E1P23D
Demonstration — Part I
Latin
Modus enim in alio est per quod concipi debet (per definitionem 5) hoc est (per propositionem 15) in solo Deo est et per solum Deum concipi potest. Si ergo modus concipitur necessario existere et infinitus esse, utrumque hoc debet necessario concludi sive percipi per aliquod Dei attributum quatenus idem concipitur infinitatem et necessitatem existentiæ sive (quod per definitionem 8 idem est) æternitatem exprimere hoc est (per definitionem 6 et propositionem 19) quatenus absolute consideratur. Modus ergo qui et necessario et infinitus existit, ex absoluta natura alicujus Dei attributi sequi debuit hocque vel immediate (de quo vide propositionem 21) vel mediante aliqua modificatione quæ ex ejus absoluta natura sequitur hoc est (per propositionem præcedentem) quæ et necessario et infinita existit. Q.E.D.
English (Elwes 1883)
A mode exists in something else, through which it must be conceived (Def. v.), that is (Prop. xv.), 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 expressing the infinity and necessity of existence, in other words (Def. viii.) 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 (Prop. xxi.) or through the means of some modification, which follows from the absolute nature of the said attribute; that is (by Prop. xxii.), which exists necessarily and as infinite.
Modern English
A mode is in something else through which it must be conceived (E1D5), that is, (E1P15), it is in God alone and can be conceived through God alone. So if a mode is conceived as existing necessarily and as infinite, both must be concluded or perceived through some attribute of God, taken as conceived to express the infinity and necessity of existence (or, what is the same (E1D8), eternity); that is (E1D6)(E1P19), taken as considered absolutely. A mode that exists both necessarily and as infinite must therefore have followed from the absolute nature of some attribute of God, either immediately (E1P21) or by means of some modification that follows from the attribute's absolute nature, that is (E1P22), a modification that itself exists both necessarily and as infinite. Q.E.D.