Preface
I now pass on to explaining the results，which must necessarily follow from the es-sence of God，or of the eternal and infinite being；not，indeed，all of them（for we proved in Part。1，Prop。16.，that an infinite number must follow in an infinite number of ways），but only those which are able to lead us，as it were by the hand，to the knowledge of the human mind and its highest blessedness。
Definitions
1.By body I mean a mode which expresses in a certain determinate manner the es-sence of God，in so far as he is considered as an extended thing。
2.I consider as belonging to the essence of a thing that，which being given，the thing is necessarily given also，and，which being removed，the thing is necessarily re-moved also；in other words，that without which the thing，and which itself without the thing，can neither be nor be conceived。
3.By idea，I mean the mental conception which is formed by the mind as a think-ing thing。
Explanation。-I say conception rather than perception，because the word percep-tion seems to imply that the mind is passive in respect to the object；whereas conception seems to express an activity of the mind。
4.By an adequate idea，I mean an idea which，in so far as it is considered in itself，without relation to the object，has all the properties or intrinsic marks of a true idea。
Explanation。-I say intrinsic，in order to exclude that mark which is extrinsic，namely，the agreement between the idea and its object。
5.Duration is the indefinite continuance of existing。
Explanation。-I say indefinite，because it cannot be determined through the exist-ence itself of the existing thing，or by its efficient cause，which necessarily gives the ex-istence of the thing，but does not take it away。
6.Reality and perfection I use as synonymous terms。
7.By particular things，I mean things which are finite and have a conditioned ex-istence；and if several individual things concur in one action，so as to be all simultane-ously the effect of one cause，I consider them all，to that extent，as one particular thing。
Axioms
1.The essence of man does not involve necessary existence，that is，it may，in the order of nature，come to pass that this or that man does or does not exist。
2.Man thinks。
3.Modes of thinking，such as love，desire，or any other of the passions，do not take place，unless there be in the same individual an idea of the thing loved，desired。But the idea can exist without the presence of any other mode of thinking。
4.We perceive that a certain body is affected in many ways。
5.We feel and perceive no particular things，save bodies and modes of thought。
Propositions
PROP。1.Thought is an attribute of God，or God is a thinking thing。
Proof。-Particular thoughts，or this or that thought，are modes which，in a certain conditioned manner，express the nature of God。God therefore possesses the attribute of which the concept is involved in all particular thoughts，which latter are conceived thereby。Thought，therefore，is one of the infinite attributes of God，which express God s eternal and infinite essence。In other words，God is a thinking thing。
PROP。2.Extension is an attribute of God，or God is an extended thing。
Proof。-The proof of this Proposition is similar to that of the last。
PROP。3.In God there is necessarily the idea not only of his essence，but also of all things which necessarily follow from his essence。
Proof。-God can think an infinite number of things in infinite ways，or can form the idea of his essence，and of all things which necessarily follow therefrom。But what-ever is in God s power necessarily exists；therefore，there is necessarily such an idea，and it is only in God。
PROP。4.God s idea，from which an infinite number of things follow in infinite ways，can only be one。
Proof。-Infinite intellect comprehends nothing save the attributes of God and his modifications。Now God is one。Therefore God s idea，wherefrom an infinite number of things follow in infinite ways，can only，be one。
PROP。5.The actual being of ideas owns God as its cause，only in so far as he is considered as a thinking thing，not insofar as he is unfolded in any other attribute；that is，the ideas both of the attributes of God and of particular things do not own as their ef-ficient cause their objects or the things perceived，but God himself in so far as he is a thinking thing。
Proof。-This Proposition is evident from Prop。3.of this Part。We there drew the conclusion，that God can form the idea of his essence，and of all things which follow necessarily therefrom，solely，because he is a thinking thing，and not because he is the object of his own idea。Wherefore the actual being of ideas owns for cause God，in so far as he is a thinking thing。It may，be differently proved as follows：the actual being of ideas is（obviously，）a mode of thought，that is a mode which expresses in a certain manner the nature of God，in so far as he is a thinking thing，and therefore involves the conception of no other attribute of God，and consequently is not the effect of any attrib-ute save thought。Therefore the actual being of ideas owns God as its cause，in so far as he is considered as a thinking thing。
