed for ever.3. Place is a part of space which a body takes up, estq; according to the space orabsolute or relative. The part of space, I say, it is not the location of the surface of the body orsurrounding. In fact, there are always equal, the equal of the solids of the place; SurfaceBut the reason of their dissimilar figures, are often unequal;, however, the situation ofproperly speaking, have no quantity, nor, for the country, as well than the affections ofplaces. Motion of the whole is the same as the sum of the motions of the parts, that is, a change-tion of the whole of the translations of the same place, the same as the sum of the parts out of their places,and therefore the same as the place of the whole of the parts of the sum of the local conditions, and therefore the internal andthroughout the body.4. The movement was acquitted from the translation of a body from the place-a place of an absolutesoluble, the relative of a relative in the relative. So in a boat that sails streaming reported,that region of the body of the ship there is a place in which the body moves about the relative, or the oral cavitywhich the body fills that part of the whole, by covering the therefore moves together with the board by one, and the restcontinuance of the body in the same part of the ship, or is relative oral cavity.But real, absolute rest, is the continuance of the body in the same part of that immovable space, in which theThe ship itself, its cavity, and all that it contains is moved. Hence, if the earthreally at rest, the body, which relatively rests in the ship, that they will be moved truly and absolutelyThe ship was in the land of which it is moved with the same velocity. Even if the land is moving, the mouth-does not imply, however, the true and absolute motion of the body and partly from the motion of the earth in spaceunmoved, partly from the relative motion of the ship in the land, and even if the body is movedrelatively in the ship, its the motion of the true will arise partly from the true motion of the Earth in spaceunmoved, partly from the relative motions of the ship in the land at that time, as well as of the body in the ship,and from these the relative motion that will arise in the land of the relative movement of the body. As if the landThat part where the ship is truly moved into the East, since the speeds of the parts of the 10010, and you want ventoq, issued at the speed of the ship in the Westten, they will walk but a sailor on board by the east with a velocity of towards the side of thethe one hand, with the sailor will be moved truly and absolutely unmoved in the space-velocities of the parts10001 in the marked in the east, and towards the West in the land of a relative velocity withnine parts.Time free of a relative distinguished in astronomy by the equationTime the common people. For the natural days are uneven, as if they were equal, who is commonlythe measure of time are considered. Astronomers correct this inequality thatDuring a more accurate measure of the celestial motions. It is possible for us to have no mo-frankincense, equable, whereby time may be accurately measured. Accelerated and retarded canthe movement of all, but one of the absolute flux of time can not be changed. Is the same durationor perseverance of the existence of things, or the movement are to be swift, or slow, or to no one;Consequently, these measures from their sensible distinguished merit and collect from same-we go through the equation Astronomer. But the determination in this equation,The necessity of phenomena, as well as by the experience of the swinging pendulum clock, as well asHenchmen Thursday evinced by the eclipse.In order that the order of the parts of time is immutable, so also the order of the parts of space.These should be moved out of their places, and will be moved (so to speak) out of themselves. ForOf their own times and spaces are, as it were of all things, and places. At the time of theregard to the order of succession, and in space as to order of situation.The essence of these is that they may be in divers places, and the places to be moved first and foremost, is absurd. Thusare therefore the absolute places, and these places are only translations of the absolute motions.But because the parts of space can not be seen, and from one another by the sense of theour distinct articles, in their stead we use sensible measures of them. From the positionsand distances of things from the body for something, which can not be shaken in order to present at the games, to define the-all the places we go, and then also & we guess aright at all with respect to the movement of theat the above places, as far as we conceive to be transferred from the same bodies. Thus in placeWe use the relative and absolute motion of no inconvenience in humanHell, in the abstract is a sense of philosophical studies. For it may bethat there is no body really at rest, to which the places motusq; reference.But are distinguished from each other by means of rest and motion, absolute and relative, the fact of the properties, causes and effects. Is a property of rest, that bodies reallyat rest do rest among themselves. Spread, since it is possible to make a body in theregions of the fixed stars, or far beyond them, absolutely at rest;, however, can not be known from theposition of bodies to one another in our regions, whether any of these things to the Long-keep the same position it was given to Adam, rest assured truths from each other, defined in terms of the situation of thesecan not.Is a property of motion, which retain given positions to that the parts of the whole,participate in