Illa quæ omnibus communia quæque æque in parte ac in toto sunt, non possunt concipi nisi adæquate.
Those which are common to all things which are equal in parts and in the whole are not possible to be conceived unless as adequate.
DEMONSTRATIO: Sit A aliquid quod omnibus corporibus commune quodque æque in parte cujuscunque corporis ac in toto est. Dico A non posse concipi nisi adæquate. Nam ejus idea (per corollarium propositionis 7 hujus) erit necessario in Deo adæquata tam quatenus ideam corporis humani quam quatenus ideas habet ejusdem affectionum quæ (per propositiones 16, 25 et 27 hujus) tam corporis humani quam corporum externorum naturam ex parte involvunt hoc est (per propositiones 12 et 13 hujus) hæc idea erit necessario in Deo adæquata quatenus mentem humanam constituit sive quatenus ideas habet quæ in mente humana sunt; mens igitur (per corollarium propositionis 11 hujus) A necessario adæquate percipit idque tam quatenus se quam quatenus suum vel quodcunque externum corpus percipit nec A alio modo potest concipi. Q.E.D.
Let there be a thing A which is common to all bodies which are equal in part of whatsoever body as well as in the whole. I say that thing A is not able to be conceived unless as adequate. For its idea (by IIP7C) will be necessarily adequate in God not only insofar as the idea of the human body but also insofar as it has ideas of its affections which (by IIP16, IIP25 and IIP27) not only of the human body but also the nature of the extended bodies which are involved that is (by IIP12 and IIP13) this idea will be adequate necessarily in God insofar as it constitutes the human mind or insofar as it has ideas which are human in the mind; therefore the mind (by IIPC11) perceives thing A as adequate necessarily and it not only insofar as itself but also insofar as its or whatever external body it perceives and is not able to conceive it in any other way.
COROLLARIUM: Hinc sequitur dari quasdam ideas sive notiones omnibus hominibus communes. Nam (per lemma 2) omnia corpora in quibusdam conveniunt, quæ (per propositionem præcedentem) ab omnibus debent adæquate sive clare et distincte percipi.
From here it follows to be given that such ideas or notions are common to all humans. For (by L2) all bodies occur in such which (by IIP37) from all things ought to be perceived as adequate or clear and distinct.
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