Title:   ON THE MOTION OF ANIMALS

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Author:   by Aristotle

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ON THE MOTION OF ANIMALS

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ON THE MOTION OF ANIMALS

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ON THE MOTION OF ANIMALS

by Aristotle

translated by A. S. L. Farquharson

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ELSEWHERE we have investigated in detail the movement of animals  after their various kinds, the

differences between them, and the  reasons for their particular characters (for some animals fly, some  swim,

some walk, others move in various other ways); there remains  an  investigation of the common ground of any

sort of animal movement  whatsoever. 

Now we have already determined (when we were discussing whether  eternal motion exists or not, and its

definition, if it does exist)  that the origin of all other motions is that which moves itself, and  that the origin of

this is the immovable, and that the prime mover  must of necessity be immovable. And we must grasp this not

only  generally in theory, but also by reference to individuals in the world  of sense, for with these in view we

seek general theories, and with  these we believe that general theories ought to harmonize. Now in  the  world

of sense too it is plainly impossible for movement to be  initiated if there is nothing at rest, and before all else

in our  present subject animal life. For if one of the parts of an animal  be  moved, another must be at rest, and

this is the purpose of their  joints; animals use joints like a centre, and the whole member, in  which the joint

is, becomes both one and two, both straight and  bent,  changing potentially and actually by reason of the joint.

And  when it  is bending and being moved one of the points in the joint is  moved and  one is at rest, just as if

the points A and D of a  diameter were at  rest, and B were moved, and DAC were generated.  However, in the

geometrical illustration, the centre is held to be  altogether  indivisible (for in mathematics motion is a fiction,

as the  phrase  goes, no mathematical entity being really moved), whereas in  the case  of joints the centres

become now one potentially and  divided actually,  and now one actually and divided potentially. But  still the

origin of  movement, qua origin, always remains at rest  when the lower part of a  limb is moved; for example,

the elbow  joint, when the forearm is  moved, and the shoulder, when the whole  arm; the knee when the tibia  is

moved, and the hip when the whole leg.  Accordingly it is plain that  each animal as a whole must have within

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itself a point at rest, whence  will be the origin of that which is  moved, and supporting itself upon  which it

will be moved both as a  complete whole and in its members. 

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But the point of rest in the animal is still quite ineffectual  unless there be something without which is

absolutely at rest and  immovable. Now it is worth while to pause and consider what has been  said, for it

involves a speculation which extends beyond animals  even  to the motion and march of the universe. For just

as there must  be  something immovable within the animal, if it is to be moved, so  even  more must there be

without it something immovable, by  supporting  itself upon which that which is moved moves. For were  that

something  always to give way (as it does for mice walking in  grain or persons  walking in sand) advance

would be impossible, and  neither would there  be any walking unless the ground were to remain  still, nor any

flying  or swimming were not the air and the sea to  resist. And this which  resists must needs be different from

what is  moved, the whole of it  from the whole of that, and what is thus  immovable must be no part of  what is

moved; otherwise there will be no  movement. Evidence of this  lies in the problem why it is that a man  easily

moves a boat from  outside, if he push with a pole, putting it  against the mast or some  other part, but if he

tried to do this when  in the boat itself he  would never move it, no not giant Tityus himself  nor Boreas

blowing  from inside the ship, if he really were blowing  in the way painters  represent him; for they paint him

sending the  breath out from the  boat. For whether one blew gently or so stoutly as  to make a very  great wind,

and whether what were thrown or pushed were  wind or  something else, it is necessary in the first place to be

supported  upon one of one's own members which is at rest and so to  push, and in  the second place for this

member, either itself, or  that of which it  is a part, to remain at rest, fixing itself against  something external  to

itself. Now the man who is himself in the  boat, if he pushes,  fixing himself against the boat, very naturally

does not move the  boat, because what he pushes against should properly  remain at rest.  Now what he is trying

to move, and what he is fixing  himself against  is in his case the same. If, however, he pushes or  pulls from

outside  he does move it, for the ground is no part of the  boat. 

