E2P9D
Demonstration — Part II
Latin
Idea rei singularis actu existentis modus singularis cogitandi est et a reliquis distinctus (per corollarium et scholium propositionis 8 hujus) adeoque (per propositionem 6 hujus) Deum quatenus est tantum res cogitans, pro causa habet. At non (per propositionem 28 partis I) quatenus est res absolute cogitans sed quatenus alio cogitandi modo affectus consideratur et hujus etiam Deus est causa quatenus alio cogitandi modo affectus est et sic in infinitum. Atqui ordo et connexio idearum (per propositionem 7 hujus) idem est ac ordo et connexio causarum; ergo unius singularis ideæ alia idea sive Deus quatenus alia idea affectus consideratur, est causa et hujus etiam quatenus alia affectus est et sic in infinitum. Q.E.D.
English (Elwes 1883)
The idea of an individual thing actually existing is an individual mode of thinking, and is distinct from other modes (by the Corollary and note to Prop. viii. of this part); thus (by Prop. vi. of this part) it is caused by God, in so far only as he is a thinking thing. But not (by Prop. xxviii. of Part i.) 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. Now, the order and connection of ideas is (by Prop. vii. of this book) the same as the order and connection of causes. Therefore of a given individual idea 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. Q.E.D.
Modern English
The idea of a singular thing that actually exists is a singular mode of thinking, distinct from all others (E2P8C). It therefore has God as its cause insofar as he is only a thinking thing (E2P6). But not (by E1P28) insofar as he is an absolutely thinking thing, only insofar as he is considered as affected by another mode of thinking. And of that mode, God is also the cause insofar as he is affected by yet another mode of thinking, and so on to infinity.
Now, the order and connection of ideas is the same as the order and connection of causes (E2P7). Therefore one singular idea has another idea, or God insofar as he is considered as affected by that other idea, as its cause. And of that second idea, God is the cause insofar as he is affected by yet another, and so on to infinity. Q.E.D.