Id quod corpori humano et quibusdam corporibus externis a quibus corpus humanum affici solet, commune est et proprium quodque in cujuscunque horum parte æque ac in toto est, ejus etiam idea erit in mente adæquata.
That which is common to the human body and to other external bodies by which the human body is accustomed to be affected and is each individual in whichever of them equal in part and in the whole, its idea will even be adequate in the mind.
DEMONSTRATIO: Sit A id quod corpori humano et quibusdam corporibus externis commune est et proprium quodque æque in humano corpore ac in iisdem corporibus externis et quod denique æque in cujuscunque corporis externi parte ac in toto est. Ipsius A dabitur in Deo idea adæquata (per corollarium propositionis 7 hujus) tam quatenus ideam corporis humani quam quatenus positorum corporum externorum ideas habet. Ponatur jam humanum corpus a corpore externo affici per id quod cum eo habet commune hoc est ab A; hujus affectionis idea proprietatem A involvet (per propositionem 16 hujus) atque adeo (per idem corollarium propositionis 7 hujus) idea hujus affectionis quatenus proprietatem A involvit, erit in Deo adæquata quatenus idea corporis humani affectus est hoc est (per propositionem 13 hujus) quatenus mentis humanæ naturam constituit adeoque (per corollarium propositionis 11 hujus) hæc idea est etiam in mente humana adæquata. Q.E.D.
Let there be thing A which is common to the human body and to other external bodies and is each individual equal in the human body and in the same external bodies and which is finally equal in part of whatsoever external body and in the whole. Thing A is given in God as adequate idea (by IIP7C) not only insofar as it has the idea of the human body but also insofar as the ideas of the placed external bodies. Indeed let it be posited that the human body is affected by an external body by which what it has in common with that is this from thing A; the idea of this affection involves the property A (by IIP16) and to such a degree (by IIP7C) the idea of this affection insofar as it involves property A, will be in God adequate insofar as the idea of the human body is affected that is (by IIP13) insofar as it constitutes the nature of the human mind to such a degree (by IIP11) this idea is also adequate in the human mind.
COROLLARIUM: Hinc sequitur quod mens eo aptior est ad plura adæquate percipiendum quo ejus corpus plura habet cum aliis corporibus communia.
From this it follows that the mind is more suited for perceiving more things adequately by which its body has more things in common with other bodies.
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