Definitions
DEFINITION I
The quantity of matter is the measure
of
the same, arising from its density
and bulk
conjointly.
THUS AIR of a double density, in a
double
space, is quadruple in quantity; in
a triple
space, sextuple in quantity. The same
thing
is to be understood of snow, and fine
dust
or powders, that are condensed by compression
or liquefaction, and of all bodies
that are
by any causes whatever differently
condensed.
I have no regard in this place to a
medium,
if any such there is, that freely pervades
the interstices between the parts of
bodies.
It is this quantity that I mean hereafter
everywhere under the name of body or
mass.
And the same is known by the weight
of each
body, for it is proportional to the
weight,
as I have found by experiments on pendulums,
very accurately made, which shall be
shown
hereafter.
DEFINITION II
The quantity of motion is the measure
of
the same, arising from the velocity
and quantity
of matter conjointly.
The motion of the whole is the sum
of the
motions of all the parts; and therefore
in
a body double in quantity, with equal
velocity,
the motion is double; with twice the
velocity,
it is quadruple.
DEFINITION III
The vis insita, or innate force of
matter,
is a power of resisting, by which every
body,
as much as in it lies, continues in
its present
state, whether it be of rest, or of
moving
uniformly forwards in a right line.
This force is always proportional to
the
body whose force it is and differs
nothing
from the inactivity of the mass, but
in our
manner of conceiving it. A body, from
the
inert nature of matter, is not without
difficulty
put out of its state of rest or motion.
Upon
which account, this vis insita may,
by a
most significant name, be called inertia
(vis inertiae) or force of inactivity.
But
a body only exerts this force when
another
force, impressed upon it, endeavours
to change
its condition; and the exercise of
this force
may be considered as both resistance
and
impulse; it is resistance so far as
the body
for maintaining its present state,
opposes
the force impressed; it is impulse
so far
as the body, by not easily giving way
to
the impressed force of another endeavours
to change the state of that other.
Resistance
is usually ascribed to bodies at rest,
and
impulse to those in motion; but motion
and
rest, as commonly conceived, are only
relatively
distinguished; nor are those bodies
always
truly at rest, which commonly are taken
to
be so.
DEFINITION IV
An impressed force is an action exerted
upon
a body, in order to change its state,
either
of rest, or of uniform motion in a
right
line.
This force consists in the action only,
and
remains no longer in the body when
the action
is over. For a body maintains every
new state
it acquires by its inertia only. But
impressed
forces are of different origins, as
from
percussion, from pressure, from centripetal
force.
DEFINITION V
A centripetal force is that by which
bodies
are drawn or impelled, or any way tend,
towards
a point as to a centre.
Of this sort is gravity, by which bodies
tend to the centre of the earth; magnetism,
by which iron tends to the loadstone;
and
that force, whatever it is, by which
the
planets are continually drawn aside
from
the rectilinear motions, which otherwise
they would pursue, and made to revolve
in
curvilinear orbits. A stone, whirled
about
in a sling, endeavours to recede from
the
hand that turns it; and by that endeavour,
distends the sling, and that with so
much
the greater force, as it is revolved
with
the greater velocity, and as it is
let go,
flies away. That force which opposes
itself
to this endeavour, and by which the
sling
continually draws back the stone towards
the hand, and retains it in its orbit,
because
it is directed to the hand as the centre
of the orbit, I call the centripetal
force.
And the same thing is to be understood
of
all bodies, revolved in any orbits.
They
all endeavour to recede from the centres
of their orbits; and were it not for
the
opposition of a contrary force which
restrains
them to, and detains them in their
orbits,
which I therefore call centripetal,
would
fly off in right lines, with an uniform
motion.
A projectile, if it was not for the
force
of gravity, would not deviate towards
the
earth, but would go off from it in
a right
line, and that with an uniform motion,
if
the resistance of the air was taken
away.
It is by its gravity, that it is drawn
aside
continually from its rectilinear course,
and made to deviate towards the earth,
more
or less, according to the force of
its gravity,
and the velocity of its motion. The
less
its gravity is, or the quantity of
its matter,
or the greater the velocity with which
it
is projected, the less will it from
a rectilinear
course, and the farther it will go.
If a
leaden ball, projected from the top
of a
mountain by the force of gunpowder,
with
a given velocity, and in a direction
parallel
to the horizon, is carried in a curved
line
to the distance of two miles before
it falls
to the ground; the same, if the resistance
of the air were taken away, with a
double
or decuple velocity, fly twice or ten
times
as far. And by increasing the velocity,
we
may at pleasure increase the distance
to
which it might be projected, and diminish
the curvature of the line which it
might
describe, till at last it should fall
at
the distance of
10, 30, or 90 degrees, or even might
go quite
round the whole earth before it falls;
or
lastly, so that it might never fall
to the
earth, but go forwards into the celestial
spaces, and proceed in its motion in
infinitum.
