P26: The human Mind does not perceive any external body as actually existing, except through the ideas of the affections of its own Body.

Dem.: If the human Body is not affected by an external body in any way, then (by P7) the idea of the human Body, i.e. (by P13) the human Mind, is also not affected in any way by the idea of the existence of that body, or it does not perceive the existence of that external body in any way. But insofar as the human Body is affected by an external body in some way, to that extent {the human Mind} (by P16 and P16 C1) perceives the external body, q.e.d.

Cor.: Insofar as the human Mind imagines an external body, it does not have adequate knowledge of it.

Dem.: When the human Mind regards external bodies through ideas of the affections of its own Body, then we say that it imagines (see P17 S); and the Mind cannot in any other way (by P26) imagine external bodies as actually existing. And so (by P25), insofar as the Mind imagines external bodies, it does not have adequate knowledge of them, q.e.d.