the movement of these wholes. For all parts of revolving bodies endeavorto recede from the axis of motion, and progressing with the force of the impulse arises from the jointall the parts. Then moved the bodies of his rivals, in a move thatrivals, relatively inactive. And that 's defined in terms of the movement of the true and absolutecan not, by the translation of it from the neighborhood of the bodies, which only seem to belonging to a quiescence appropriately. They should, as if they were external bodies at rest: not only were considered, but alsoreally quiet. Otherwise, everything included, besides the translation from near-solicitationto those who travel, partake likewise of their true motions, and it was lifted up that translation not really rest, but only to watch as at rest, are en-included as part of the exterior to the interior part of the command to the ambient, or tocortex to the nucleus. Moving the bark, even the nucleus, without; translation ofnear the shell, as being part of the whole, is moved.Affinity to the property of the preceding is, that the thing moved is moved in place of one thing in place,and therefore the body which is moved is moved out of the place, also participates in the motion of its place.And so, all the motions, who was of the places in motion, are no other than parts of the movements ofentire and absolute, and the movement of the heart of every entire motion is composed of-pores at first out of his place, and the motion of the place of this out of his place, and so on, until theyou come to the place, motionless, as in the above-mentioned example of the sailor. Whenceof the absolute, and there is nothing but the whole motions can be decided by immovable places, and on that accountto these immovable places, but relative to the movable mentioned above, the climate is not fixedthey are, all of them from infinity to infinity, but such things as retain given positions to the the-recompense, render this Discourse account must ever remain unmoved, spatiumq; make up that can not be shakenappeal.The causes by which they are distinguished from one another relative and true motion are, the forcesimpressed upon bodies to generate motion. True motion is neither generated norunless it is changed by the powers in the movement of the seal to the body itself, whereas, the relative motion ofbe generated, and can be changed without any; force impressed upon the body. For it is sufficientare impressed on the bodies of which the former is only in the other relation, as came up in titles will be changedor one in which the relative motion of the rest of this relation consists. Again, true motionis changed into the body of the motion of the always impressed by forces, but by the relative motion of thethese forces not necessarily changed. In fact, if these same forces also in the other bodies,to which is compared, so impressed that the relative position of conserved, preservedin which the relative motion of a relation consists. Therefore it is possible to change the movement of the whole relation-is preserved when the true suffers prior to circumcision, and to be preserved when the true suffers is altered, and, because of the movement of theconsists in such relations is not at all true.The effects which the movement of the absolute and relative distinguished from each other, there arethe forces of receding from the axis of circular motion. In fact, these are purely relative circular motion in theare no such forces, but in a true and absolute greater or less, according to the quantitymovement. If bucket hangs from a string of very long agaturq; constantly in rotation untilwire windings from quite become fixed, and then filled with water, and with waterat rest in power and any sudden movement is going on in the other world, and the thread itselfrelax, longer continue in this motion, the surface of the water at the beginning of the flatshall be even as before the motion of the vessel, but after it, little by little, into the water by the force ofimpressed, caused the vessel, as this is also a sensible way to begin to revolve, she will retirelittle by little, out of the midst, ascendetq, to the sides of the vessel, the figure of putting on concave, (such asI experienced it myself) and the motion of the always incitatiore will come up more and more, untilrevolutions in equal times with the vessel to carry out the rest in the samerelatively. It refers to here the ascent is its endeavor to recede from the axis of motion, and by means of suchand the attempt is made known and the true and absolute circular motion of the water is measured,motuiq; relative contrary here. Initially there was a great movement of waterthe relative in a vessel, it produced no endeavor to recede from the axis, water isnot to the sides of the ascending tendency to the circumference of the vessel, but remained flat,And therefore its true circular motion had not yet begun. But after thatthe relative motion of the water has decreased, the ascent thereof towards the sides of the vessel proved its endeavorto recede from the axis, to render this Discourse this endeavor showed the real circular motion ofis constantly expanding, and, finally, the most important has been done in a vessel, where the water was at restrelatively. And therefore this endeavor does not depend on the translation of the bodies of water with respect to thethe ambient, and therefore the true circular motion be defined by such translationcan not. Is the only body of each rotating movement truly circular, enterprisesin reply, as if it were the one and only proper and adequate effect, but the motion of a relativevarious