PROP。6.The modes of any given attribute are caused by God，in so far as he is considered through the attribute of which they are modes，and not in so far as he is con-sidered through any other attribute。
Proof。-Each attribute is conceived through itself，without any other；wherefore the modes of each attribute involve the conception of that attribute，but not of any other。Thus they are caused by God，only in so far as he is considered through the attribute whose modes they，are，and not in so far as he is considered through any other。
Corollary。-Hence the actual being of things，which are not modes of thought，does not follow from the divine nature，because that nature has prior knowledge of the things。Things represented in ideas follow，and are derived from their particular attrib-ute，in the same manner，and with the same necessity as ideas follow（according to what we have shown）from the attribute of thought。
PROP。7.The order and connection of ideas is the same as the order and connec-tion of things。
Proof。-This Proposition is evident from Part 1，Ax。4.For the idea of each thing caused depends on the knowledge of the cause of which it is the effect。
Corollary。-Hence God s power of thinking is equal to his realized power of action，that is，whatever follows formally from God s infinite nature follows objectively in God from his idea in the same order and with the same connection。
PROP。8.The ideas of particular things，or of modes，that do not exist，must be comprehended in the infinite idea of God，in the same way as the formal essences of par-ticular things or modes are contained in the attributes of God。
Proof。-This Proposition is evident from the last。
Corollary。-Hence，so long as particular things do not exist，except in so far as they，are comprehended in the attributes of God，their objective being，or ideas，do not exist，except in so far as the infinite idea of God exists；and when particular things are said to exist，not only in so far as they，are involved in the attributes of God，but also in so far as they are said to have duration，their ideas will also involve existence，through which they are said to have duration。
PROP。9.The idea of an individual thing actually existing is caused by God，not in so far as he is infinite，but in so far as he is considered as affected by another idea of a thing if actually existing，of which he is the cause，in so far as he is affected by a third idea，and so on to infinity。
Proof。-The idea of an individual thing actually existing is an individual mode of thinking，and is distinct from other modes；thus it is caused by God，in so far only as he is a thinking thing。But not in so far as he is a thing thinking absolutely，only in so far as he is considered as affected by another mode of thinking；and he is the cause of this latter，as being affected by a third，and so on to infinity。But the order and connec-tion of ideas is the same as the order and connection of causes。Therefore，the cause of one individual idea is another individual idea，or God，in so far as he is considered as modified by that idea，is the cause；and of this second idea God is the cause，in so far as he is affected by another idea，and so on to infinity。
Corollary。-Whatsoever takes place in the individual object of any idea，the knowledge thereof is in God，in so far only as he has the idea of the object。
PROP。10.The being of substance does not appertain to the essence of man，in other words，substance does not constitute the actual being of man。
Proof。-The being of substance involves necessary existence。If，therefore，the be-ing of substance appertains to the essence of man，substance being granted，man would necessarily be granted also，and，consequently，man would necessarily exist，which is absurd。Therefore，the being of substance does not appertain to the essence of man。
Corollary。-Hence it follows，that the essence of man is constituted by certain modifications of the attributes of God。For the being of substance does not belong to the essence of man。That essence therefore is something which is in God，and which without God can neither be nor be conceived，whether it be a modification，or a mode which ex-presses God s nature in a certain conditioned manner。
PROP。11.The first element，which constitutes the actual being of the human mind，is the idea of some particular thing actually existing。
Proof。-The essence of man is constituted by certain modes of the attributes of God，namely，by the modes of thinking，of all which the idea is prior in nature，and，when the idea is given，the other modes（namely，those of which the idea is prior in na-ture）must be in the same individual。Therefore an idea is the first element constituting the human mind。But not the idea of a non-existent thing，for then the idea itself cannot be said to exist；it must therefore be the idea of something actually existing。But not of an infinite thing。For an infinite thing，must always necessarily exist；this would involve an absurdity。Therefore the first element，which constitutes the actual being of the hu-man mind，is the idea of something actually existing。
