E2P18D
Demonstration — Part II
Latin
Mens (per corollarium præcedentis) corpus aliquod ea de causa imaginatur quia scilicet humanum corpus a corporis externi vestigiis eodem modo afficitur disponiturque ac affectum est cum quædam ejus partes ab ipso corpore externo fuerunt impulsæ sed (per hypothesin) corpus tum ita fuit dispositum ut mens duo simul corpora imaginaretur; ergo jam etiam duo simul imaginabitur atque mens ubi alterutrum imaginabitur, statim et alterius recordabitur. Q.E.D.
English (Elwes 1883)
The mind (II. xvii. Coroll.) imagines any given body, because the human body is affected and disposed by the impressions from an external body, in the same manner as it is affected when certain of its parts are acted on by the said external body; but (by our hypothesis) the body was then so disposed, that the mind imagined two bodies at once; therefore, it will also in the second case imagine two bodies at once, and the mind, when it imagines one, will straightway remember the other. Q.E.D.
Modern English
The mind (E2P17C) imagines any given body because the human body is affected and disposed by the traces of an external body in the same way it was affected when some of its parts were driven by that external body. By hypothesis, however, the body was at that time disposed so that the mind imagined two bodies at once. Therefore now too it will imagine both at once, and when the mind imagines either one, it will at once remember the other as well. Q.E.D.