E1P11D2
Demonstration — Part I
Latin
Cujuscunque rei assignari debet causa seu ratio tam cur existit quam cur non existit. Exempli gratia si triangulus existit, ratio seu causa dari debet cur existit; si autem non existit, ratio etiam seu causa dari debet quæ impedit quominus existat sive quæ ejus existentiam tollat. Hæc vero ratio seu causa vel in natura rei contineri debet vel extra ipsam. Exempli gratia rationem cur circulus quadratus non existat, ipsa ejus natura indicat; nimirum quia contradictionem involvit. Cur autem contra substantia existat, ex sola etiam ejus natura sequitur quia scilicet existentiam involvit (vide propositionem 7). At ratio cur circulus vel triangulus existit vel cur non existit, ex eorum natura non sequitur sed ex ordine universæ naturæ corporeæ; ex eo enim sequi debet vel jam triangulum necessario existere vel impossibile esse ut jam existat. Atque hæc per se manifesta sunt. Ex quibus sequitur id necessario existere cujus nulla ratio nec causa datur quæ impedit quominus existat. Si itaque nulla ratio nec causa dari possit quæ impedit quominus Deus existat vel quæ ejus existentiam tollat, omnino concludendum est eundem necessario existere. At si talis ratio seu causa daretur, ea vel in ipsa Dei natura vel extra ipsam dari deberet hoc est in alia substantia alterius naturæ. Nam si ejusdem naturæ esset, eo ipso concederetur dari Deum. At substantia quæ alterius esset naturæ, nihil cum Deo commune habere (per 2 propositionem) adeoque neque ejus existentiam ponere neque tollere posset. Cum igitur ratio seu causa quæ divinam existentiam tollat, extra divinam naturam dari non possit, debebit necessario dari, siquidem non existit, in ipsa ejus natura, quæ propterea contradictionem involveret. Atqui hoc de Ente absolute infinito et summe perfecto affirmare absurdum est; ergo nec in Deo nec extra Deum ulla causa seu ratio datur quæ ejus existentiam tollat ac proinde Deus necessario existit. Q.E.D.
English (Elwes 1883)
Of everything whatsoever a cause or reason must be assigned, either for its existence, or for its non--existence--e.g. if a triangle exist, a reason or cause must be granted for its existence; if, on the contrary, it does not exist, a cause must also be granted, which prevents it from existing, or annuls its existence. This reason or cause must either be contained in the nature of the thing in question, or be external to it. For instance, the reason for the non--existence of a square circle is indicated in its nature, namely, because it would involve a contradiction. On the other hand, the existence of substance follows also solely from its nature, inasmuch as its nature involves existence. (See Prop. vii.)
But the reason for the existence of a triangle or a circle does not follow from the nature of those figures, but from the order of universal nature in extension. From the latter it must follow, either that a triangle necessarily exists, or that it is impossible that it should exist. So much is self--evident. It follows therefrom that a thing necessarily exists, if no cause or reason be granted which prevents its existence.
If, then, no cause or reason can be given, which prevents the existence of God, or which destroys his existence, we must certainly conclude that he necessarily does exist. If such a reason or cause should be given, it must either be drawn from the very nature of God, or be external to him--that is, drawn from another substance of another nature. For if it were of the same nature, God, by that very fact, would be admitted to exist. But substance of another nature could have nothing in common with God (by Prop. ii.), and therefore would be unable either to cause or to destroy his existence.
As, then, a reason or cause which would annul the divine existence cannot be drawn from anything external to the divine nature, such cause must perforce, if God does not exist, be drawn from God's own nature, which would involve a contradiction. To make such an affirmation about a being absolutely infinite and supremely perfect is absurd; therefore, neither in the nature of God, nor externally to his nature, can a cause or reason be assigned which would annul his existence. Therefore, God necessarily exists. Q.E.D.
Modern English
For everything whatsoever, a reason or cause must be assigned, both for why it exists and for why it does not. If a triangle exists, a reason or cause must be given for its existence; if it does not exist, a reason or cause must also be given that prevents it from existing, or that removes its existence. This reason or cause must either be contained in the nature of the thing itself or lie outside it. The reason a square circle does not exist is indicated by its very nature: it involves a contradiction. The reason a substance exists, on the contrary, follows from its nature alone, because its nature involves existence (see (E1P7)).
But the reason why a circle or a triangle exists, or does not exist, does not follow from their nature. It follows from the order of corporeal nature as a whole; from that order it must follow either that a triangle now necessarily exists, or that it is impossible that it should now exist. These points are self-evident. From them it follows that a thing necessarily exists if no reason or cause is given that prevents its existence.
If, then, no reason or cause can be given that prevents God from existing, or that would remove his existence, it must be concluded that he necessarily exists. But if such a reason or cause were given, it would have to lie either in God's own nature or outside it, that is, in another substance of another nature. If of the same nature, that very fact would concede that God exists. A substance of another nature could have nothing in common with God (by (E1P2)), and so could neither posit his existence nor remove it.
Since a reason or cause that would remove the divine existence cannot be given outside the divine nature, it would have to be given, if God does not exist, in his own nature, which would then involve a contradiction. But to affirm this of an absolutely infinite and supremely perfect being is absurd. Therefore, neither in God nor outside God is any cause or reason given that would remove his existence, and so God necessarily exists. Q.E.D.