E5P1D
Demonstration — Part V
Latin
Ordo et connexio idearum idem est (per propositionem 7 partis II) ac ordo et connexio rerum et vice versa ordo et connexio rerum idem est (per corollaria propositionum 6 et 7 partis II) ac ordo et connexio idearum. Quare sicuti ordo et connexio idearum in mente fit secundum ordinem et concatenationem affectionum corporis (per propositionem 18 partis II) sic vice versa (per propositionem 2 partis III) ordo et connexio affectionum corporis fit prout cogitationes rerumque ideæ ordinantur et concatenantur in mente. Q.E.D.
English (Elwes 1883)
The order and connection of ideas is the same (II. vii.) as the order and connection of things, and vice versa the order and connection of things is the same (II. vi. Coroll. and vii.) as the order and connection of ideas. Wherefore, even as the order and connection of ideas in the mind takes place according to the order and association of modifications of the body (II. xviii.), so vice versa (III. ii.) the order and connection of modifications of the body takes place in accordance with the manner, in which thoughts and the ideas of things are arranged and associated in the mind. Q.E.D.
Modern English
The order and connection of ideas is the same as the order and connection of things (E2P7), and conversely the order and connection of things is the same as the order and connection of ideas (E2P6C). Therefore, just as the order and connection of ideas in the mind follows the order and connection of the body's affections (E2P18), so conversely (E3P2) the order and connection of the body's affections follows the way thoughts and ideas of things are ordered and connected in the mind. Q.E.D.