external relations for the innumerable, and the equivalent of the reports, the effectsof spring were left on at all, except in so far concerning that truth, and participate in a single motion.Hence, the Heaven of heavens in their system who are below our world in the Heaven of heavens of the fixedrevolve would have it, the planets along with the referral; & the planets, every one of the part of the heavens,which are indeed relatively at rest in their heavens, move really. Changefor their positions to one another (which never happens in the spring at rest) 'each;conducted to heaven when they participate in their movements, and as parts of revolving wholes,attempt to move away from their hubs.Wherefore relative quantities are not the quantities themselves, whose names either accuratethey bear, but those sensible measures of them (or inaccurate), which areThe people using the measured position. But if the words are to be determined from the use of the sign-building, by those names have During this period, space, and motion, properly speaking, be understood of the localthese are the measures they will be, and if the expression will be unusual, and purely mathematical quantitiesthe measured subintelligantur. Accordingly, the force that they bring the sacred wordsinterpret these for the measured quantities there. Nor, less defileMathematical and philosophical truths that are real quantities with their relations andconfuse ordinary measures.Some of the individual body movements to know, and from the apparenteffectually to distinguish, it is most difficult: therefore will I-or rather, that the parts of space are of thatbile in which the bodies really are moved by, it does not come under the observation of the senses. The reason for theis not completely desperate. For we have arguments, some of the movements apparents, which are the differences of the true motions, and partly from the forces, which arecauses and effects of the true motions. As if the two balls at a given distance from each otherness thread connected the intervention, the uniform around the center of gravity;from the tension of the motion of the endeavor of the globes to recede from the axis, and hence mightmight compute the quantity circular motion. Then if any equal forces in theon their faces to the circular motion of the spheres at the same time enlarging or diminishingimprinted, known to increase or decrease the tension increase orthe decrement of the motion, and hence would be found on the faces of the spheres into which thepowers ought to be impressed, so that the movement be greatly increased, that is, the faces of the back door, orin the circular motion that follow. Now we make the following information andthe faces of the opposites that go before, we knew of the determination of the movement. In thisway could be found and the quantity and the determination of this motion in the circularany huge vacuum where nothing survive external and sensible, and with which the ballsthey could be compared. If the space is already established in that body of some distantto each other, keeping to the given position, such as a fixed star in our regions are:indeed it could not be known from the relative translation of the globes among the bodies, whetherbe attributed to them, or whether these would be the movement. But if you looked at the wire and foundthat it exists and the tension of the motion of the spheres of his or seek after them, to concludethe motion of the spheres would be allowed to be, and it was only then from the translation of the globes among thebodies, the determination of this motion to collect. But the movement of theircauses, and the effects of the differences that appear to collect them, and on the contrary, that is, from the movements oftruths or apparent, their causes and effects, will be taught more fully in the following pages.For him the end of the following composed.
--- ORIGINAL LATIN ---
D. ISAACI NEWTONI
Sæculi Gentisque nostræ Decus egregium.
En tibi norma Poli, & divæ libramina Molis,
Computus atque Jovis; quas, dum primordia rerum
Pangeret, omniparens Leges violare Creator
Noluit, æternique operis fundamina fixit.
Intima panduntur victi penetralia cæli,
Nec latet extremos quæ Vis circumrotat Orbes.
Sol solio residens ad se jubet omnia prono
Tendere descensu, nec recto tramite currus
Sidereos patitur vastum per inane moveri;
Sed rapit immotis, se centro, singula Gyris.
Jam patet horrificis quæ sit via flexa Cometis;
Jam non miramur barbati Phænomena Astri.
Discimus hinc tandem qua causa argentea Phœbe
Passibus haud æquis graditur; cur subdita nulli
Hactenus Astronomo numerorum fræna recuset:
Cur remeant Nodi, curque Auges progrediuntur.
Discimus & quantis refluum vaga Cynthia Pontum
Viribus impellit, dum fractis fluctibus Ulvam
Deserit, ac Nautis suspectas nudat arenas;
Alternis vicibus suprema ad littora pulsans.
Quæ toties animos veterum torsere Sophorum,
Quæque Scholas frustra rauco certamine vexant
Obvia conspicimus nubem pellente Mathesi.
Jam dubios nulla caligine prægravat error
Queis Superum penetrare domos atque ardua Cœli
Scandere sublimis Genii concessit acumen.
Surgite Mortales, terrenas mittite curas
Atque hinc cœligenæ vires dignoscite Mentis
A pecudum vita longe lateque remotæ.
Qui scriptis jussit Tabulis compescere Cædes
Furta & Adulteria, & perjuræ crimina Fraudis;
Quive vagis populis circumdare mœnibus Urbes
Autor erat; Cererisve beavit munere gentes;
Vel qui curarum lenimen pressit ab Uva;
Vel qui Niliaca monstravit arundine pictos
Consociare sonos, oculisque exponere Voces;
Humanam sortem minus extulit; utpote pauca
Respiciens miseræ solummodo commoda vitæ.
