E1P8D
Demonstration — Part I
Latin
Substantia unius attributi non nisi unica existit (per propositionem 5) et ad ipsius naturam pertinet existere (per propositionem 7). Erit ergo de ipsius natura vel finita vel infinita existere. At non finita. Nam (per definitionem 2) deberet terminari ab alia ejusdem naturæ quæ etiam necessario deberet existere (per propositionem 7) adeoque darentur duæ substantiæ ejusdem attributi, quod est absurdum (per propositionem 5). Existit ergo infinita. Q.E.D.
English (Elwes 1883)
There can only be one substance with an identical attribute, and existence follows from its nature (Prop. vii.); its nature, therefore, involves existence, either as finite or infinite. It does not exist as finite, for (by Def. ii.) it would then be limited by something else of the same kind, which would also necessarily exist (Prop. vii.); and there would be two substances with an identical attribute, which is absurd (Prop. v.). It therefore exists as infinite. Q.E.D.
Modern English
There can be only one substance of any single attribute (E1P5), and existence belongs to its nature (E1P7). So by its nature it must exist either as finite or as infinite. But it cannot be finite. For (E1D2) it would have to be bounded by another of the same nature, which would also necessarily exist (E1P7); and there would then be two substances of the same attribute, which is absurd (E1P5). So it exists as infinite. Q.E.D.