Newton's Principia: Definitions: I - IV
From: Isaac Newton (eric_baird_at_compuserve.com)
Date: 11/14/04
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Date: Sun, 14 Nov 2004 03:43:49 +0000 (UTC)
This is the first chapter of Newton's Principia, split into two posts:
(hopefully with no OCR nasties)
[quote starts]
:: D E F I N I T I O N S
: 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, endeavors 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, endeavors 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 arc 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, endeavors to recede from the hand that turns it; and by that
endeavor, distends the sling, and that with so much the greater force,
as it is revolved with the greater velocity, and as soon as it is let
go, flies away. That force which opposes itself to this endeavor, 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
endeavor 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 deviate 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, would 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 it towards 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 orbit towards 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 he 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 accelerative 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 that
tend 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 endeavor 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 he
propagated through the spaces round about; whether that cause he 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 surface 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 sort towards 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.
[ quote ends ]
( Principia, pp 1 - 6 )
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