Jam vero Superis convivæ admittimur, alti
Jura poli tractare licet, jamque abdita cœcæ
Claustra patent Terræ rerumque immobilis ordo,
Et quæ præteriti latuerunt sæcula mundi.
Talia monstrantem mecum celebrate Camænis,
Vos qui cœlesti gaudetis nectare vesci,
NEWTONVM clausi reserantem scrinia Veri,
NEWTONVM Musis charum, cui pectore puro
Phœbus adest, totoque incessit Numine mentem:
Nec fas est propius Mortali attingere Divos.
Quantitas Materiæ est mensura ejusdem orta ex illius Densitate &
Aer duplo densior in duplo spatio quadruplus est. Idem intellige de Nive
et Pulveribus per compressionem vel liquefactionem condensatis. Et par est
ratio corporum omnium, quæ per causas quascunq; diversimode condensantur.
Medii interea, si quod fuerit, interstitia partium libere pervadentis, hic nullam
rationem habeo. Hanc autem quantitatem sub nomine corporis vel Massæ in
sequentibus passim intelligo. Innotescit ea per corporis cujusq; pondus. Nam
ponderi proportionalem esse reperi per experimenta pendulorum accuratissime
instituta, uti posthac docebitur.
Quantitas motus est mensura ejusdem orta ex Velocitate et quantitate Materiæ
Motus totius est summa motuum in partibus singulis, adeoq; in corpore dup-
lo majore æquali cum Velocitate duplus est, et dupla cum Velocitate quadruplus.
Materiæ vis insita est potentia resistendi, qua corpus unumquodq;, quantum in
se est, perseverat in statu suo vel quiescendi vel movendi uniformiter in
Hæc semper proportionalis est suo corpori, neq; differt quicquam ab inertia
Massæ, nisi in modo concipiendi. Per inertiam materiæ fit ut corpus omne de
statu suo vel quiescendi vel movendi difficulter deturbetur. Unde etiam vis in-
sita nomine significantissimo vis inertiæ dici possit. Exercet vero corpus hanc
vim solummodo in mutatione status sui per vim aliam in se impressam facta,
estq; exercitium ejus sub diverso respectu et Resistentia et Impetus: Resistentia
quatenus corpus ad conservandum statum suum reluctatur vi impressæ; Impetus
quatenus corpus idem, vi resistentis obstaculi difficulter cedendo, conatur sta-
tum ejus mutare. Vulgus Resistentiam quiescentibus et Impetum moventibus
tribuit; sed motus et quies, uti vulgo concipiuntur, respectu solo distinguun-
tur ab invicem, neq; semper vere quiescunt quæ vulgo tanquam quiescentia
Vis impressa est actio in corpus exercita, ad mutandum ejus statum vel
quiescendi vel movendi uniformiter in directum.
Consistit hæc vis in actione sola, neq; post actionem permanet in corpore.
Perseverat enim corpus in statu omni novo per solam vim inertiæ. Est autem
vis impressa diversarum originum, ut ex ictu, ex pressione, ex vi centripeta.
Vis centripeta est qua corpus versus punctum aliquod tanquam ad centrum
trahitur, impellitur, vel utcunq; tendit.
Hujus generis est gravitas, qua corpus tendit ad centrum Terræ: Vis magnet-
ica, qua ferrum petit centrum Magnetis, et vis illa, quæcunq; sit, qua Planetæ
perpetuo retrahuntur a motibus rectilineis, et in lineis curvis revolvi coguntur.
Est autem vis centripetæ quantitas trium generum, absoluta, acceleratrix et
Vis centripetæ quantitas absoluta est mensura ejusdem major vel minor pro
efficacia causæ eam propagantis a centro per regiones in circuitu.
Uti virtus Magnetica major in uno magnete, minor in alio.
Vis centripetæ quantitas acceleratrix est ipsius mensura Velocitati
proportionalis, quam dato tempore generat.
Uti Virtus Magnetis ejusdem major in minori Distantia, minor in majori: vel
vis gravitans major in Vallibus, minor in cacuminibus præaltorum montium (ut
experimento pendulorum constat) atq; adhuc minor (ut posthac patebit) in ma-
joribus distantiis a Terra; in æqualibus autem distantiis eadem undiq; propterea
quod corpora omnia cadentia (gravia an levia, magna an parva) sublata Aeris
resistentia, æqualiter accelerat.
