AXIOMATA, SIVE LEGES MOTUS
[Leges solæ descripta sunt, commentariis prætermissis.]
Lex I
Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus illud a viribus impressis cogitur statum suum mutare.
Lex II
Mutationem motus proportionalem esse vi motrici impressæ, & fieri secundum lineam rectam qua vis illa imprimitur.
Lex III
Actioni contrariam semper & æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales & in partes contrarias dirigi.
Here are what they are explained in a very nice way. If you have kids who are interested or you are refreshing your understanding of these laws, this site is really good.
Newtons's first law of motion:
An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
Newton's second law of motion can be formally stated as follows:
The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
This verbal statement can be expressed in equation form as follows:
a = F/m
The above equation is often rearranged to a more familiar form as shown below. The net force is equated to the product of the mass times the acceleration.
F = m a
Formally stated, Newton's third law is:
For every action, there is an equal and opposite reaction
the most common misconception
This excellent physics classroom site states, in connection with Newton's First Law, the most common misconception -
that an object has to have its motion reinforced to keep it going.
Many, if not most people, even physics students (who aren't aware of the misconception they bring with them) think that an object will stop if you don't keep pushing it.
The following from Fr. Stanley Jaki is excerpts from an article which addresses those scientists who preceded Newton (who himself said that he stood on the shoulders of giants) and set the stage for Newton's laws. Importantly, how they, with a singularly Christian viewpoint, laid the foundation for Newton's first law and how they did not fall into the common misconception
The Christological Origins of Newton's first law by Stanley Jaki
Excerpts
"Duhem indeed found that Copernicus himself stood on the shoulders of
giants. They were Johannes Buridanus, professor at the Sorbonne and his
disciple, Nicole Oresme, who subsequently became bishop of Lisieux. As a
student in Cracow around 1490, Copernicus learned natural philosophy or
physics from Buridan’s commentaries on Aristotle’s De coelo or On the
Heavens. By then those commentaries had been about a century and a half
old, available in many copies in medieval universities all over Europe. Even
today there are about a dozen copies of those commentaries in Cracow. A
reason for this is the fact that professors in those universities had very often
been former students at the Sorbonne where the number of students was
about sixty thousand or so in Buridan’s time. Paris at that time was the
unrivalled capital of learning.
In those commentaries the first law appears in the form of the impetus
theory, or the idea that in order to produce motion it is enough to give an
impetus or push to a body and have it thereby move by itself. Buridan illus-
trates the idea with a reference both to terrestrial motions and to the
motion of the celestial bodies. In the texts that follow the gist of the impe-
tus theory is given in italics, so that it may stand out in its context which
remains, of course, very important if one is to appreciate its novelty and the
source of that novelty. The text, which I will quote in English, first appeared
in print in the original Latin and in French translation in 1913, in the third
volume of Duhem’s epoch-making work Etudes sur Léonard de Vinci, ceux
qu’il a lus et ceux qui l’ont lu. Duhem’s full-scale discussion of the topic, in
the sixth and seventh volumes of his Système du monde should have
appeared in 1917 and 1918, but they did not see print until forty years later.
They finally were printed because Louis De Broglie, the discoverer of the
wave nature of matter and Perpetual Secretary of the Académie des
Sciences in Paris, refused to tolerate any longer an anti-Duhem conspiracy
in Paris and threatened the publisher Hermann, which was part of that con-
spiracy, with a law suit. 13
But back to Buridan’s passages as they stand in English translation in
Marshall Clagett’s The Science of Mechanics in the Middle Ages. 14
[The impetus then also explains why] one who wishes to jump a
long distance drops back a way in order to run faster, so that by run-
ning he might acquire an impetus which would carry him a longer
distance in the jump. Whence the person so running and jumping
does not feel the air moving him, but [rather] feels the air in front
strongly resisting him.
And you have an experiment [to support this position]: If you cause
a large and very heavy smith’s mill [ie, a wheel] to rotate and you then
cease to move it, it will still move a while longer by this impetus it has
acquired. Nay, you cannot immediately bring it to rest, but on
account of the resistance from the gravity of the mill, the impetus
would be continually diminished until the mill would cease to move.
And if the mill would last forever without some diminution or alter-
ation of it, and there were no resistance corrupting the impetus, the
mill would be moved perpetually by that impetus.
Buridan amplifies his first example with a reference to what may
appear a very strange notion, but was not strange to Aristotle or to those
who were raised on Aristotle. The notion, of which more later, is the notion
of antiperistasis, or the idea that the body moves forward because the air
which it separates as it moves forward flows past it, and then closes in
behind it and acts thereby as a propellant.
