PROP。20.The existence of God and his essence are one and the same。
Proof。-God and all his attributes are eternal，that is each of his attributes expres-ses existence。Therefore the same attributes of God which explain his eternal essence，explain at the same time his eternal existence，in other words，that which constitutes God s essence constitutes at the same time his existence。Wherefore God s existence and God s essence are one and the same。
CorollaryⅠ。-Hence it follows that God s existence，like his essence，is an eter-nal truth。
Corollary Ⅱ。-Secondly，it follows that God，and all the attributes of God，are unchangeable。For if they changed as to their existence，they would also change as to their essence；that is，obviously，be changed from true to false，which is absurd。
PROP。21.All things which follow from the absolute nature of any attribute of God must always exist and be infinite，or，in other words，are eternal and infinite through the said attribute。
Proof。-If you deny this，then conceive（if you can）that in some attribute of God there follows from its absolute nature something that is finite and has a determinate exist-ence，or duration，for instance，the God s idea in thought。Now thought，in so far as it is supposed to be an attribute of God，is necessarily in its nature infinite。But，in so far as it possesses God s idea，it is supposed finite。It cannot，however，be conceived as fi-nite，unless it be limited by thought；but it is not limited by thought itself，in so far as it has constituted God s idea（for so far it is supposed to be finite）；therefore，it is lim-ited by thought，in so far as it has not constituted God s idea，which nevertheless must necessarily exist。Therefore，there is thought which does not constitute God s idea，and，accordingly，God s idea does not naturally follow from its nature in so far as it is absolute thought（for it is conceived as constituting，and also as not constituting，God s idea），which is against our hypothesis。Wherefore，if God s idea in thought，or anything else in any attribute of God（for we may take any example，as the proof is of universal applica-tion）follows from the necessity of the absolute nature of the said attribute，the said thing must necessarily be infinite。This was the first thing to be proven。
Next，a thing which thus follows from the necessity of the nature of any attribute cannot have a limited duration。For if you deny this，then suppose there is a thing，in some attribute of God，a thing which follows from the necessity of the nature of that at-tribute-for instance，God s idea in thought-and suppose at some time not to have existed，or to be about not to exist。Now thought being an attribute of God，must neces-sarily exist unchanged；and beyond the limits of the duration of God s idea（supposing the latter at some time not to have existed，or not to be going to exist），thought would perforce have existed without God s idea。But this is contrary to the hypothesis，for it is supposed that God s idea follows necessarily from the given thought。Therefore God s i-dea in thought，or anything which necessarily follows from the absolute nature of some attribute of God，cannot have a limited duration，but through the said attribute is eter-nal。This was the second thing to be proven。Bear in mind that the same Proposition may be affirmed of anything，which in any attribute necessarily follows from God s abso-lute nature。
PROP。22.Whatsoever follows from any attribute of God，in so far as it is modified by a modification，which exists necessarily and as infinite，through the said attribute，must also exist necessarily and as infinite。
Proof。-The proof of this Proposition is similar to that of the preceding one。
PROP。23.Every mode，which exists both necessarily and as infinite，must neces-sarily follow either from the absolute nature of some attribute of God，or from an attribute modified by a modification which exists necessarily，and as infinite。
Proof。-A mode exists in something else，through which it must be conceived，that is，it exists solely in God，and solely through God can be conceived。If，therefore，a mode is conceived as necessarily existing and infinite，it must necessarily be inferred or perceived through some attribute of God，in so far as such attribute is conceived as ex-pressing the infinity and necessity of existence，in other words eternity；that is，in so far as it is considered absolutely。A mode，therefore，which necessarily exists as infinite，must follow from the absolute nature of some attribute of God，either immediately or through the means of some modification，which follows from the absolute nature of the said attribute；that is，which exists necessarily and as infinite。
PROP。24.The essence of things produced by God does not involve existence。
Proof。-This Proposition is evident from Def。1.For that of which the nature in-volves existence is self-caused，and exists by the sole necessity of its own nature。
Corollary。-Hence it follows that God is not only the cause of things coming into existence，but also of their continuing in existence，that is，in scholastic phraseology，God is cause of the being of things。For whether things exist，or do not exist，whenever we contemplate their essence，we see that it involves neither existence nor duration。So their essence can be the cause neither of their existence nor of their duration，but only God，to whose nature alone it pertains to exist，can be the cause。
PROP。25.God is the efficient cause not only of the existence of things，but also of their essence。
Proof。-If this be denied，then God is not the cause of the essence of things；and therefore the essence of things can be conceived without God。This is absurd。There-fore，God is the cause of the essence of things。
Corollary。-Particular things are nothing but modifications of God s attributes，or modes by which God s attributes are expressed in a certain and determinate way。The demonstration is evident from P15 and D5.