Corollary。-Hence it follows，that the human mind is part of the infinite intellect of God；thus when we say，that the human mind perceives this or that，we make the asser-tion，that God has this or that idea，not in so far as he is infinite，but in so far as he is displayed through the nature of the human mind，or in so far as he constitutes the essence of the human mind；and when we say that God has this or that idea，not only in so far as he constitutes the essence of the human mind，but also in so far as he，simultaneously with the human mind，has the further idea of another thing，we assert that the human mind perceives a thing in part or inadequately。
PROP。12.Whatsoever comes to pass in the object of the idea，which constitutes the human mind，must be perceived by the human mind，or there will necessarily be an idea in the human mind of the said occurrence。That is，if the object of the idea consti-tuting the human mind be a body，nothing can take place in that body without being per-ceived by the mind。
Proof。-Whatsoever comes to pass in the object of any idea，the knowledge thereof is necessarily in God，in so far as he is considered as affected by the idea of the said ob-ject，that is，in so far as he constitutes the mind of anything。Therefore，whatsoever takes place in the object constituting the idea of the human mind，the knowledge thereof is necessarily in God，in so far as he constitutes the nature of the human mind；that is the knowledge of the said thing will necessarily be in the mind，in other words the mind perceives it。
PROP。13.The object of the idea constituting the human mind is the body，in oth-er words a certain mode of extension which actually exists，and nothing else。
Proof。-If indeed the body were not the object of the human mind，the ideas of the modifications of the body would not be in God in virtue of his constituting our mind，but in virtue of his constituting the mind of something else；that is the ideas of the modifica-tions of the body would not be in our mind；but we do possess the ideas of the modifica-tions of the body。Therefore the object of the idea constituting the human mind is the body，and the body as it actually exists。Further，if there were any other object of the i-dea constituting the mind besides body，then，as nothing can exist from which some effect does not follow there would necessarily have to be in our mind an idea，which would be the effect of that other object；but there is no such idea。Wherefore the object of our mind is the body as it exists，and nothing else。
Corollary。-From this it follows that man consists of a mind and a body，and that the human body exists，as we are aware of it。
Axiom 1.All bodies are either in motion or at rest。
Axiom 2.Every body is moved sometimes more slowly，sometimes more quickly。
Lemma 1.Bodies are distinguished from one another in respect of motion and rest，quickness and slowness，and not in respect of substance。
Lemma 2.All bodies agree in certain respects。
Proof。-All bodies agree in that they involve the conception of one and the same attribute。Further，in that they may be moved less or more quickly，and may be abso-lutely in motion or at rest。
Lemma 3.A body in motion or at rest must be determined to motion or rest by an-other body，which other body has been determined to motion or rest by a third body，and that third again by a fourth，and so on to infinity。
Proof。-Bodies are individual things，which are distinguished one from the other in respect to motion and rest；thus each must necessarily be determined to motion or rest by another individual thing，namely，by another body，which other body is also in mo-tion or at rest。And this body again can only have been set in motion or caused to rest by being determined by a third body to motion or rest。This third body again by a fourth，and so on to infinity。
Corollary。-Hence it follows，that a body in motion keeps in motion，until it is de-termined to a state of rest by some other body；and a body at rest remains so，until it is determined to a state of motion by some other body。This is indeed self-evident。For when I suppose，for instance，that a given body，A，is at rest，and do not take into consideration other bodies in motion，I cannot affirm anything concerning the body A，except that it is at rest。If it afterwards comes to pass that A is in motion，this cannot have resulted from its having been at rest，for no other consequence could have been in-volved than its remaining at rest。If，on the other hand，A be given in motion，we shall，so long as we only consider A，be unable to affirm anything concerning it，except that it is in motion。If A is subsequently found to be at rest，this rest cannot be the re-sult of A s previous motion，for such motion can only have led to continued motion；the state of rest therefore must have resulted from something，which was not in A，namely，from an external cause determining A to a state of rest。
