E1P16D
Demonstration — Part I
Latin
Hæc propositio unicuique manifesta esse debet si modo ad hoc attendat quod ex data cujuscunque rei definitione plures proprietates intellectus concludit, quæ revera ex eadem (hoc est ipsa rei essentia) necessario sequuntur et eo plures quo plus realitatis rei definitio exprimit hoc est quo plus realitatis rei definitæ essentia involvit. Cum autem natura divina infinita absolute attributa habeat (per definitionem 6) quorum etiam unumquodque infinitam essentiam in suo genere exprimit, ex ejusdem ergo necessitate infinita infinitis modis (hoc est omnia quæ sub intellectum infinitum cadere possunt) necessario sequi debent. Q.E.D.
English (Elwes 1883)
This proposition will be clear to everyone, who remembers that from the given definition of any thing the intellect infers several properties, which really necessarily follow therefrom (that is, from the actual essence of the thing defined); and it infers more properties in proportion as the definition of the thing expresses more reality, that is, in proportion as the essence of the thing defined involves more reality. Now, as the divine nature has absolutely infinite attributes (by Def. vi.), of which each expresses infinite essence after its kind, it follows that from the necessity of its nature an infinite number of things (that is, everything which can fall within the sphere of an infinite intellect) must necessarily follow. Q.E.D.
Modern English
This proposition must be clear to anyone who notes this much: from the given definition of any thing, the intellect infers a number of properties that really do follow necessarily from it, that is, from the very essence of the thing, and the more such properties, the more reality the definition expresses, that is, the more reality the essence of the thing defined involves. Now since the divine nature has absolutely infinite attributes (E1D6), each of which also expresses an infinite essence in its own kind, infinite things in infinite ways (that is, everything that can fall under an infinite intellect) must necessarily follow from its necessity. Q.E.D.