And after the same manner that a projectile,
by the force of gravity, may be made
to revolve
in an orbit, and go round the whole
earth,
the moon also, either by the force
of gravity,
if it is endued with gravity, or by
any other
force, that impels iowards the earth,
may
be continually drawn aside towards
the earth,
out of the rectilinear way which by
its innate
force it would pursue; and would be
made
to revolve in the orbit which it now
describes;
nor could the moon without some such
force
be retained in its orbit. If this force
was
too small, it would not sufficiently
turn
the moon out of a rectilinear course;
if
it was too great, it would turn it
too much,
and draw down the moon from its orbiowards
the earth. It is necessary that the
force
be of a just quantity, and it belongs
to
the mathematicians to find the force
that
may serve exactly to retain a body
in a given
orbit with a given velocity; and vice
versa,
to determine the curvilinear way into
which
a body projected from a given place,
with
a given velocity, may be made to deviate
from its natural rectilinear way, by
means
of a given force.
The quantity of any centripetal force
may
be considered as of three kinds: absolute,
accelerative, and motive.
DEFINITION VI
The absolute quantity of a centripetal
force
is the measure of the same, proportional
to the efficacy of the cause that propagates
it from the centre, through the spaces
round
about.
Thus the magnetic force is greater
in one
loadstone and less in another, according
to their sizes and strength of intensity.
DEFINITION VII
The accclerative quantity of a centripetal
force is the measure of the same, proportional
to the velocity which it generates
in a given
time.
Thus the force of the same loadstone
is greater
at a less distance, and less at a greater:
also the force of gravity is greater
in valleys,
less on tops of exceeding high mountains;
and yet less (as shall hereafter be
shown),
at greater distances from the body
of the
earth; but at equal distances, it is
the
same everywhere; because (taking away,
or
allowing for, the resistance of the
air),
it equally accelerates all falling
bodies,
whether heavy or light, great or small.
DEFINITION VIII
The motive quantity of a centripetal
force
is the measure of the same, proportional
to the motion which it generates in
a given
time.
Thus the weight is greater in a greater
body,
less in a less body; and, in the same
body,
it is greater near to the earth, and
less
at remoter distances. This sort of
quantity
is the centripetency, or propension
of the
whole body towards the centre, or,
as I may
say, its weight; and it is always known
by
the quantity of an equal and contrary
force
just sufficient to hinder the descent
of
the body.
These quantities of forces, we may,
for the
sake of brevity, call by the names
of motive,
accelerative, and absolute forces;
and, for
the sake of distinction, consider them
with
respect to the bodies thaend to the
centre,
to the places of those bodies, and
to the
centre of force towards which they
tend;
that is to say, I refer the motive
force
to the body as an endeavour and propensity
of the whole towards a centre, arising
from
the propensities of the several parts
taken
together; the accelerative force to
the place
of the body, as a certain power diffused
from the centre to all places around
to move
the bodies that are in them; and the
absolute
force to the centre, as endued with
some
cause, without which those motive forces
would not be propagated through the
spaces
round about; whether that cause be
some central
body (such as is the magnet in the
centre
of the magnetic force, or the earth
in the
centre of the gravitating force), or
anything
else that does not yet appear. For
I here
design only to give a mathematical
notion
of those forces, without considering
their
physical causes and seats.
Wherefore the accelerative force will
stand
in the same relation to the motive,
as celerity
does to motion. For the quantity of
motion
arises from the celerity multiplied
by the
quantity of matter; and the motive
force
arises from the accelerative force
multiplied
by the same quantity of matter. For
the sum
of the actions of the accelerative
force,
upon the several particles of the body,
is
the motive force of the whole. Hence
it is,
that near the suffice of the earth,
where
the accelerative gravity, or force
productive
of gravity, in all bodies is the same,
the
motive gravity or the weight is as
the body;
but if we should ascend to higher regions,
where the accelerative gravity is less,
the
weight would be equally diminished,
and would
always be as the product of the body,
by
the accelerative gravity. So in those
regions,
where the accelerative gravity is diminished
into one-half, the weight of a body
two or
three times less, will be four or six
times
less.
I likewise call attractions and impulses,
in the same sense, accelerative, and
motive;
and use the words attraction, impulse,
or
propensity of any sorowards a centre,
promiscuously,
and indifferently, one for another;
considering
those forces not physically, but mathematically:
wherefore the reader is not to imagine
that
by those words I anywhere take upon
me to
define the kind, or the manner of any
action,
the causes or the physical reason thereof,
or that I attribute forces, in a true
and
physical sense, to certain centres
(which
are only mathematical points); when
at any
time I happen to speak of centres as
attracting,
or as endued with attractive powers.
SCHOLIUM
Hitherto I have laid down the definitions
of such words as are less known, and
explained
the sense in which I would have them
to be
understood in the following discourse.
I
do not define time, space, place, and
motion,
as being well known to all. Only I
must observe,
that the common people conceive those
quantities
under no other notions but from the
relation
they bear to sensible objects. And
thence
arise certain prejudices, for the removing
of which it will be convenient to distinguish
them into absolute and relative, true
and
apparent, mathematical and common.
I. Absolute, true, and mathematical
time,
of itself, and from its own nature,
flows
equably without relation to anything
external,
and by another name is called duration:
relative,
apparent, and common time, is some
sensible
and external (whether accurate or unequable)
measure of duration by the means of
motion,
which is commonly used instead of true
time;
such as an hour, a day, a month, a
year.