Vis centripetæ quantitas motrix est ipsius mensura proportionalis motui, quem
dato tempore generat.
Uti pondus majus in majori corpore, minus in minore; inq; corpore eodem
majus prope terram, minus in cælis. Hæc vis est corporis totius centripetentia
seu propensio in centrum & (ut ita dicam) pondus, & innotescit semper per vim
ipsi contrariam & æqualem, qua descensus corporis impediri potest.
Hasce virium quantitates brevitatis gratia nominare licet vires absolutas,
acceleratrices & motrices, & distinctionis gratia referre ad corpora, ad corpo-
rum loca, & ad centrum virium: Nimirum vim motricem ad corpus, tanquam
conatum & propensionem totius in centrum, ex propensionibus omnium par-
tium compositum; & vim acceleratricem ad locum corporis, tanquam efficaciam
quandam, de centro per loca singula in circuitu diffusam, ad movenda corpo-
ra quæ in ipsis sunt; vim autem absolutam ad centrum, tanquam causa aliqua
præditum, sine qua vires motrices non propagantur per regiones in circuitu; sive
causa illa sit corpus aliquod centrale (quale est Magnes in centro vis Magneticæ
vel Terra in centro vis gravitantis) sive alia aliqua quæ non apparet. Mathe-
maticus saltem est hic conceptus. Nam virium causas & sedes physicas jam non
Est igitur vis acceleratrix ad vim motricem ut celeritas ad motum. Oritur
enim quantitas motus ex celeritate ducta in quantitatem Materiæ, & vis motrix
ex vi acceleratrice ducta in quantitatem ejusdem materiæ. Nam summa action-
um vis acceleratricis in singulas corporis particulas est vis motrix totius. Unde
juxta Superficiem Terræ, ubi gravitas acceleratrix seu vis gravitans in corporibus
universis eadem est, gravitas motrix seu pondus est ut corpus: at si in regiones
ascendatur ubi gravitas acceleratrix fit minor, pondus pariter minuetur, eritq;
semper ut corpus in gravitatem acceleratricem ductum. Sic in regionibus ubi
gravitas acceleratrix duplo minor est, pondus corporis duplo vel triplo minoris
erit quadruplo vel sextuplo minus.
Porro attractiones et impulsus eodem sensu acceleratrices & motrices nomi-
no. Voces autem attractionis, impulsus vel propensionis cujuscunq; in cen-
trum, indifferenter et pro se mutuo promiscue usurpo, has vires non physice
sed Mathematice tantum considerando. Unde caveat lector ne per hujusmodi
voces cogitet me speciem vel modum actionis causamve aut rationem physicam
alicubi definire, vel centris (quæ sunt puncta Mathematica) vires vere et physice
tribuere, si forte aut centra trahere, aut vires centrorum esse dixero.
Hactenus voces minus notas, quo in sensu in sequentibus accipiendæ sunt,
explicare visum est. Nam tempus, spatium, locum et motum ut omnibus no-
tissima non definio. Dicam tamen quod vulgus quantitates hasce non aliter
quam ex relatione ad sensibilia concipit. Et inde oriuntur præjudicia quædam,
quibus tollendis convenit easdem in absolutas & relativas, veras & apparentes,
Mathematicas et vulgares distingui.
I. Tempus absolutum verum & Mathematicum, in se & natura sua absq;
relatione ad externum quodvis, æquabiliter fluit, alioq; nomine dicitur Duratio;
relativum apparens & vulgare est sensibilis & externa quævis Durationis per
motum mensura, (seu accurata seu inæquabilis) qua vulgus vice veri temporis
utitur; ut Hora, Dies, Mensis, Annus.
II. Spatium absolutum natura sua absq; relatione ad externum quodvis sem-
per manet similare & immobile; relativum est spatii hujus mensura seu dimensio
quælibet mobilis, quæ a sensibus nostris per situm suum ad corpora definitur,
& a vulgo pro spatio immobili usurpatur: uti dimensio spatii subterranei, aerei
vel cælestis definita per situm suum ad Terram. Idem sunt spatium absolutum
& relativum, specie & magnitudine, sed non permanent idem semper numero.
Nam si Terra, verbi gratia, movetur, spatium Aeris nostri quod relative & re-
spectu Terræ semper manet idem, nunc erit una pars spatii absoluti in quam
Aer transit, nunc alia pars ejus, & sic absolute mutabitur perpetuo.
