E1P28D
Demonstration — Part I
Latin
Quicquid determinatum est ad existendum et operandum, a Deo sic determinatum est (per propositionem 26 et corollarium propositionis 24). At id quod finitum est et determinatam habet existentiam, ab absoluta natura alicujus Dei attributi produci non potuit; quicquid enim ex absoluta natura alicujus Dei attributi sequitur, id infinitum et æternum est (per propositionem 21). Debuit ergo ex Deo vel aliquo ejus attributo sequi quatenus aliquo modo affectum consideratur; præter enim substantiam et modos nil datur (per axioma 1 et definitionibus 3 et 5) et modi (per corollarium propositionis 25) nihil sunt nisi Dei attributorum affectiones. At ex Deo vel aliquo ejus attributo quatenus affectum est modificatione quæ æterna et infinita est, sequi etiam non potuit (per propositionem 22). Debuit ergo sequi vel ad existendum et operandum determinari a Deo vel aliquo ejus attributo quatenus modificatum est modificatione quæ finita est et determinatam habet existentiam. Quod erat primum. Deinde hæc rursus causa sive hic modus (per eandem rationem qua primam partem hujus jam jam demonstravimus) debuit etiam determinari ab alia quæ etiam finita est et determinatam habet existentiam et rursus hæc ultima (per eandem rationem) ab alia et sic semper (per eandem rationem) in infinitum. Q.E.D.
English (Elwes 1883)
Whatsoever is conditioned to exist and act, has been thus conditioned by God (by Prop. xxvi. and Prop. xxiv., Coroll.).
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 nature of any attribute of God is infinite and eternal (by Prop. xxi.). It must, therefore, follow from some attribute of God, in so far as the said attribute is considered as in some way modified; for substance and modes make up the sum total of existence (by Ax. i. and Def. iii., v.), while modes are merely modifications of the attributes of God. But from God, or from any of his attributes, in so far as the latter is modified by a modification infinite and eternal, a conditioned thing cannot follow. Wherefore it must follow from, or be conditioned for, existence and action by God or one of his attributes, in so far as the latter are modified by some modification which is finite, and has a conditioned existence. This is our first point. Again, this cause or this modification (for the reason by which we established the first part of this proof) must in its turn be conditioned by another cause, which also is finite, and has a conditioned existence, and, again, this last by another (for the same reason); and so on (for the same reason) to infinity. Q.E.D.
Modern English
Whatever is determined to exist and to act has been so determined by God (E1P26), (E1P24C). But what is finite and has a determinate existence could not have been produced by the absolute nature of any of God's attributes; for whatever follows from the absolute nature of any of God's attributes is infinite and eternal (E1P21). It must therefore have followed from God, or from some attribute of him, insofar as that attribute is considered as affected in some way — for besides substance and modes there is nothing (E1A1), (E1D3), (E1D5), and modes are nothing but affections of God's attributes (E1P25C). But it could not have followed from God or any of his attributes insofar as that attribute is affected by a modification that is eternal and infinite, either (E1P22). So it must have followed from, or been determined to exist and to act by, God or some attribute of him insofar as that attribute is modified by a modification that is finite and has a determinate existence. That was the first point.
Next, this cause in turn, or this mode, must itself have been determined by another that is likewise finite and has a determinate existence (by the same reasoning by which we have just now demonstrated the first part of this proof); and again this last (by the same reasoning) by another, and so on always (by the same reasoning) to infinity. Q.E.D.