II. Absolute space, in its own nature,
without
relation to anything external, remains
always
similar and immovable. Relative space
is
some movable dimension or measure of
the
absolute spaces; which our senses determine
by its position to bodies; and which
is commonly
taken for immovable space; such is
the dimension
of a subterraneous, an aerial, or celestial
space, determined by its position in
respect
of the earth. Absolute and relative
space
are the same in figure and magnitude;
but
they do not remain always numerically
the
same. For if the earth, for instance,
moves,
a space of our air, which relatively
and
in respect of the earth remains always
the
same, will at one time be one part
of the
absolute space into which the air passes;
at another time it will be another
part of
the same, and so, absolutely understood,
it will be continually changed.
III. Place is a part of space which
a body
takes up, and is according to the space,
either absolute or relative. I say,
a part
of space; not the situation, nor the
external
surface of the body. For the places
of equal
solids are always equal; but their
suffices,
by reason of their dissimilar figures,
are
often unequal. Positions properly have
no
quantity, nor are they so much the
places
themselves, as the properties of places.
The motion of the whole is the same
with
the sum of the motions of the parts;
that
is, the translation of the whole, out
of
its place, is the same thing with the
sum
of the translations of the parts out
of their
places; and therefore the place of
the whole
is the same as the sum of the places
of the
parts, and for that reason, it is internal,
and in the whole body.
IV. Absolute motion is the translation
of
a body from one absolute place into
another;
and relative motion, the translation
from
one relative place into another. Thus
in
a ship under sail, the relative place
of
a body is that part of the ship which
the
body possesses; or that part of the
cavity
which the body fills, and which therefore
moves together with the ship: and relative
rest is the continuance of the body
in the
same part of the ship, or of its cavity.
But real, absolute rest, is the continuance
of the body in the same part of that
immovable
space, in which the ship itself, its
cavity,
and all that it contains, is moved.
Wherefore,
if the earth is really at rest, the
body,
which relatively rests in the ship,
will
really and absolutely move with the
same
velocity which the ship has on the
earth.
But if the earth also moves, the true
and
absolute motion of the body will arise,
partly
from the true motion of the earth,
in immovable
space, partly from the relative motion
of
the ship on the earth; and if the body
moves
also relatively in the ship, its true
motion
will arise, partly from the true motion
of
the earth, in immovable space, and
partly
from the relative motions as well of
the
ship on the earth, as of the body in
the
ship; and from these relative motions
will
arise the relative motion of the body
on
the earth. As if that part of the earth,
where the ship is, was truly moved
towards
the east, with a velocity of 10,010
parts;
while the ship itself, with a fresh
gale,
and full sails, is carried towards
the west,
with a velocity expressed by 10 of
those
parts; but a sailor walks in the ship
towards
the east, with I part of the said velocity;
then the sailor will be moved truly
in immovable
space towards the east, with a velocity
of
10,001 parts, and relatively on the
earth
towards the west, with a velocity of
g of
those parts.
Absolute time, in astronomy, is distinguished
from relative, by the equation or correction
of the apparenime. For the natural
days are
truly unequal, though they are commonly
considered
as equal, and used for a measure of
time;
astronomers correct this inequality
that
they may measure the celestial motions
by
a more accurate time. It may be, that
there
is no such thing as an equable motion,
whereby
time may be accurately measured. All
motions
may be accelerated and retarded, but
the
flowing of absolute time is not liable
to
any change. The duration or perseverance
of the existence of things remains
the same,
whether the motions are swift or slow,
or
none at all: and therefore this duration
ought to be distinguished from what
are only
sensible measures thereof; and from
which
we deduce it, by means of the astronomical
equation. The necessity of this equation,
for determining the times of a phenomenon,
is evinced as well from the experiments
of
the pendulum clock, as by eclipses
of the
satellites of Jupiter.
As the order of the parts of time is
immutable,
so also is the order of the parts of
space.
Suppose those parts to be moved out
of their
places, and they will be moved (if
the expression
may be allowed) out of themselves.
For times
and spaces are, as it were, the places
as
well of themselves as of all other
things.
All things are placed in time as to
order
of succession; and in space as to order
of
situation. It is from their essence
or nature
that they are places; and that the
primary
places of things should be movable,
is absurd.
These are therefore the absolute places;
and translations out of those places,
are
the only absolute motions.
But because the parts of space cannot
be
seen, or distinguished from one another
by
our senses, therefore in their stead
we use
sensible measures of them. For from
the positions
and distances of things from any body
considered
as immovable, we define all places;
and then
with respect to such places, we estimate
all motions, considering bodies as
transferred
from some of those places into others.
And
so, instead of absolute places and
motions,
we use relative ones; and that without
any
inconvenience in common affairs; but
in philosophical
disquisitions, we ought to abstract
from
our senses, and consider things themselves,
distinct from what are only sensible
measures
of them. For it may be that there is
no body
really at rest, to which the places
and motions
of others may be referred.
But we may distinguish rest and motion,
absolute
and relative, one from the other by
their
properties, causes, and effects. It
is a
property of rest, that bodies really
at rest
do rest in respect to one another.
And therefore
as it is possible, that in the remote
regions
of the fixed stars, or perhaps far
beyond
them, there may be some body absolutely
at
rest; but impossible to know, from
the position
of bodies to one another in our regions,
whether any of these do keep the same
position
to that remote body, it follows that
absolute
rest cannot be determined from the
position
of bodies in our regions.