III. Locus est pars spatii quam corpus occupat, estq; pro ratione spatii vel
absolutus vel relativus. Partem dico spatii, non situm corporis vel superficiem
ambientem. Nam solidorum æqualium æquales semper sunt loci; Superficies
autem ob dissimilitudinem figurarum ut plurimum inæquales sunt; situs vero
proprie loquendo quantitatem non habent, neq; tam sunt loca quam affectiones
locorum. Motus totius idem est cum summa motuum partium, hoc est, transla-
tio totius de ipsius loco eadem cum summa translationum partium de locis suis,
adeoq; locus totius idem cum summa locorum partium, & propterea internus &
in corpore toto.
IV. Motus absolutus est translatio corporis de loco absoluto in locum ab-
solutum, relativus de relativo in relativum. Sic in Navi quæ velis passis fertur,
relativus corporis locus est navis regio illa in qua corpus versatur, seu cavitatis
totius pars illa quam corpus implet, quæq; adeo movetur una cum Navi; & Quies
relativa est permansio corporis in eadem illa navis regione vel parte cavitatis.
At Quies vera est permansio corporis in eadem parte spatii illius immoti in qua
Navis ipsa una cum cavitate sua & contentis universis movetur. Unde si Terra
vere quiescit, corpus quod relative quiescit in Navi, movebitur vere et absolute
ea cum Velocitate qua Navis movetur in Terra. Sin Terra etiam movetur, ori-
etur verus et absolutus corporis motus partim ex Terræ motu vero in spatio
immoto, partim ex Navis motu relativo in Terra; et si corpus etiam movetur
relative in Navi, orietur verus ejus motus partim ex vero motu Terræ in spatio
immoto, partim ex relativis motibus tum Navis in Terra, tum corporis in Navi,
et ex his motibus relativis orietur corporis motus relativus in Terra. Ut si Terræ
pars illa ubi Navis versatur moveatur vere in Orientem, cum Velocitate partium
10010, et velis ventoq; feratur Navis in Occidentem cum Velocitate partium
decem, Nauta autem ambulet in Navi Orientem versus cum Velocitatis parte
una, movebitur Nauta vere et absolute in spatio immoto cum Velocitatis part-
ibus 10001 in Orientem, et relative in Terra Occidentem versus cum Velocitatis
Tempus absolutum a relativo distinguitur in Astronomia per Æquationem
Temporis vulgi. Inæquales enim sunt dies Naturales, qui vulgo tanquam æquales
pro Mensura Temporis habentur. Hanc inæqualitatem corrigunt Astronomi ut
ex veriore Tempore mensurent motus cælestes. Possibile est ut nullus sit mo-
tus æquabilis quo Tempus accurate mensuretur. Accelerari & retardari possunt
motus omnes, sed fluxus Temporis absoluti mutari nequit. Eadem est duratio
seu perseverantia existentiæ rerum, sive motus sint celeres, sive tardi, sive nulli;
proinde hæc a mensuris suis sensibilibus merito distinguitur, & ex ijsdem collig-
itur per Æquationem Astronomicam. Hujus autem æquationis in determinandis
Phænomenis necessitas, tum per experimentum Horologii oscillatorii, tum etiam
per Eclipses Satellitum Jovis evincitur.
Ut partium Temporis ordo est immutabilis, sic etiam ordo partium Spatii.
Moveantur hæ de locis suis, & movebuntur (ut ita dicam) de seipsis. Nam
Tempora & Spatia sunt sui ipsorum & rerum omnium quasi loca. In Tempore
quoad ordinem successionis; in Spatio quoad ordinem situs locantur universa.
De illorum Essentia est ut sint loca, & loca primaria moveri absurdum est. Hæc
sunt igitur absoluta loca, & solæ translationes de his locis sunt absoluti motus.
Verum quoniam hæ spatii partes videri nequeunt, & ab invicem per sensus
nostros distingui, earum vice adhibemus mensuras sensibiles. Ex positionibus
enim & distantiis rerum a corpore aliquo, quod spectamus ut immobile, defin-
imus loca universa; deinde etiam & omnes motus æstimamus cum respectu
ad prædicta loca, quatenus corpora ab iisdem transferri concipimus. Sic vice
locorum & motuum absolutorum relativis utimur, nec incommode in rebus hu-
manis: in Philosophicis autem abstrahendum est a sensibus. Fieri etenim potest
ut nullum revera quiescat corpus, ad quod loca motusq; referantur.