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Here we may ask the difficult question whether if something moves  the whole heavens this mover must be

immovable, and moreover be no  part of the heavens, nor in the heavens. For either it is moved itself  and

moves the heavens, in which case it must touch something immovable  in order to create movement, and then

this is no part of that which  creates movement; or if the mover is from the first immovable it  will  equally be

no part of that which is moved. In this point at least  they  argue correctly who say that as the Sphere is carried

round in  a  circle no single part remains still, for then either the whole would  necessarily stand still or its

continuity be torn asunder; but they  argue less well in supposing that the poles have a certain force,  though

conceived as having no magnitude, but as merely termini or  points. For besides the fact that no such things

have any  substantial  existence it is impossible for a single movement to be  initiated by  what is twofold; and

yet they make the poles two. From  a review of  these difficulties we may conclude that there is something  so

related  to the whole of Nature, as the earth is to animals and  things moved by  them. 

And the mythologists with their fable of Atlas setting his feet  upon  the earth appear to have based the fable

upon intelligent  grounds.  They make Atlas a kind of diameter twirling the heavens about  the  poles. Now as

the earth remains still this would be reasonable  enough,  but their theory involves them in the position that the

earth  is no  part of the universe. And further the force of that which  initiates  movement must be made equal to

the force of that which  remains at  rest. For there is a definite quantity of force or power by  dint of  which that

which remains at rest does so, just as there is of  force by  dint of which that which initiates movement does so;

and as  there is a  necessary proportion between opposite motions, so there is  between  absences of motion.

Now equal forces are unaffected by one  another,  but are overcome by a superiority of force. And so in their

theory  Atlas, or whatever similar power initiates movement from  within,  must exert no more force than will


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exactly balance the  stability of  the earth otherwise the earth will be moved out of her  place in the  centre of

things. For as the pusher pushes so is the  pushed pushed,  and with equal force. But the prime mover moves

that  which is to begin  with at rest, so that the power it exerts is  greater, rather than  equal and like to the power

which produces  absence of motion in that  which is moved. And similarly also the power  of what is moved

and so  moves must be greater than the power of that  which is moved but does  not initiate movement.

Therefore the force of  the earth in its  immobility will have to be as great as the force of  the whole heavens,

and of that which moves the heavens. But if that is  impossible, it  follows that the heavens cannot possibly be

moved by  any force of this  kind inside them. 

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There is a further difficulty about the motions of the parts of  the heavens which, as akin to what has gone

before, may be  considered  next. For if one could overcome by force of motion the  immobility of  the earth he

would clearly move it away from the centre.  And it is  plain that the power from which this force would

originate  will not be  infinite, for the earth is not infinite and therefore  its weight is  not. Now there are more

senses than one of the word  'impossible'. When  we say it is impossible to see a sound, and when we  say it is

impossible to see the men in the moon, we use two senses  of the word;  the former is of necessity, the latter,

though their  nature is to be  seen, cannot as a fact be seen by us. Now we suppose  that the heavens  are of

necessity impossible to destroy and to  dissolve, whereas the  result of the present argument would be to do

away with this  necessity. For it is natural and possible for a  motion to exist  greater than the force by dint of

which the earth is  at rest, or than  that by dint of which Fire and Aether are moved. If  then there are  superior

motions, these will be dissolved in succession  by one  another: and if there actually are not, but might possibly

be  (for the  earth cannot be infinite because no body can possibly be  infinite),  there is a possibility of the

heavens being dissolved.  For what is to  prevent this coming to pass, unless it be impossible?  And it is not

impossible unless the opposite is necessary. This  difficulty, however,  we will discuss elsewhere. 

To resume, must there be something immovable and at rest outside  of what is moved, and no part of it, or

not? And must this necessarily  be so also in the case of the universe? Perhaps it would be thought  strange

were the origin of movement inside. And to those who so  conceive it the word of Homer would appear to

have been well spoken: 

'Nay, ye would not pull Zeus, highest of all from heaven to the  plain, no not even if ye toiled right hard;

come, all ye gods and  goddesses! Set hands to the chain'; for that which is entirely  immovable cannot

possibly be moved by anything. And herein lies the  solution of the difficulty stated some time back, the

possibility or  impossibility of dissolving the system of the heavens, in that it  depends from an original which

is immovable. 

Now in the animal world there must be not only an immovable  without,  but also within those things which

move in place, and  initiate their  own movement. For one part of an animal must be moved,  and another  be at

rest, and against this the part which is moved will  support  itself and be moved; for example, if it move one of

its parts;  for one  part, as it were, supports itself against another part at  rest. 