It is a property of motion, that the
parts,
which retain given positions to their
wholes,
do partake of the motions of those
wholes.
For all the parts of revolving bodies
endeavour
to recede from the axis of motion;
and the
impetus of bodies moving forwards arises
from the joint impetus of all the parts.
Therefore, if surrounding bodies are
moved,
those that are relatively at rest within
them will partake of their motion.
Upon which
account, the true and absolute motion
of
a body cannot be determined by the
translation
of it from those which only seem to
rest;
for the external bodies ought not only
to
appear at rest, but to be really at
rest.
For otherwise, all included bodies,
besides
their translation from near the surrounding
ones, partake likewise of their true
motions;
and though tharanslation were not made,
they
would not be really at rest, but only
seem
to be so. For the surrounding bodies
stand
in the like relation to the surrounded
as
the exterior part of a whole does to
the
interior, or as the shell does to the
kernel;
but if the shell moves, the kernel
will also
move, as being part of the whole, without
any removal from near the shell.
A property, near akin to the preceding,
is
this, that if a place is moved, whatever
is placed therein moves along with
it; and
therefore a body, which is moved from
a place
in motion, partakes also of the motion
of
its place. Upon which account, all
motions,
from places in motion, are no other
than
parts of entire and absolute motions;
and
every entire motion is composed of
the motion
of the body out of its first place,
and the
motion of this place out of its place;
and
so on, until we come to some immovable
place,
as in the before-mentioned example
of the
sailor. Wherefore, entire and absolute
motions
can be no otherwise determined than
by immovable
places; and for that reason I did before
refer those absolute motions to immovable
places, but relative ones to movable
places.
Now no other places are immovable but
those
that, from infinity to infinity, do
all retain
the same given position one to another;
and
upon this account must ever remain
unmoved;
and do thereby constitute immovable
space.
The causes by which true and relative
motions
are distinguished, one from the other,
are
the forces impressed upon bodies to
generate
motion. True motion is neither generated
nor altered, but by some force impressed
upon the body moved; but relative motion
may be generated or altered without
any force
impressed upon the body. For it is
sufficient
only to impress some force on other
bodies
with which the former is compared,
that by
their giving way, that relation may
be changed,
in which the relative rest or motion
of this
other body did consist. Again, true
motion
suffers always some change from any
force
impressed upon the moving body; but
relative
motion does not necessarily undergo
any change
by such forces. For if the same forces
are
likewise impressed on those other bodies,
with which the comparison is made,
that the
relative position may be preserved,
then
that condition will be preserved in
which
the relative motion consists. And therefore
any relative motion may be changed
when the
true motion remains unaltered, and
the relative
may be preserved when the true suffers
some
change. Thus, true motion by no means
consists
in such relations.
The effects which distinguish absolute
from
relative motion are, the forces of
receding
from the axis of circular motion. For
there
are no such forces in a circular motion
purely
relative, but in a true and absolute
circular
motion, they are greater or less, according
to the quantity of the motion. If a
vessel,
hung by a long cord, is so often turned
abouhahe
cord is strongly twisted, then filled
with
water, and held at resogether with
the water;
thereupon, by the sudden action of
another
force, it is whirled about the contrary
way,
and while the cord is untwisting itself,
the vessel continues for some time
in this
motion; the surface of the water will
at
first be plain, as before the vessel
began
to move; but after that, the vessel,
by gradually
communicating its motion to the water,
will
make it begin sensibly to revolve,
and recede
by little and little from the middle,
and
ascend to the sides of the vessel,
forming
itself into a concave figure (as I
have experienced),
and the swifter the motion becomes,
the higher
will the water rise, till at last,
performing
its revolutions in the same times with
the
vessel, it becomes relatively at rest
in
it. This ascent of the water shows
its endeavour
to recede from the axis of its motion;
and
the true and absolute circular motion
of
the water, which is here directly contrary
to the relative, becomes known, and
may be
measured by this endeavour. At first,
when
the relative motion of the water in
the vessel
was greatest, it produced no endeavour
to
recede from the axis; the water showed
no
tendency to the circumference, nor
any ascenowards
the sides of the vessel, but remained
of
a plain surface, and therefore its
true circular
motion had not yet begun. But afterwards,
when the relative motion of the water
had
decreased, the ascenhereof towards
the sides
of the vessel proved its endeavour
to recede
from the axis; and this endeavour showed
the real circular motion of the water
continually
increasing, till it had acquired its
greatest
quantity, when the water rested relatively
in the vessel. And therefore this endeavour
does not depend upon any translation
of the
water in respect of the ambient bodies,
nor
can true circular motion be defined
by such
translation. There is only one real
circular
motion of any one revolving body, corresponding
to only one power of endeavouring to
recede
from its axis of motion, as its proper
and
adequate effect; but relative motions,
in
one and the same body, are innumerable,
according
to the various relations it bears to
external
bodies, and, like other relations,
are altogether
destitute of any real effect, any otherwise
than they may perhaps partake of that
one
only true motion. And therefore in
their
system who suppose that our heavens,
revolving
below the sphere of the fixed stars,
carry
the planets along with them; the several
parts of those heavens, and the planets,
which are indeed relatively at rest
in their
heavens, do yet really move. For they
change
their position one to another (which
never
happens to bodies truly at rest), and
being
carried together with their heavens,
partake
of their motions, and as parts of revolving
wholes, endeavour to recede from the
axis
of their motions.