Distinguuntur autem Quies & Motus absoluti & relativi ab invicem per eo-
rum proprietates, causas & effectus. Quietis proprietas est, quod corpora vere
quiescentia quiescunt inter se. Ideoq; cum possibile sit ut corpus aliquod in
regionibus fixarum, aut longe ultra, quiescat absolute; sciri autem non possit ex
situ corporum ad invicem in regionibus nostris, utrum horum aliquod ad long-
inquum illud datam positionem servet, quies vera ex horum situ inter se definiri
Motus proprietas est, quod partes quæ datas servant positiones ad tota,
participant motus eorundem totorum. Nam gyrantium partes omnes conantur
recedere de axe motus, et progredientium impetus oritur ex conjuncto impetu
partium singularum. Igitur motis corporibus ambientibus, moventur quæ in
ambientibus relative quiescunt. Et propterea motus verus et absolutus definiri
nequit per translationem e vicinia corporum, quæ tanquam quiescentia spectan-
tur. Debent corpora externa non solum tanquam quiescentia spectari, sed etiam
vere quiescere. Alioquin inclusa omnia, præter translationem e vicinia ambien-
tium, participabunt etiam ambientium motus veros, et sublata illa translatione
non vere quiescent, sed tanquam quiescentia solummodo spectabuntur; sunt en-
im ambientia ad inclusa ut totius pars exterior ad partem interiorem, vel ut
cortex ad nucleum. Moto autem cortice, nucleus etiam, absq; translatione de
vicinia corticis, ceu pars totius, movetur.
Præcedenti proprietati affinis est, quod moto loco movetur una locatum,
adeoq; corpus, quod de loco moto movetur, participat etiam loci sui motum.
Igitur motus omnes, qui de locis motis fiunt, sunt partes solummodo motuum
integrorum et absolutorum, et motus omnis integer componitur ex motu cor-
poris de loco suo primo, et motu loci hujus de loco suo, et sic deinceps, usq; dum
perveniatur ad locum immotum, ut in exemplo Nautæ supra memorato. Unde
motus integri et absoluti non nisi per loca immota definiri possunt, et propterea
hos ad loca immota, relativos ad mobilia supra retuli: Loca autem immota non
sunt, nisi quæ omnia ab infinito in infinitum datas servant positiones ad in-
vicem, atq; adeo semper manent immota, spatiumq; constituunt quod immobile
Causæ, quibus motus veri et relativi distinguuntur ab invicem, sunt vires
in corpora impressæ ad motum generandum. Motus verus nec generatur nec
mutatur nisi per vires in ipsum corpus motum impressas: at motus relativus
generari et mutari potest absq; viribus impressis in hoc corpus. Sufficit enim ut
imprimantur in alia solum corpora ad quæ fit relatio, ut ijs cedentibus mutetur
relatio illa in qua hujus quies vel motus relativus consistit. Rursus motus verus
a viribus in corpus motum impressis semper mutatur, at motus relativus ab
his viribus non mutatur necessario. Nam si eædem vires in alia etiam corpora,
ad quæ fit relatio, sic imprimantur ut situs relativus conservetur, conservabitur
relatio in qua motus relativus consistit. Mutari igitur potest motus omnis rela-
tivus ubi verus conservatur, et conservari ubi verus mutatur; et propterea motus
verus in ejusmodi relationibus minime consistit.
Effectus quibus motus absoluti et relativi distinguuntur ab invicem, sunt
vires recedendi ab axe motus circularis. Nam in motu circulari nude relativo hæ
vires nullæ sunt, in vero autem et absoluto majores vel minores pro quantitate
motus. Si pendeat situla a filo prælongo, agaturq; perpetuo in orbem donec
filum a contorsione admodum rigescat, dein impleatur aqua, et una cum aqua
quiescat; tum vi aliqua subitanea agatur motu contrario in orbem, et filo se
relaxante, diutius perseveret in hoc motu: superficies aquæ sub initio plana
erit, quemadmodum ante motum vasis, at postquam, vi in aquam paulatim
impressa, effecit vas, ut hæc quoq; sensibiliter revolvi incipiat, recedet ipsa
paulatim e medio, ascendetq; ad latera vasis, figuram concavam induens, (ut
ipse expertus sum) et incitatiore semper motu ascendet magis & magis, donec
revolutiones in æqualibus cum vase temporibus peragendo, quiescat in eodem
relative. Indicat hic ascensus conatum recedendi ab axe motus, & per talem
conatum & innotescit & mensuratur motus aquæ circularis verus & absolutus,
motuiq; relativo hic omnino contrarius. Initio ubi maximus erat aquæ motus
relativus in vase, motus ille nullum excitabat conatum recedendi ab axe: Aqua
non petebat circumferentiam ascendendo ad latera vasis, sed plana manebat,
& propterea motus illius circularis verus nondum inceperat. Postea vero ut
aquæ motus relativus decrevit, ascensus ejus ad latera vasis indicabat conatum
recedendi ab axe, atq; hic conatus monstrabat motum illius circularem verum
perpetuo crescentem, ac tandem maximum factum ubi aqua quiescebat in vase
relative. Igitur conatus iste non pendet a translatione aquæ respectu corporum
ambientium, & propterea motus circularis verus per tales translationes definiri
nequit. Unicus est corporis cujusq; revolventis motus vere circularis, conatui
unico tanquam proprio & adæquato effectui respondens; motus autem relativi
pro varijs relationibus ad externa innumeri sunt, & relationum instar, effectibus
veris omnino destituuntur, nisi quatenus de vero illo & unico motu participant.