In the second example, which is about the moving of a smith’s wheel, or
in modern terms a flywheel, Buridan amplified on motion by impetus with
a clear reference to the role of resistance and also to the idea of perpetual
motion. In other words, he states nothing less than that in the absence of
resistance the motion would go on undiminished. But unlike the motion of
a long jumper, which is more or less linear, the wheel’s motion is circular. It
would have been too much to expect from Buridan to distinguish the two
motions, that appear, almost three hundred years later, undistinguished
also in Galileo’s idea of inertial motion.
But Buridan’s idea of inertial motion contains something far more
important and decisive than the distinction between linear and circular
motions or rather inertia. Most important is the idea that the mover and the
moved thing need not remain in continual contact in order to make the
motion of the moved thing a continued reality. Here too the novelty
becomes clear if one considers it against its Aristotelian background. Again
the words that carry the idea of motion by impetus, or inertial motion, are
given in italics.
Also, since the Bible does not state that appropriate intelligences
move the celestial bodies, it could be said that it does not appear
necessary to posit intelligences of this kind, because it would be
answered that God, when He created the world, moved each of the
celestial orbs as He pleased, and in moving them He impressed in
them impetuses which moved them without His having to move them
any more except by the method of general influence whereby he con-
curs as a co-agent in all things which take place;“for thus on the sev-
enth day He rested from all work which He had executed by com-
mitting to others the actions and the passions in turn.” And these
impetuses which He impressed in the celestial bodies were not
decreased nor corrupted afterwards, because there was no inclination
of the celestial bodies for other movements. Nor was there resistance
which would be corruptive or repressive of that impetus. But this I do
not say assertively, but [rather tentatively] so that I might seek from
the theological masters what they may teach me in these matters as
to how these things take place...
And thus one could imagine that it is unnecessary to posit
intelligences as the movers of celestial bodies since the Holy
Scriptures do not inform us that intelligences must be posited. For
it could be said that when God created the celestial spheres, He began
to move each of them as He wished, and they are still moved by the
impetus which He gave to them because, there being no resistance, the
impetus is neither corrupted nor diminished.
The intelligences Buridan refers to come from Hellenistic writings in
which Aristotelian and Neoplatonic ideas are fused together, especially as is
the case in Plotinus and Pseudo-Dionysius. In the latter they appear as
angels in charge of celestial bodies. Buridan rightly notes that those intelli-
gences cannot be found in the Bible and that therefore the Christian is not
obligated to take them seriously.
Buridan’s reference to inclinations of bodies echoes, of course, the
Aristotelian notion that bodies are propelled according to the volition prop-
er to their nature. This notion is of Socratic origin, set forth in the Phaedo.
There Socrates tried to overcome the mechanistic physics or rather ideolo-
gy of the Ionians which left no room for purpose and free will. That mech-
anistic philosophy was dirty bathwater containing the baby, or the nascent
quantitative physics. It would have been too much to expect from Socrates
to distinguish between the two. The entire Socratic-Platonic-Aristotelian
tradition was, with respect to science, a fatally wrong move, whereby the
baby was thrown out with the dirty bathwater. 15
The reaction to the problem of purpose in the 17th, the 18th, and 19th
centuries was the reverse. There purpose was thrown out in the interest of
purely quantitative or mechanistic considerations. But back to Buridan, or
rather to the theological matrix of his impetus theory or idea of inertial
motion. While in reference to terrestrial motions it was possible to refer to
another terrestrial agent that triggers the motion, in the case of celestial bod-
ies, or the universe, this was not the case. There a Christian, like Buridan,
could refer only to the Creator. This is what Buridan did, and, most natural-
ly, with an almost explicit reference to the words of Genesis 1,“In the
Beginning when God made the heaven and the earth...” Far more impor-
tantly, Buridan also states that once God creates, whether bodies or their
motions, He keeps those entities in existence simply by a “general influence.”
In saying this Buridan simply restated the theological distinction
between two divine actions: one is creation out of nothing, the other is the
conservation in existence of what has already been created. It is in this dis-
tinction, so clear in Thomas Aquinas, who wrote two generations before
Buridan, that lies the idea of the autonomous character of the laws of
nature or the laws of science. In the Christian theological idea of creation,
and there alone, nature can be both fully created and fully autonomous at
the same time. For only a God that can create out of nothing, can give an
autonomous existence to something created, without having his power
diminished. Hence the independence of science, which does not become an
a priori imposition of this or that human idea on nature.