Wherefore relative quantities are not
the
quantities themselves, whose names
they bear,
but those sensible measures of them
(either
accurate or inaccurate), which are
commonly
used instead of the measured quantities
themselves.
And if the meaning of words is to be
determined
by their use, then by the names time,
space,
place, and motion, their [sensible]
measures
are properly to be understood; and
the expression
will be unusual, and purely mathematical,
if the measured quantities themselves
are
meant. On this account, those violate
the
accuracy of language, which ought to
be kept
precise, who interprehese words for
the measured
quantities. Nor do those less defile
the
purity of mathematical and philosophical
truths, who confound real quantities
with
their relations and sensible measures.
It is indeed a matter of great difficulty
to discover, and effectually to distinguish,
the true motions of particular bodies
from
the apparent; because the parts of
that immovable
space, in which those motions are performed,
do by no means come under the observation
of our senses. yet the thing is not
altogether
desperate; for we have some arguments
to
guide us, partly from the apparent
motions,
which are the differences of the true
motions;
partly from the forces, which are the
causes
and effects of the true motions. For
instance,
if two globes, kept at a given distance
one
from the other by means of a cord that
connects
them, were revolved about their common
centre
of gravity, we might, from the tension
of
the cord, discover the endeavour of
the globes
to recede from the axis of their motion,
and from thence we might compute the
quantity
of their circular motions. And then
if any
equal forces should be impressed at
once
on the alternate faces of the globes
to augment
or diminish their circular motions,
from
the increase or decrease of the tension
of
the cord, we might infer the increment
or
decrement of their motions; and thence
would
be found on what faces those forces
ought
to be impressed, that the motions of
the
globes might be most augmented; that
is,
we might discover their hindmost faces,
or
those which, in the circular motion,
do follow.
But the faces which follow being known,
and
consequently the opposite ones that
precede,
we should likewise know the determination
of their motions. And thus we might
find
both the quantity and the determination
of
this circular motion, even in an immense
vacuum, where there was nothing external
or sensible with which the globes could
be
compared. But now, if in that space
some
remote bodies were placed that kept
always
a given position one to another, as
the fixed
stars do in our regions, we could not
indeed
determine from the relative translation
of
the globes among those bodies, whether
the
motion -did belong to the globes or
to the
bodies. But if we observed the cord,
and
found that its tension was that very
tension
which the motions of the globes required,
we might conclude the motion to be
in the
globes, and the bodies to be at rest;
and
then, lastly, from the translation
of the
globes among the bodies, we should
find the
determination of their motions. But
how we
are to obtain the true motions from
their
causes, effects, and apparent differences,
and the converse, shall be explained
more
at large in the following treatise.
For to
this end it was that I composed it.
--------------------------------------------------------------------------------
AXIOMS, OR LAWS OF MOTION
LAW I
Every body continues in its state of
rest,
or of uniform motion in a right line,
unless
it is compelled to change that state
by forces
impressed upon it.
PROJECTILES continue in their motions,
so
far as they are not retarded by the
resistance
of the air, or impelled downwards by
the
force of gravity. A top, whose parts
by their
cohesion are continually drawn aside
from
rectilinear motions, does not cease
its rotation,
otherwise than as it is retarded by
the air.
The greater bodies of the planets and
comets,
meeting with less resistance in freer
spaces,
preserve their motions both progressive
and
circular for a much longer time.
LAW II
The change of motion is proportional
to the
motive force impressed; and is made
in the
direction of the right line in which
that
force is impressed.
If any force generates n motion, a
double
force will generate double the motion,
a
triple force triple the motion, whether
that
force be impressed altogether and at
once,
or gradually and successively. And
this-
motion (being always directed the same
way
with the generating force), if the
body moved
before, is added to or subtracted from
the
former motion, according as they directly
conspire with or are directly contrary
to
each other; or obliquely joined, when
they
are oblique, so as to produce a new
motion
compounded from the determination of
both.
LAW III
To every action there is always opposed
an
equal reaction: or, the mutual actions
of
two bodies upon each other are always
equal,
and directed to contrary parts.
Whatever draws or presses another is
as much
drawn or pressed by that other. If
you press
a stone with your finger, the finger
is also
pressed by the stone. If a horse draws
a
stone tied to a rope, the horse (if
I may
say so) will be equally drawn back
towards
the stone; fro the distended rope,
by the
saame endeavour to relax or unbend
itself,
will draw the horse as muchas it does
the
stone towards the horse, and will obstruche
progress of the one as much as it advances
that of the other. For, because the
motions
are equally changed, the changes of
the velocities
made towards contrary parts are inversely
proportional to the bodies. This law
takes
place also in attractions, as will
be proved
in the next Scholium. ...
Book One, The Motion of Bodies ...
Book Two: The Motion of Bodies in Resisting
Mediums ...