Unde & in Systemate eorum qui Cælos nostros infra Cælos fixarum in orbem
revolvi volunt, & Planetas secum deferre; Planetæ & singulæ Cælorum partes,
qui relative quidem in Cælis suis proximis quiescunt, moventur vere. Mutant
enim positiones suas ad invicem (secus quam fit in vere quiescentibus) unaq;
cum cælis delati participant eorum motus, & ut partes revolventium totorum,
ab eorum axibus recedere conantur.
Igitur quantitates relativæ non sunt eæ ipsæ quantitates quarum nomina
præ se ferunt, sed earum mensuræ illæ sensibiles (veræ an errantes) quibus
vulgus loco mensuratarum utitur. At si ex usu definiendæ sunt verborum signi-
ficationes; per nomina illa Temporis, Spatij, Loci & Motus proprie intelligendæ
erunt hæ mensuræ; & sermo erit insolens & pure Mathematicus si quantitates
mensuratæ hic subintelligantur. Proinde vim inferunt Sacris literis qui voces
hasce de quantitatibus mensuratis ibi interpretantur. Neq; minus contaminant
Mathesin & Philosophiam qui quantitates veras cum ipsarum relationibus &
vulgaribus mensuris confundunt.
Motus quidem veros corporum singulorum cognoscere, & ab apparentibus
actu discriminare, difficillimum est; propterea quod partes spatij illius immo-
bilis in quo corpora vere moventur, non incurrunt in sensus. Causa tamen
non est prorsus desperata. Nam suppetunt argumenta partim ex motibus ap-
parentibus, qui sunt motuum verorum differentiæ, partim ex viribus quæ sunt
motuum verorum causæ & effectus. Ut si globi duo ad datam ab invicem distan-
tiam filo intercedente connexi, revolverentur circa commune gravitatis centrum;
innotesceret ex tensione fili conatus globorum recedendi ab axe motus, & inde
quantitas motus circularis computari posset. Deinde si vires quælibet æquales in
alternas globorum facies ad motum circularem augendum vel minuendum simul
imprimerentur, innotesceret ex aucta vel diminuta fili tensione augmentum vel
decrementum motus; & inde tandem inveniri possent facies globorum in quas
vires imprimi deberent, ut motus maxime augeretur, id est facies posticæ, sive
quæ in motu circulari sequuntur. Cognitis autem faciebus quæ sequuntur &
faciebus oppositis quæ præcedunt, cognosceretur determinatio motus. In hunc
modum inveniri posset & quantitas & determinatio motus hujus circularis in
vacuo quovis immenso, ubi nihil extaret externum & sensibile, quocum globi
conferri possent. Si jam constituerentur in spatio illo corpora aliqua longinqua
datam inter se positionem servantia, qualia sunt stellæ fixæ in regionibus nostris:
sciri quidem non posset ex relativa globorum translatione inter corpora, utrum
his an illis tribuendus esset motus. At si attenderetur ad filum & inveniretur
tensionem ejus illam ipsam esse quam motus globorum requireret; concludere
liceret motum esse globorum, & tum demum ex translatione globorum inter
corpora, determinationem hujus motus colligere. Motus autem veros ex eorum
causis, effectibus & apparentibus differentijs colligere, & contra, ex motibus seu
veris seu apparentibus, eorum causas & effectus, docebitur fusius in sequentibus.
Hunc enim in finem Tractatum sequentem composui.