But about things without life which are moved one might ask the  question whether all contain in themselves

both that which is at  rest  and that which initiates movement, and whether they also, for  instance  fire, earth, or

any other inanimate thing, must support  themselves  against something outside which is at rest. Or is this

impossible and  must it not be looked for rather in those primary  causes by which they  are set in motion? For

all things without life  are moved by something  other, and the origin of all things so moved  are things which

move  themselves. And out of these we have spoken  about animals (for they  must all have in themselves that

which is at  rest, and without them  that against which they are supported); but  whether there is some  higher

and prime mover is not clear, and an  origin of that kind  involves a different discussion. Animals at any  rate


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which move  themselves are all moved supporting themselves on what  is outside  them, even when they

inspire and expire; for there is no  essential  difference between casting a great and a small weight, and  this is

what men do when they spit and cough and when they breathe  in and  breathe out. 

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But is it only in that which moves itself in place that there must  be a point at rest, or does this hold also of

that which causes its  own qualitative changes, and its own growth? Now the question of  original generation

and decay is different; for if there is, as we  hold, a primary movement, this would be the cause of generation

and  decay, and probably of all the secondary movements too. And as in  the  universe, so in the animal world

this is the primary movement,  when  the creature attains maturity; and therefore it is the cause of  growth,

when the creature becomes the cause of its own growth, and the  cause too of alteration. But if this is not the

primary movement  then  the point at rest is not necessary. However, the earliest  growth and  alteration in the

living creature arise through another and  by other  channels, nor can anything possibly be the cause of its own

generation  and decay, for the mover must exist before the moved, the  begetter  before the begotten, and

nothing is prior to itself. 

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Now whether the soul is moved or not, and how it is moved if it be  moved, has been stated before in our

treatise concerning it. And since  all inorganic things are moved by some other thing and the manner  of  the

movement of the first and eternally moved, and how the first  mover  moves it, has been determined before in

our Metaphysics, it  remains to  inquire how the soul moves the body, and what is the origin  of  movement in a

living creature. For, if we except the movement of  the  universe, things with life are the causes of the

movement of all  else,  that is of all that are not moved by one another by mutual  impact. And  so all their

motions have a term or limit, inasmuch as the  movements  of things with life have such. For all living things

both  move and are  moved with some object, so that this is the term of all  their  movement, the end, that is, in

view. Now we see that the  living  creature is moved by intellect, imagination, purpose, wish, and  appetite.

And all these are reducible to mind and desire. For both  imagination and sensation are on common ground

with mind, since all  three are faculties of judgement though differing according to  distinctions stated

elsewhere. Will, however, impulse, and appetite,  are all three forms of desire, while purpose belongs both to

intellect  and to desire. Therefore the object of desire or of intellect first  initiates movement, not, that is, every

object of intellect, only  the  end in the domain of conduct. Accordingly among goods that which  moves  is a

practical end, not the good in its whole extent. For it  initiates  movement only so far as something else is for

its sake, or  so far as  it is the object of that which is for the sake of  something else. And  we must suppose that

a seeming good may take the  room of actual good,  and so may the pleasant, which is itself a  seeming good.

From these  considerations it is clear that in one regard  that which is eternally  moved by the eternal mover is

moved in the  same way as every living  creature, in another regard differently,  and so while it is moved

eternally, the movement of living creatures  has a term. Now the  eternal beautiful, and the truly and primarily

good (which is not at  one time good, at another time not good), is too  divine and precious  to be relative to

anything else. The prime mover  then moves, itself  being unmoved, whereas desire and its faculty are  moved

and so move.  But it is not necessary for the last in the chain  of things moved to  move something else;

wherefore it is plainly  reasonable that motion in  place should be the last of what happens  in the region of

things  happening, since the living creature is  moved and goes forward by  reason of desire or purpose, when

some  alteration has been set going  on the occasion of sensation or  imagination. 

