E2P43D
Demonstration — Part II
Latin
Idea vera in nobis est illa quæ in Deo quatenus per naturam mentis humanæ explicatur, est adæquata (per corollarium propositionis 11 hujus). Ponamus itaque dari in Deo quatenus per naturam mentis humanæ explicatur, ideam adæquatam A. Hujus ideæ debet necessario dari etiam in Deo idea quæ ad Deum eodem modo refertur ac idea A (per propositionem 20 hujus cujus demonstratio universalis est). At idea A ad Deum referri supponitur quatenus per naturam mentis humanæ explicatur; ergo etiam idea ideæ A ad Deum eodem modo debet referri hoc est (per idem corollarium propositionis 11 hujus) hæc adæquata idea ideæ A erit in ipsa mente quæ ideam adæquatam A habet adeoque qui adæquatam habet ideam sive (per propositionem 34 hujus) qui vere rem cognoscit, debet simul suæ cognitionis adæquatam habere ideam sive veram cognitionem hoc est (ut per se manifestum) debet simul esse certus. Q.E.D.
English (Elwes 1883)
A true idea in us is an idea which is adequate in God, in so far as he is displayed through the nature of the human mind (II. xi. Coroll.). Let us suppose that there is in God, in so far as he is displayed through the human mind, an adequate idea, A. The idea of this idea must also necessarily be in God, and be referred to him in the same way as the idea A (by II. xx., whereof the proof is of universal application). But the idea A is supposed to be referred to God, in so far as he is displayed through the human mind; therefore, the idea of the idea A must be referred to God in the same manner; that is (by II. xi. Coroll.), the adequate idea of the idea A will be in the mind, which has the adequate idea A; therefore he, who has an adequate idea or knows a thing truly (II. xxxiv.), must at the same time have an adequate idea or true knowledge of his knowledge; that is, obviously, he must be assured. Q.E.D.
Modern English
A true idea in us is one that is adequate in God insofar as he is expressed through the nature of the human mind (E2P11C). Suppose, then, that there is in God, insofar as he is expressed through the nature of the human mind, an adequate idea A. There must necessarily also be in God an idea of this idea, related to God in the same way as idea A (E2P20). But idea A is supposed to be related to God insofar as he is expressed through the nature of the human mind; therefore the idea of idea A must be related to God in the same way, that is, by (E2P11C) again, this adequate idea of idea A will be in the very mind that has adequate idea A. Therefore whoever has an adequate idea, or by (E2P34) truly knows a thing, must at the same time have an adequate idea, that is, a true knowledge, of that knowledge. In other words, as is obvious by itself, that person must at the same time be certain. Q.E.D.