--------------------------------------------------------------------------------
Book Three
SYSTEM OF THE WORLD
(IN MATHEMATICAL TREATMENT)
IN THE PRECEDING BOOKS I have laid
down the
principles of philosophy; principles
not
philosophical but mathematical: such,
namely,
as we may 1 build our reasonings upon
in
philosophical inquiries. These principles
are the laws and conditions of certain
motions,
and powers or forces, which chiefly
have
respect to philosophy; but, lest they
should
have appeared of themselves dry and
barren,
I have illustrated them here and there
with
some philosophical scholiums, giving
an account
of such things as are of more general
nature,
and which philosophy seems chiefly
to be
founded on; such as the density and
the resistance
of bodies, spaces void of all bodies,
and
the motion of light and sounds. It
remains
that, from the same principles, I now
demonstrate
the frame of the System of the World.
Upon
this subject I had, indeed, composed
the
third Book in a popular method, that
it might
be read by many; but afterwards, considering
that such as had not sufficiently entered
into the principles could not easily
discern
the strength of the consequences, nor
lay
aside the prejudices to which they
had been
many years accustomed, therefore, to
prevent
the disputes which might be raised
upon such
accounts, I chose to reduce the substance
of this Book into the form of Propositions
(in the mathematical way), which should
be
read by those only who had first made
themselves
masters of the principles established
in
0 the preceding Books: not that I would
advise
anyone to the previous study of every
Proposition
of those Books; for they abound with
such
as might cosoo much time, even to readers
of good mathematical learning. It is
. enough
if one carefully reads the Definitions,
the
Laws of Motion, and the first three
sections
of the first Book. He may then pass
on to
this Book, and consult such of the
remaining
Propositions of the first two Books,
as the
references in this, and his occasions,
shall
require.
--------------------------------------------------------------------------------
RULES OF REASONING IN PHILOSOPHY
RULE I
We are to admit no more causes of natural
things than such as are both true and
sufficient
to explain their appearances.
To this purpose the philosophers say
that
Nature does nothing in vain, and more
is
in vain when less will serve; for Nature
is pleased with simplicity, and affects
not
the pomp of superfluous causes.
RULE II
Therefore to the same natural effects
we
must, as far as possible, assign the
same
causes.
As to respiration in a man and in a
beast;
the descent of stones in Europe and
in America;
the light of our culinary fire and
of the
sun; the reflection of light in the
earth,
and in the planets.
RULE III
The qualities of bodies, which admit
neither
intensification nor remission of degrees,
and which are found to belong to all
bodies
within the reach of our experiments,
are
to be esteemed the universal qualities
of
all bodies whatsoever.
For since the qualities of bodies are
only
known to us by experiments, we are
to hold
for universal all such as universally
agree
with experiments; and such as are not
liable
to diminution can never be quite taken
away.
We are certainly not to relinquish
the evidence
of experiments for the sake of dreams
and
vain fictions of our own devising;
nor are
we to recede from the analogy of Nature,
which is wono be simple, and always
consonano
itself. We no other way know the extension
of bodies than by our senses, nor do
these
reach it in all bodies; but because
we perceive
extension in all tht are sensible,
therefore
we ascribe it universally to all others
also.
That abundance of bodies are hard,
we learn
by experience; and because the hardness
of
the whole arises from the hardness
of the
parts, we therefore justly infer the
hardness
of the undivided particles not only
of the
bodies we feel but of all others. That
all
bodies are impenetrable, we gather
not from
reason, but from sensation. The bodies
which
we handle we find impenetrable, and
thence
conclude impenetrability to be an universal
property of all bodies whatsoever.
That all
bodies are movable, and endowed with
certain
powers
(which we call the inertia) of persevering
in their motion, or in their rest,
we only
infer from the like properties observed
in
the bodies which we have seen. The
extension,
hardness, impenetrability, mobility,
and
inertia of the whole, result from the
extension,
hardness, impenetrability, mobility,
and
inertia of the parts; and hence we
conclude
the least particles of all bodies to
be also
all extended, and hard and impenetrable,
and movable, and endowed with their
proper
inertia. And this is the foundation
of all
philosophy. Moreover, that the divided
but
contiguous particles of bodies may
be separated
from one another, is matter of observation;
and, in the particles that remain undivided,
our minds are able to distinguish yet
lesser
parts, as is mathematically demonstrated.
But whether the parts so distinguished,
and
not yet divided, may, by the powers
of Nature,
be actually divided and separated from
one
another, we cannot certainly determine.
Yet,
had we the proof of but one experiment
that
any undivided particle, in breaking
a hard
and solid body, suffered a division,
we might
by virtue of this rule conclude that
the
undivided as well as the divided particles
may be divided and actually separated
to
infinity.
Lastly, if it universally appears,
by experiments
and astronomical observations, that
all bodies
about the earth gravitate towards the
earth,
and that in proportion to the quantity
of
matter which they severally contain;
that
the moon likewise, according to the
quantity
of its matter, gravitates towards the
earth;
that, on the other hand, our sea gravitates
towards the moon; and, all the planets
one
towards another; and the comets in
like manner
towards- the sun; we must, in consequence
of this rule, universally allow that
all
bodies whatsoever are endowed with
a principle
of mutual gravitation.
For the argument from the appearances
concludes
with more force for the universal gravitation
of all bodies than for their impenetrability;
of which, among those in the celestial
regions,
we have no experiments, nor any manner
of
observation. Not that I affirm gravity
to
be essential to bodies: by their vis
insita
I mean nothing but their inertia. This
is
immutable. Their gravity is diminished
as
they recede from the earth.