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But how is it that thought (viz. sense, imagination, and thought  proper) is sometimes followed by action,

sometimes not; sometimes by  movement, sometimes not? What happens seems parallel to the case of


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thinking and inferring about the immovable objects of science. There  the end is the truth seen (for, when one

conceives the two  premisses,  one at once conceives and comprehends the conclusion),  but here the  two

premisses result in a conclusion which is an  action for example,  one conceives that every man ought to

walk, one  is a man oneself:  straightway one walks; or that, in this case, no man  should walk, one  is a man:

straightway one remains at rest. And one so  acts in the two  cases provided that there is nothing in the one

case  to compel or in  the other to prevent. Again, I ought to create a good,  a house is  good: straightway I make

a house. I need a covering, a coat  is a  covering: I need a coat. What I need I ought to make, I need a  coat: I

make a coat. And the conclusion I must make a coat is an  action. And  the action goes back to the beginning

or first step. If  there is to be  a coat, one must first have B, and if B then A, so  one gets A to begin  with. Now

that the action is the conclusion is  clear. But the  premisses of action are of two kinds, of the good and  of the

possible. 

And as in some cases of speculative inquiry we suppress one  premise so here the mind does not stop to

consider at all an obvious  minor premise; for example if walking is good for man, one does not  dwell upon

the minor 'I am a man'. And so what we do without  reflection, we do quickly. For when a man actualizes

himself in  relation to his object either by perceiving, or imagining or  conceiving it, what he desires he does at

once. For the actualizing of  desire is a substitute for inquiry or reflection. I want to drink,  says appetite; this is

drink, says sense or imagination or mind:  straightway I drink. In this way living creatures are impelled to

move  and to act, and desire is the last or immediate cause of movement, and  desire arises after perception or

after imagination and conception.  And things that desire to act now create and now act under the  influence of

appetite or impulse or of desire or wish. 

The movements of animals may be compared with those of automatic  puppets, which are set going on the

occasion of a tiny movement; the  levers are released, and strike the twisted strings against one  another; or

with the toy wagon. For the child mounts on it and moves  it straight forward, and then again it is moved in a

circle owing to  its wheels being of unequal diameter (the smaller acts like a centre  on the same principle as

the cylinders). Animals have parts of a  similar kind, their organs, the sinewy tendons to wit and the bones;  the

bones are like the wooden levers in the automaton, and the iron;  the tendons are like the strings, for when

these are tightened or  leased movement begins. However, in the automata and the toy wagon  there is no

change of quality, though if the inner wheels became  smaller and greater by turns there would be the same

circular movement  set up. In an animal the same part has the power of becoming now  larger and now smaller,

and changing its form, as the parts increase  by warmth and again contract by cold and change their quality.

This  change of quality is caused by imaginations and sensations and by  ideas. Sensations are obviously a

form of change of quality, and  imagination and conception have the same effect as the objects so  imagined

and conceived For in a measure the form conceived be it of  hot or cold or pleasant or fearful is like what the

actual objects  would be, and so we shudder and are frightened at a mere idea. Now all  these affections

involve changes of quality, and with those changes  some parts of the body enlarge, others grow smaller. And

it is not  hard to see that a small change occurring at the centre makes great  and numerous changes at the

circumference, just as by shifting the  rudder a hair's breadth you get a wide deviation at the prow. And

further, when by reason of heat or cold or some kindred affection a  change is set up in the region of the heart,

even in an  imperceptibly  small part of the heart, it produces a vast difference  in the  periphery of the body,

blushing, let us say, or turning white,  gooseskin and shivers and their opposites. 

8

But to return, the object we pursue or avoid in the field of  action is, as has been explained, the original of

movement, and upon  the conception and imagination of this there necessarily follows a  change in the

temperature of the body. For what is painful we avoid,  what is pleasing we pursue. We are, however,

unconscious of what  happens in the minute parts; still anything painful or pleasing is  generally speaking

accompanied by a definite change of temperature  in  the body. One may see this by considering the affections.


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Blind  courage and panic fears, erotic motions, and the rest of the corporeal  affections, pleasant and painful,

are all accompanied by a change of  temperature, some in a particular member, others in the body  generally.

So, memories and anticipations, using as it were the  reflected images of these pleasures and pains, are now

more and now  less causes of the same changes of temperature. And so we see the  reason of nature's

handiwork in the inward parts, and in the centres  of movement of the organic members; they change from

solid to moist,  and from moist to solid, from soft to hard and vice versa. And so when  these are affected in

this way, and when besides the passive and  active have the constitution we have many times described, as

often as  it comes to pass that one is active and the other passive, and neither  of them falls short of the

elements of its essence, straightway one  acts and the other responds. And on this account thinking that one

ought to go and going are virtually simultaneous, unless there be  something else to hinder action. The organic

parts are suitably  prepared by the affections, these again by desire, and desire by  imagination. Imagination in

its turn depends either upon conception or  senseperception. And the simultaneity and speed are due to the

natural correspondence of the active and passive. 

