E1P5D
Demonstration — Part I
Latin
Si darentur plures distinctæ, deberent inter se distingui vel ex diversitate attributorum vel ex diversitate affectionum (per propositionem præcedentem). Si tantum ex diversitate attributorum, concedetur ergo non dari nisi unam ejusdem attributi. At si ex diversitate affectionum, cum substantia sit prior natura suis affectionibus (per propositionem 1) depositis ergo affectionibus et in se considerata hoc est (per definitionem 3 et axioma 6) vere considerata, non poterit concipi ab alia distingui hoc est (per propositionem præcedentem) non poterunt dari plures sed tantum una. Q.E.D.
English (Elwes 1883)
If several distinct substances be granted, they must be distinguished one from the other, either by the difference of their attributes, or by the difference of their modifications (Prop. iv.). If only by the difference of their attributes, it will be granted that there cannot be more than one with an identical attribute. If by the difference of their modifications--as substance is naturally prior to its modifications (Prop. i.),--it follows that setting the modifications aside, and considering substance in itself, that is truly, (Deff. iii. and vi.), there cannot be conceived one substance different from another,--that is (by Prop. iv.), there cannot be granted several substances, but one substance only. Q.E.D.
Modern English
Suppose several distinct substances were granted. They would have to be distinguished from one another either by a difference in attributes or by a difference in affections (E1P4). If only by a difference in attributes, then it is granted that no more than one substance can have a given attribute. But if by a difference in affections, then since substance is prior in nature to its affections (E1P1), once the affections are set aside and substance is considered in itself, that is, considered truly (E1D3)(E1A6), no substance can be conceived as distinguished from another. And so (E1P4) there cannot be several substances, but only one. Q.E.D.