RULE IV
In experimental philosophy we are to
look,
upon propositions inferred by general
induction
from phenomena as accurately or very
nearly
true, notwithstanding any contrary
hypotheses
that may be imagined, till such time
as other
phenomena occur, by which they may
cither
be made more accurate, or liable to
exceptions.
This rule we must follow, that the
argument
of induction may not be evaded by hypotheses.
--------------------------------------------------------------------------------
Phenomena
Propositions and Theorems ...
--------------------------------------------------------------------------------
GENERAL SCHOLIUM
The hypothesis of vortices is pressed
with
many difficulties. That every planet
by a
radius drawn to the sun may describe
areas
proportional to the times of description,
the periodic times of the several parts
of
the vortices should observe the square
of
their distances from the sun; but that
the
periodic times of the planets may obtain
the 3/2th power of their distances
from the
sun, the periodic times of the parts
of the
vortex ought to be as the 3/2th power
of
their distances. that the smaller vortices
may maintain their lesser revolutions
about
Saturn, Jupiter, and other planets,
and swim
quietly and undisturbed in the greater
vortex
of the sun, the periodic times of the
parts
of the sun's vortex should be equal;
but
the rotation of the sun and planets
about
their axes, which ought to correspond
with
the motions of their vortices, recede
far
from all these proportions. The motions
of
the comets are exceedingly regular,
are governed
by the same laws with the motions of
the
planets, and can by no means be accounted
for by the hypothesis of vortices;
for comets
are carried with very eccentric motions
through
all parts of the heavens indifferently,
with
a freedom that is incompatible with
the notion
of a vortex.
Bodies projected in our air suffer
no resistance
but from the air. Withdraw the air,
as is
done in Mr. Boyle's vacuum, and the
resistance
ceases; for in this void a bit of fine
down
and a piece of solid gold descend with
equal
velocity. And the same argument must
apply
to the celestial spaces above the earth's
atmosphere; in these spaces, where
there
is no air to resist their motions,
all bodies
will move with the greatest freedom;
and
the planets and comets will constantly
pursue
their revolutions in orbits given in
kind
and position, according to the laws
above
explained; but though these bodies
may, indeed,
continue in their orbits by the mere
laws
of gravity, yet they could by no means
have
at first derived the regular position
of
the orbits themselves from those laws.
The six primary planets are revolved
about
the sun in circles concentric with
the sun,
and with motions directed towards the
same
parts, and almost in the same plane.
Ten
moons are revolved about the earth,
Jupiter,
and Saturn, in circles concentric with
them,
with the same direction of motion,
and nearly
in the planes of the orbits of those
planets;
but it is not to be conceived that
mere mechanical
causes could give birth to so many
regular
motions, since the comets range over
all
parts of the heavens in very eccentric
orbits;
for by that kind of motion they pass
easily
through the orbs of the planets, and
with
great rapidity; and in their aphelions,
where
they move the slowest, and are detained
the
longest, they recede to the greatest
distances
from each other, and hence suffer the
least
disturbance from their mutual attractions.
This most beautiful system of the sun,
planets,
and comets, could only proceed from
the counsel
and dominion of an intelligent and
powerful
Being. And if the fixed stars are the
centres
of other like systems, these, being
formed
by the like wise counsel, must be all
subject
to the dominion of One; especially
since
the light of the fixed stars is of
the same
nature with the light of the sun, and
from
every system light passes into all
the other
systems: and lest the systems of the
fixed
stars should, by their gravity, fall
on each
other, he hath placed those systems
at immense
distances from one another.
This Being governs all things, not
as the
soul of the world, but as Lord over
all;
and on account of his dominion he is
wono
be called Lord God pantokrator, or
Universal
Ruler; for God is a relative word,
and has
a respect to servants; and Deity is
the dominion
of God not over his own body, as those
imagine
who fancy God to be the soul of the
world,
but over servants. The Supreme God
is a Being
eternal, infinite, absolutely perfect;
but
a being, however perfect, without dominion,
cannot be said to be Lord God; for
we say,
my God, your God, the God of Israel,
the
God of Gods, and Lord of Lords; but
we do
not say, my Eternal, your Eternal,
the Eternal
of Israel, the Eternal of Gods; we
do not
say, my Infinite, or my Perfect: these
are
titles which have no respect to servants.
The word God' usually signifies Lord;
but
every lord is not a God. It is the
dominion
of a spiritual being which constitutes
a
God: a true, supreme, or imaginary
dominion
makes a true, supreme, or imaginary
God.
And from his true dominion it follows
that
the true God is a living, intelligent,
and
powerful Being; and, from his other
perfections,
that he is supreme, or most perfect.
He is
eternal and infinite, omnipotent and
omniscient;
that is, his duration reaches from
eternity
to eternity; his presence from infinity
to
infinity; he governs all things, and
knows
all things that are or can be done.