However, that which first moves the animal organism must be  situate in a definite original. Now we have said

that a joint is the  beginning of one part of a limb, the end of another. And so nature  employs it sometimes as

one, sometimes as two. When movement arises  from a joint, one of the extreme points must remain at rest,

and the  other be moved (for as we explained above the mover must support  itself against a point at rest);

accordingly, in the case of the  elbowjoint, the last point of the forearm is moved but does not  move

anything, while, in the flexion, one point of the elbow, which  lies in  the whole forearm that is being moved,

is moved, but there  must also  be a point which is unmoved, and this is our meaning when we  speak of  a point

which is in potency one, but which becomes two in  actual  exercise. Now if the arm were the living animal,

somewhere in  its  elbowjoint would be situate the original seat of the moving soul.  Since, however, it is

possible for a lifeless thing to be so related  to the hand as the forearm is to the upper (for example, when a

man  moves a stick in his hand), it is evident that the soul, the  original  of movement, could not lie in either of

the two extreme  points,  neither, that is, in the last point of the stick which is  moved, nor  in the original point

which causes movement. For the  stick too has an  end point and an originative point by reference to  the hand.

Accordingly, this example shows that the moving original  which derives  from the soul is not in the stick and

if not, then not  in the hand;  for a precisely similar relation obtains between the hand  and the  wrist, as between

the wrist and the elbow. In this matter it  makes no  difference whether the part is a continuous part of the  body

or not;  the stick may be looked at as a detached part of the  whole. It follows  then of necessity that the original

cannot lie in  any individual  origin which is the end of another member, even  though there may lie  another

part outside the one in question. For  example, relatively to  the end point of the stick the hand is the  original,

but the original  of the hand's movement is in the wrist. And  so if the true original is  not in the hand, bethere

is still  something higher up, neither is the  true original in the wrist, for  once more if the elbow is at rest the

whole part below it can be moved  as a continuous whole. 

9

Now since the left and the right sides are symmetrical, and these  opposites are moved simultaneously, it

cannot be that the left is  moved by the right remaining stationary, nor vice versa; the  original  must always be

in what lies above both. Therefore, the  original seat  of the moving soul must be in that which lies in the

middle, for of  both extremes the middle is the limiting point; and  this is similarly  related to the movements

from above [and below,]  those that is from  the head, and to the bones which spring from the  spinal column, in

creatures that have a spinal column. 

And this is a reasonable arrangement. For the sensorium is in our  opinion in the centre too; and so, if the

region of the original of  movement is altered in structure through senseperception and thus  changes, it

carries with it the parts that depend upon it and they too  are extended or contracted, and in this way the

movement of the  creature necessarily follows. And the middle of the body must needs be  in potency one but


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in action more than one; for the limbs are moved  simultaneously from the original seat of movement, and

when one is  at  rest the other is moved. For example, in the line BAC, B is  moved, and  A is the mover. There

must, however, be a point at rest  if one is to  move, the other to be moved. A (AE) then being one in  potency

must be  two in action, and so be a definite spatial  magnitude not a  mathematical point. Again, C may be

moved  simultaneously with B. Both  the originals then in A must move and  be, and so there must be

something other than them which moves but  is not moved. For otherwise,  when the movement begins, the

extremes,  i.e. the originals, in A would  rest upon one another, like two men  putting themselves back to back

and so moving their legs. There must  then be some one thing which  moves both. This something is the soul,

distinct from the spatial  magnitude just described and yet located  therein. 