PROP。26.A thing which is conditioned to act in a particular manner，has neces-sarily been thus conditioned by God；and that which has not been conditioned by God cannot condition itself to act。
Proof。-That by which things are said to be conditioned to act in a particular man-ner is necessarily something positive；therefore both of its essence and of its existence God by the necessity of his nature is the efficient cause；this is our first point。And from it the second thing asserted also follows very clearly。For if a thing，which has not been conditioned by God，could condition itself，the first part of our proof would be false，and this，as we have shown，is absurd。
PROP。27.A thing，which has been conditioned by God to act in a particular manner，cannot render itself unconditioned。
Proof。-This Proposition is evident from the third axiom。
PROP。28.Every individual thing，or everything which is finite and has a condi-tioned existence，cannot exist or be conditioned to act，unless it be conditioned for ex-istence and action by a cause other than itself，which also is finite，and has a condi-tioned existence；and likewise this cause cannot in its turn exist，or be conditioned to act，unless it be conditioned for existence and action by another cause，which also is fi-nite，and has a conditioned existence，and so on to infinity。
Proof。-Whatsoever is conditioned to exist and act，has been thus conditioned by God。But that which is finite and has a conditioned existence，cannot be produced by the absolute nature of any attribute of God；for whatsoever follows from the absolute na-ture of any attribute of God is infinite and eternal。It must，therefore，follow from some attribute of God，in so far as the said attribute is considered as in some way modified。For there is nothing except substance and its modes，and modes are merely modifications of the attributes of God。But from God，or from any of his attributes，in so far as the lat-ter is modified by a modification infinite and eternal，a conditioned thing cannot follow。It had，therefore，to follow from，or be conditioned to exist and act by God or an attrib-ute of God insofar as it is modified by a modification which is finite and has a determi-nate existence。This is our first point。Again，this cause or this modification must in its turn be conditioned by another cause，which also is finite，and has a conditioned exist-ence，and again，this last by another；and so on to infinity。
PROP。29.Nothing in the universe is contingent，but all things are conditioned to exist and operate in a particular manner by the necessity of the divine nature。
Proof。-Whatsoever is，is in God。But God cannot be called a thing contingent。For he exists necessarily，and not contingently。Further，the modes of the divine nature follow therefrom necessarily，and not contingently-either in so far as the divine nature is considered absolutely，or in so far as it is considered to be determined to act in a cer-tain way。Further，God is not only the cause of these modes，in so far as they simply ex-ist，but also in so far as they are considered as conditioned for operating in a particular manner。If they be not conditioned by God，it is impossible，and not contingent，that they should condition themselves；contrariwise，if they be conditioned by God，it is im-possible，and not contingent that they should render themselves unconditioned。Where-fore all things are conditioned by the necessity of the divine nature，not only to exist，but also to exist and operate in a particular manner，and there is nothing that is contin-gent。
PROP。30.Intellect，in function finite，or in function infinite，must comprehend the attributes of God and the modifications of God，and nothing else。
Proof。-A true idea must agree with its object，in other words，that which is con-tained in the intellect in representation must necessarily be granted in nature。But in na-ture there is no substance save God，nor any modifications save those which are in God，and cannot without God either be or be conceived。Therefore the intellect，in function finite，or in function infinite，must comprehend the attributes of God and the modifica-tions of God，and nothing else。
PROP。31.The intellect in function，whether finite or infinite，as will，desire，love，etc。，should be referred to passive nature and not to active nature。
Proof。-By the intellect we do not mean absolute thought，but only a certain mode of thinking，differing from other modes，such as love，desire，etc。，and therefore requi-ring to be conceived through absolute thought。It must be so conceived through some at-tribute of God which expresses the eternal and infinite essence of thought，that without such attribute it could neither be nor be conceived。It must therefore be referred to na-ture passive rather than to nature active，as must also the other modes of thinking。