He is
not eternity and infinity, but eternal
and
infinite; he is not duration or space,
but
he endures and is present. He endures
forever,
and is everywhere present- and, by
existing
always and everywhere, he constitutes
duration
and space. Since every particle of
space
is always, and every indivisible moment
of
duration is everywhere, certainly the
Maker
and Lord of all things cannot be never
and
nowhere. Every soul that has perception
is,
though in different times and in different
organs of sense and motion, still the
same
indivisible person. There are given
successive
parts in duration, coexistent parts
in space,
but neither the one nor the other in
the
person of a man, or his thinking principle;
and much less can they be found in
the thinking
substance of God. Every man, so far
as he
is a thing that has perception, is
one and
the same man during his whole life,
in all
and each of his organs of sense. God
is the
same God, always and everywhere. He
is omnipresent
not virtually only, but also substantially;
for virtue cannot subsist without substance.
In him are all things contained and
moved;
yet neither affects the other: God
suffers
nothing from the motion of bodies;
bodies
find no resistance from the omnipresence
of God. It is allowed by all that the
Supreme
God exists necessarily; and by the
same necessity
he exists always and everywhere. Whence
also
he is all similar, all eye, all ear,
all
brain, all arm, all power to perceive,
to
understand, and to act; but in a manner
not
at all human, in a manner not at all
corporeal,
in a manner utterly unknown to us.
As a blind
man has no idea of colours, so have
we no
idea of the manner by which the all-wise
God perceives and understands all things.
He is utterly void of all body and
bodily
figure, and can therefore neither be
seen,
nor heard, nor touched; nor ought he
to be
worshiped under the representation
of any
corporeal thing. We have ideas of his
attributes,
but what the real substance of anything
is
we know not. In bodies, we see only
their
figures and colours, we hear only the
sounds,
we touch only their outward surfaces,
we
smell only the smells, and taste the
savours;
but their inward substances are not
to be
known either by our senses, or by any
reflex
act of our minds: much less, then,
have we
any idea of the substance of God. We
know
him only by his most wise and excellent
contrivances
of things, and final causes; we admire
him
for his perfections; but we reverence
and
adore him on account of his dominion:
for
we adore him as his servants; and a
god without
dominion, providence, and final causes,
is
nothing else but Fate and Nature. Blind
physical
necessity, which is certainly the same
always
and everywhere, could produce no variety
of things. All that diversity of natural
things which we find suited to different
times and places could arise from nothing
but the ideas and will of a Being necessarily
existing. But, by way of allegory,
God is
said to see, to speak, to laugh, to
love,
to hate, to desire, to give, to receive,
to rejoice, to be angry, to fight,
to frame,
to work, to build; for all our notions
of
God are taken from the ways of mankind
by
a certain similitude, which, though
not perfect,
has some likeness, however. And thus
much
concerning God; to discourse of whom
from
the appearances of things, does certainly
belong to Natural Philosophy.
Hitherto we have explained the phenomena
of the heavens and of our sea by the
power
of gravity, but have not yet assigned
the
cause of this power. This is certain,
that
it must proceed from a cause that penetrates
to the very centres of the sun and
planets,
without suffering the least diminution
of
its force; that operates not according
to
the quantity of the surfaces of the
particles
upon which it acts (as mechanical causes
used to do), but according to the quantity
of the solid matter which they contain,
and
propagates its virtue on all sides
to immense
distances, decreasing always as the
inverse
square of the distances. Gravitation
towards
the sun is made up out of the gravitations
towards the several particles of which
the
body of the sun is composed; and in
receding
from the sun decreases accurately as
the
inverse square of the distances as
far as
the orbit of Saturn, as evidently appears
from the quiescence of the aphelion
of the
planets; nay, and even to the remotest
aphelion
of the comets, if those aphelions are
also
quiescent.
But hitherto I have not been able to
discover
the cause of those properties of gravity
from phenomena, and I frame no hypotheses;
for whatever is not deduced from the
phenomena
is to be called an hypothesis; and
hypotheses,
whether physical or physical, whether
of
occult qualities or mechanical, have
no place
in experimental philosophy. In this
philosophy
particular propositions are inferred
from
the phenomena, and afterwards rendered
general
by induction. Thus it was that the
impenetrability,
the mobility, and the impulsive force
of
bodies, and the laws of motion and
of gravitation,
were discovered. And to us it is enough
that
gravity does really exist, and act
according
to the laws which we have explained,
and
abundantly serves to account for all
the
motions of the celestial bodies, and
of our
sea.
And now we might add something concerning
a certain most subtle spirit which
pervades
and lies hid in all gross bodies; by
the
force and action of which spirit the
particles
of bodies attract one another at near
distances,
and cohere, if contiguous; and electric
bodies
operate to greater distances, as well
repelling
as attracting the neighbouring corpuscles;
and light is emitted, reflected, refracted,
inflected, and heats bodies; and all
sensation
is excited, and the members of animal
bodies
move at the command of the will, namely,
by the vibrations of this spirit, mutually
propagated along the solid filaments
of the
nerves, from the outward organs of
sense
to the brain, and from the brain into
the
muscles. But these are things that
cannot
be explained in few words, nor are
we furnished
with that sufficiency of experiments
which
is required to an accurate determination
and demonstration of the laws by which
this
electric and elastic spirit operates.
END OF THE PRINCIPIA
The Mathematical Principles of Natural
Philosophy
(1729) Newton's Principles of Natural
Philosophy,
Dawsons of Pall Mall, 1968; Opening
pages
of the Principia up to the three laws
of
motion; opening pages of Book III,
The System
of the World, with rules for Philosophy,
plus the closing comments with his
view of
God, etc.
|
Evans Experientialism 