10

Although from the point of view of the definition of movement a  definition which gives the cause desire is

the middle term or  cause,  and desire moves being moved, still in the material animated  body  there must be

some material which itself moves being moved. Now  that  which is moved, but whose nature is not to initiate

movement,  is  capable of being passive to an external force, while that which  initiates movement must needs

possess a kind of force and power. Now  experience shows us that animals do both possess connatural spirit

and  derive power from this. (How this connatural spirit is maintained in  the body is explained in other

passages of our works.) And this spirit  appears to stand to the soulcentre or original in a relation  analogous

to that between the point in a joint which moves being moved  and the unmoved. Now since this centre is for

some animals in the  heart, in the rest in a part analogous with the heart, we further  see  the reason for the

connatural spirit being situate where it  actually  is found. The question whether the spirit remains always  the

same or  constantly changes and is renewed, like the cognate  question about the  rest of the parts of the body,

is better postponed.  At all events we  see that it is well disposed to excite movement and  to exert power;  and

the functions of movement are thrusting and  pulling. Accordingly,  the organ of movement must be capable of

expanding and contracting;  and this is precisely the characteristic of  spirit. It contracts and  expands naturally,

and so is able to pull and  to thrust from one and  the same cause, exhibiting gravity compared  with the fiery

element,  and levity by comparison with the opposites of  fire. Now that which is  to initiate movement without

change of  structure must be of the kind  described, for the elementary bodies  prevail over one another in a

compound body by dint of  disproportion; the light is overcome and kept  down by the heavier, and  the heavy

kept up by the lighter. 

We have now explained what the part is which is moved when the  soul originates movement in the body, and

what is the reason for this.  And the animal organism must be conceived after the similitude of a

wellgoverned commonwealth. When order is once established in it there  is no more need of a separate

monarch to preside over each several  task. The individuals each play their assigned part as it is  ordered,  and

one thing follows another in its accustomed order. So  in animals  there is the same orderliness nature taking

the place of  custom and  each part naturally doing his own work as nature has  composed them.  There is no

need then of a soul in each part, but she  resides in a  kind of central governing place of the body, and the

remaining parts  live by continuity of natural structure, and play  the parts Nature  would have them play. 

11

So much then for the voluntary movements of animal bodies, and the  reasons for them. These bodies,

however, display in certain members  involuntary movements too, but most often nonvoluntary movements.

By  involuntary I mean motions of the heart and of the privy member;  for  often upon an image arising and

without express mandate of the  reason  these parts are moved. By nonvoluntary I mean sleep and waking  and

respiration, and other similar organic movements. For neither  imagination nor desire is properly mistress of

any of these; but since  the animal body must undergo natural changes of quality, and when  the  parts are so

altered some must increase and other decrease, the  body  must straightway be moved and change with the


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changes that nature  makes dependent upon one another. Now the causes of the movements  are  natural

changes of temperature, both those coming from outside the  body, and those taking place within it. So the

involuntary movements  which occur in spite of reason in the aforesaid parts occur when a  change of quality

supervenes. For conception and imagination, as we  said above, produce the conditions necessary to

affections, since they  bring to bear the images or forms which tend to create these states.  And the two parts

aforesaid display this motion more conspicuously  than the rest, because each is in a sense a separate vital

organism,  the reason being that each contains vital moisture. In the case of the  heart the cause is plain, for the

heart is the seat of the senses,  while an indication that the generative organ too is vital is that  there flows from

it the seminal potency, itself a kind of organism.  Again, it is a reasonable arrangement that the movements

arise in  the  centre upon movements in the parts, and in the parts upon  movements in  the centre, and so reach

one another. Conceive A to be  the centre or  starting point. The movements then arrive at the  centre from each

letter in the diagram we have drawn, and flow back  again from the  centre which is moved and changes, (for

the centre is  potentially  multiple) the movement of B goes to B, that of C to C, the  movement of  both to both;

but from B to C the movements flow by dint  of going from  B to A as to a centre, and then from A to C as

from a  centre. 

Moreover a movement contrary to reason sometimes does and  sometimes does not arise in the organs on the

occasion of the same  thoughts; the reason is that sometimes the matter which is passive  to  the impressions is

there in sufficient quantity and of the right  quality and sometimes not. 

And so we have finished our account of the reasons for the parts  of each kind of animal, of the soul, and

furthere of senseperception,  of sleep, of memory, and of movement in general; it remains to speak  of animal

generation. 

THE END 


ON THE MOTION OF ANIMALS

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1. Table of Contents, page = 3

2. ON THE MOTION OF ANIMALS, page = 4

   3. by Aristotle, page = 4

   4.  1, page = 4

   5.  2, page = 5

   6.  3, page = 5

   7.  4, page = 6

   8.  5, page = 7

   9.  6, page = 7

   10.  7, page = 7

   11.  8, page = 8

   12.  9, page = 9

   13.  10, page = 10

   14.  11, page = 10