This is to be kept in mind in reading Buridan’s reference to “theological
masters.” The reference is a roundabout expression of Buridan’s conviction
that the theological masters would find nothing wrong with the idea of
impetus or inertial motion. This is exactly what happened, in a tacit recog-
nition of the fact the theology is not about the how of the motion but only
about its ultimate origin or why. Buridan’s impetus theory found no oppo-
sition, theological or other. Clearly Buridan’s expressed something that was
in full harmony with a number of implicit and explicit assumptions, or to
use an expression coined in Newton’s time, with the “climate of thought.”
In Buridan’s simultaneous application of the same law to celestial and
terrestrial motions one can see anticipated Newton’s view that the same law
governs the motion of the moon and the fall of a stone on the earth.
Buridan also anticipates Popper’s dictum that all science is cosmology. The
true laws of physics, or rather the laws of true physics, must have a validi-
ty throughout the cosmos or the universe.
Of course, the motion of the earth is not a rectilinear inertial motion.
But Buridan’s idea, as applied both to the celestial bodies and to various
motions on earth, implies what is the very essence of inertial motion. The
idea was never stated before because it was revolutionary. The idea con-
sists in the view that it is possible to give with a single, instantaneous act
a quantity of motion, or impetus (or momentum to use the modern word)
to a body and that the quantity would be maintained undiminished if the
body moved in a frictionless medium.
Now why is this notion so revolutionary? Not so much because nobody
had said it before, but because it represents a radical break with all early
standard thinking about motion, especially about the motion of the celestial
bodies or of the heavenly sphere. To see this one should recall briefly
Aristotle’s ideas of motion. According to Aristotle the origin of all motion is
in the motion of the heavenly sphere of the fixed stars. This motion is some-
how transmitted to the planets down to the moon. The earth itself is
motionless.
The transmission is not by means of some mechanism but by some
desire. The farther a planet is from the celestial sphere, the less perfect is
its desire for the source of motion and therefore the more irregular is its
motion. The sphere of the fixed stars alone has a perfectly regular motion,
or a motion with constant velocity, because it alone is in direct contact with
the Prime Mover, which is not really different from the sphere itself.
Aristotle, let this not be forgotten, is a thorough pantheist. The universe
for him is a living entity and divine in its upper parts. In line with this,
Aristotle posits that the mechanism causing the motion of the sphere of the
fixed stars is not a mechanism but a desire of that sphere for the Prime Mover.
In modern terms, there is a continual contact between the source of
motion and the things moved. Now if such is the case one is in the presence
of an uninterrupted application of force. Therefore, in terms of Newtonian
physics the result can only be an accelerated motion. But, of course, the
sphere of the fixed stars is not accelerated. It moves at constant velocity.
Clearly, Aristotelian physics and Newtonian physics are poles apart.
This difference between the two can also be seen in a much less dis-
cussed remark of Aristotle about a theory of motion, called antiperistasis,
already mentioned above. According to that theory a stone which is thrown
moves through the air because it separates the air in front of it, so that the
air is forced to flow past the stone. The air therefore finds a vacuum in the
wake of the stone and, since nature abhors vacuum, the air quickly closes
in behind the stone and acts like a moving force. One can only wish this
were true. There would be much less need for gasoline to drive our automo-
biles, but I am afraid space travel would be impossible.
The really revealing thing in this remark of Aristotle is that he does not
reject it out of hand. Why not? Because, being a very systematic thinker, he
might have seen antiperistasis as the natural part of a much broader theo-
ry of motion. There everything was moved in terms of a continual contact
between the mover and moved. This was certainly the case with Aristotle’s
explanation of celestial motion. The explanation well illustrated the dictum
that all science is cosmology. And if one does not forget Aristotle’s panthe-
ism one may just as well say that all cosmology is theology.
This is true not only of Aristotle, Ptolemy and Plotinus, but also of
Copernicus, Newton, Laplace, Einstein and especially of all those who have
been the chief spokesmen of the various forms of modern scientific cos-
mology, the Big Bang, the steady state, and the theory of multiple univers-
es. They would have generated far more light if they had come clean with
their theologies or countertheologies.
But back to Newton, about whom Alexander Pope wrote:“Nature and
Nature’s laws lay hid in night: God said:‘Let Newton be!’and all was light.”
The real light Newton generated was his recognition that in the motion of
the moon or any of the planets two kinds of motions were fused together.
One was an accelerated motion, the gravitation of the body toward the cen-
ter, the other was a tangential motion. In the absence of gravitation, the
moon would fly away from the earth, and the planets from the sun, and
they would do so along a rectilinear path.