Axiom 1.All modes，wherein one body is affected by another body，follow simulta-neously from the nature of the body affected and the body affecting；so that one and the same body may be moved in different modes，according to the difference in the nature of the bodies moving it；on the other hand，different bodies may be moved in different modes by one and the same body。
Axiom 2.When a body in motion impinges on another body at rest，which it is un-able to move，it recoils，in order to continue its motion，and the angle made by the line of motion in the recoil and the plane of the body at rest，whereon the moving body has impinged，will be equal to the angle formed by the line of motion of incidence and the same plane。
So far we have been speaking only of the most simple bodies，which are only distin-guished one from the other by motion and rest，quickness and slowness。We now pass on to compound bodies。
Definition。When a number of bodies，whether of the same or of different size，are so constrained by other bodies that they lie upon one another，or if they so move，wheth-er with the same degree or different degrees of speed，that they communicate their mo-tions to each other in a certain fixed manner，we shall say that those bodies are united with one another and that they all together compose one body or individual，which is dis-tinguished from the others by this union of bodies。
Axiom 3.In proportion as the parts of an individual，or a compound body，are in contact over a greater or less superficies，they will with greater or less difficulty admit of being moved from their position；consequently the individual will，with greater or less difficulty，be brought to assume another form。Those bodies，whose parts are in contact over large superficies，are called hard；those，whose parts are in contact over small su-perficies，are called soft；those，whose parts are in motion among，one another，are called fluid。
Lemma 4.If from a body or individual，compounded of several bodies，certain bodies be separated，and if，at the same time，an equal number of other bodies or the same nature take，take their place，the individual will preserve its nature as before，without any change in its actuality。
Proof。-For bodies are not distinguished in respect to substance；what consti-tutes the form of the Individual consists in the union of the bodies。But this（by hy-pothesis）is retained even if a continual change of bodies occurs。Therefore，the Indi-vidual will retain its nature，as before，both in respect to substance，and in respect to mode。
Lemma 5.If the parts composing an individual become greater or less，but in such proportion，that they all preserve the same mutual relations of motion and rest，the indi-vidual will still preserve its original nature，and its actuality will not be changed。
Proof。-The same as for the last Lemma。
Lemma 6.If certain bodies composing an individual be compelled to change the motion，which they have in one direction，for motion in another direction，but in such a manner，that they be able to continue their motions and their mutual communication in the same relations as before，the individual will retain its own nature without any change of its actuality。
Proof。-This Proposition is self-evident，for the individual is supposed to retain all that，which，in its definition，we spoke of as its actual being。
Lemma 7.Furthermore，the individual thus composed preserves its nature，wheth-er it be，as a whole，in motion or at rest，whether it be moved in this or that direction；so long as each part retains its motion，and preserves its communication with other parts as before。
Proof。-This Proposition is evident from the definition of an individual prefixed to Lemma 4.
Postulates
1.The human body is composed of a number of individual parts，of diverse nature，each one of which is in itself extremely complex。
2.Of the individual parts composing the human body some are fluid，some soft，some hard。
3.The individual parts composing the human body，and consequently the human body itself，are affected in a variety of ways by external bodies。
4.The human body stands in need for its preservation of a number of other bodies，by which it is continually，so to speak，regenerated。
5.When the fluid part of the human body is determined by an external body to im-pinge often on another soft part，it changes the surface of the latter，and，as it were，impresses on the soft part certain traces of the external body striking against the fluid part。
6.The human body can move external bodies，and arrange them in a variety of ways。
Propositions
PROP。14.The human Mind is capable of perceiving a great many things，and is the more capable，the more its body can be disposed in a great many ways。