PROP。32.Will cannot be called a free cause，but only a necessary cause。
Proof。-Will is only a particular mode of thinking，like intellect；therefore no voli-tion can exist，nor be conditioned to act，unless it be conditioned by some cause other than itself，which cause is conditioned by a third cause，and so on to infinity。But if will be supposed infinite，it must also be conditioned to exist and act by God，not by virtue of his being substance absolutely infinite，but by virtue of his possessing an attrib-ute which expresses the infinite and eternal essence of thought。Thus，however it be conceived，whether as finite or infinite，it requires a cause by which it should be condi-tioned to exist and act。Thus it cannot be called a free cause，but only a necessary or constrained cause。
Corollary 1.-Hence it follows，first，that God does not act according to freedom of the will。
Corollary 2.-It follows secondly，that will and intellect stand in the same relation to the nature of God as do motion，and rest，and absolutely all natural phenomena，which must be conditioned by God to exist and act in a particular manner。For will，like the rest，stands in need of a cause，by which it is conditioned to exist and act in a parti-cular manner。And although，when will or intellect be granted，an infinite number of re-sults may follow，yet God cannot on that account be said to act from freedom of the will，any more than he can be said to act from freedom of motion and rest on account of those things that follow from motion and rest（for infinitely many things also follow from motion and rest）。Wherefore will no more appertains to God s nature than does anything else in nature，but stands in the same relation to him as motion，rest，and the like，which we have shown to follow from the necessity of the divine nature，and to be conditioned by it to exist and act in a particular manner。
PROP。33.Things could have been produced by God in no other way，and in no other order than they have been produced。
Proof。-All things necessarily follow from the nature of God，and by the nature of God are conditioned to exist and act in a particular way。If things，therefore，could have been of a different nature，or have been conditioned to act in a different way，so that the order of nature would have been different，God s nature would also have been able to be different from what it now is；and therefore that different nature also would have perforce existed，and consequently there would have been able to be two or more Gods。This is absurd。Therefore things could not have been brought into being by God in any other manner，etc。
PROP。34.God s power is identical with his essence。
Proof。-From the sole necessity of the essence of God it follows that God is the cause of himself and of all things。Wherefore the power of God，by which he and all things are and act，is identical with his essence。
PROP。35.Whatsoever we conceive to be in the power of God，necessarily exists。
Proof。-Whatsoever is in God s power must be so comprehended by his essence that it necessarily follows therefrom，and therefore necessarily exists。
PROP。36.Nothing exists from whose nature some effect does not follow。
Proof。-Whatsoever exists expresses God s nature or essence in a given conditioned manner；that is，whatsoever exists，expresses in a given conditioned manner God s pow-er，which is the cause of all things，therefore an effect must necessarily follow。
Appendix
In the foregoing I have explained the nature and properties of God。I have shown that he necessarily exists，that he is one；that he is，and acts solely by the necessity of his own nature；that he is the free cause of all things，and how he is so；that all things are in God，and so depend on him，that without him they could neither exist nor be con-ceived；lastly，that all things are pre-determined by God，not through his free will or absolute fiat，but from the very nature of God or infinite power。I have further，where occasion offered，taken care to remove the prejudices，which might impede the compre-hension of my demonstrations。Yet there still remain misconceptions not a few，which might and may prove very grave hindrances to the understanding of the concatenation of things，as I have explained it above。I have therefore thought it worth while to bring these misconceptions before the bar of reason。