About the origin of the force of attraction among gravitating bodies
Newton had no clear ideas. He seemed to think that the gravitational and
the inertial mass were the same but also that the force of gravitation was
inherent in matter. It was not in the Principia that he rejected as absurd the
idea of action at a distance. He seemed to lean toward the idea of a mechan-
ical transmission of gravitation.
But Newton was rather clear on the origin of the inertial motion of bod-
ies. In the Scholium, which appeared in the second edition of Newton’s
Principia, Newton ascribes the inertial motion of planets to an act of God
who carefully adjusted the measure of that inertial motion to the central
force. His statement is very similar to Buridan’s statement.
Therefore if we look for the origin of that kind of exact science which is
the quantitative study of the motion, the question of the origin of the idea
of inertial motion should seem central. Its original appearance in Buridan’s
writings, or in 14th-century Sorbonne, cannot be disputed. But the regis-
tering of a fact is not its explanation. To us moderns nothing may seem
more obvious, more natural, more self-explanatory than the idea of inertial
motion. Actually its formulation represents the greatest, the most decisive
breakthrough in natural philosophy.
That breakthrough took place less than seven hundred years ago. In the
span of man’s three-million-year-old history it happened a mere moment
ago. And the novelty remains intact even in reference to the first construc-
tion of the pyramids, an extraordinary engineering feat, five thousand years
ago or with the invention of phonetic writing, an even greater intellectual
achievement, about that time. The question therefore rightly arises why
Buridan’s breakthrough came so late? Why is science such a latecomer in
human history? The answer lies with the plainly theological context of the
first appearance of that first law of motion.
There is nothing speculative about the fact that Buridan’s dictum is in
a clear theological context. It is the context of the doctrine, for Buridan a
dogma, of creation out of nothing and in time. For him, in all evidence a
genuine Christian believer, that doctrine was a dogma, defined in the fourth
Lateran Council in 1215. Of course, the Council merely defined a long
standing belief. Already around 200 AD, Tertullian insisted that the
Christian doctrine of creation is a doctrine about creation out of nothing,
or else the Creator would be in need of some pre-existing matter. Such a
pre-existing matter was invariably postulated in all the gnostic distortions
of early Christian beliefs, such as a book by the gnostic Hermogenes, whose
illogicalities Tertullian exposed. 16
Equally ancient was the conviction of genuine Christians that the past
history of the universe is strictly finite. This is what is meant by creation
in time. They may or may not have understood the biblical phrase,“In the
beginning” or bereshit, which, after all, is an anomaly in Hebrew gram-
mar, 17 but they took that phrase to mean that there was an absolute begin-
ning for all. It also inspired the notion that history, human and cosmic, is
not a circular treadmill but a linear move toward a goal, a move best
symbolized by an arrow.
The next point to be kept in mind is that Buridan’s breakthrough comes
in reference to Aristotelian physics or rather pantheism. Buridan knew full
well that for Aristotle the universe was uncreated and eternal. Buridan was
not, of course, the first medieval Christian to disagree on that point with
Aristotle. But he was the first to probe into the physical manner in which
that beginning might have taken place. The result was a breakthrough
toward a new theory of motion, toward the eventual full or live birth of
modern science.
But, one may ask, why one had to wait for Buridan or for the Christian
Middle Ages for that breakthrough? Had not Aristotle’s writings been wide-
ly known to Jews and Muslims for many centuries before the Christian
medievals became acquainted with them from the mid 13th century on? On
the Jewish side there were Maimonides and Crescas who studied Aristotle
at great length. But there is nothing similar to Buridan’s statement in their
works, including Maimonides’ The Guide for the Perplexed and Crescas’Critique of Aristotle.
The same is true of the great Muslim Aristotelians, Avicenna and
Averroes. They were, of course, more Aristotelian than Muslim. Neither of
them believed in creation and Creator. This disbelief of theirs they careful-
ly kept hidden for fear of their lives from the persecutions of Muslim ortho-
doxy. But neither does one find the idea of impetus in the writings of the
truly believing branch of Muslim philosophers, such as al-Ashari and al-
Ghazzali, both believers to the point of being mystics. The reason for this
is that both rejected, for reasons of Muslim orthodoxy, the idea that there
can be laws of nature.
The question therefore may be raised for purely historical reasons
about whether there was something special in Buridan’s belief in creation
and Creator. That something was simply the fact that Buridan’s belief was
a Christian’s belief. . . .
Let me add one more datum, but simply as a historical fact or rather a
sort of cultural thought experiment. Imagine that you live in the time of
Plutarch who died around 120 AD Assume further that Plutarch had a
Christian friend, perhaps from the wider senatorial clan of the Anicii.
Assume further that this friend of Plutarch’s suggested to him that he read
John’s Gospel which by then had been widely available. A fragment of a
copy of it can with certainty be dated to about 120 AD It contains parts of
the phrase,“And Pilate asked Jesus: Are you a king?” The other side of the
fragment contains recipes for cooking.
So let us assume that Plutarch, once a chief priest in Delphi, begins to
read John’s Gospel. He would have stopped reading it with the first chap-
ter. For there he would have read the phrase about a mere Jew, Jesus of
Nazareth, that he was the only begotten or monogenes son of the Father.
Now Plutarch, thoroughly familiar with the entire classical tradition, knew
full well that in that tradition the word monogenes was used in two senses.
One was the trivial daily sense about the only son of a father. The other was
a cosmological sense. Monogenes meant also the cosmos or the universe in
the writings of Plato, Cicero and others, including Plutarch himself. 18 In
that sense the universe was the first emanation and the only universal ema-
nation from the First Principle which in turn was not different from the
universe. This doctrine found a fully cosmological elaboration in Plotinus’
Enneads around 250 AD
Plutarch therefore would be faced with a decision: if he accepts Christ
as the monogenes, he has to stop considering the universe as the mono-
genes. The choice was not a question of mere semantics. The choice was
and still is a choice between Christian monotheism and pantheism. The
choice cannot be evaded by replacing pantheism with panentheism, unless
one clearly states that panentheism still means creation out of nothing and
in time and not a gradual emergence from the first cause or principle. But
this is the kind of statement which is skirted by most champions of panen-
theism nowadays.
Still something is to be said of the pantheism that dominated not only
ancient Greece and Hellenistic culture, but all the great ancient cultures,
especially India and China. It should be easy to imagine how different histo-
ry would have become if Buridan’s breakthrough had occurred there and not
in the Christian West. Today a maharajah might reside in a palace, where
Buckingham Palace, or the Elysée Palace, or the White House stands nowa-
days. What could be true of a maharajah, might also be true of a mandarin.
So much in a nutshell about the most ignored and most crucial ques-
tion of the history of science. The question has two sides to it. One is the
invariable stillbirths of science in all ancient cultures. 19 All of them could
boast of great intellects and of great technical achievements. But science,
which is the science of motion, they failed to come up with. If it is true that
all science is cosmology, then the ultimate reason for that failure is to be
looked for in the pantheistic cosmologies that dominated all those cultures
in the form of the idea of eternal returns. The swastika was its invariable
symbol, which in turn implied a circle, which, because all points of it were
equivalent, could not inspire the idea of an absolute start.
The other side of the question is not merely monotheism of which the
idea of creation out of nothing is a strict corollary. If one considers the fact
that the actual forms of monotheism—Jewish, Christian and Muslim—are
rooted in the same revelation given to Abraham at a given point in the past,
it is possible to see a natural connection between the idea of creation out of
nothing and the idea of creation in time. The latter, of course, simply means
that the past history of the universe is strictly finite. Neither of those ideas
can be proved or disproved by science. Science can no more specify the
truly first moment of cosmic existence than it can prove the eternity of the
universe. There is no measurement either of the nothing or of eternity.
But if one considers the fact that neither the Jewish nor the Muslim
sages were able to come up with the true form of the science of motion, but
only Christian scholars could do this, then one has to look beyond mere
monotheism to Christian monotheism. As pointed out above, Christian
monotheism is riveted in belief in Jesus in whom the Father created all. In
other words, Christ would also loom large as the Savior of science, a point
worth pondering in this year 2000. 20
Regardless of the merit of this conclusion, the question remains about
the origin of science, the most fundamental and least discussed question
about science itself. One may be in error about giving a specific answer, and
there have been some patently erroneous ones, which I discussed over
twenty years ago in a series of lectures given at Oxford. 21 Those very wrong
answers date mostly from the 18th and 19th centuries. Silence about the
question has been almost total during the 20th century, which, in view of
the vast evidence made available by Duhem, is inexcusable.
At any rate, truth comes out much sooner from saying something erro-
neous than from saying nothing or from resolutely refusing to acknowledge
that there is a question, and a most serious one. It is simply not enough to
say that those origins are medieval. And it flies in the face of the historical
and scientific method when escape from the weight of that medieval prove-
nance is sought in the facile remark that Buridan’s insight would have come
anyhow. 22 The anyhow is an easy escape from the clutches of the how and
of the why. Of these two words, the how keeps science on the move, the
other, the why, keeps the human intellect alive in the broadest sense, and
makes thereby possible science as well.
