E3P12D
Demonstration — Part III
Latin
Quamdiu humanum corpus affectum est modo qui naturam corporis alicujus externi involvit tamdiu mens humana idem corpus ut præsens contemplabitur (per propositionem 17 partis II) et consequenter (per propositionem 7 partis II) quamdiu mens aliquod externum corpus ut præsens contemplatur hoc est (per ejusdem propositionis 17 scholium) imaginatur tamdiu humanum corpus affectum est modo qui naturam ejusdem corporis externi involvit atque adeo quamdiu mens ea imaginatur quæ corporis nostri agendi potentiam augent vel juvant tamdiu corpus affectum est modis qui ejusdem agendi potentiam augent vel juvant (vide postulatum 1 hujus) et consequenter (per propositionem 11 hujus) tamdiu mentis cogitandi potentia augetur vel juvatur ac proinde (per propositionem 6 vel 9 hujus) mens quantum potest eadem imaginari conatur. Q.E.D.
English (Elwes 1883)
So long as the human body is affected in a mode, which involves the nature of any external body, the human mind will regard that external body as present (II. xvii.), and consequently (II. vii.), so long as the human mind regards an external body as present, that is (II. xvii. note), conceives it, the human body is affected in a mode, which involves the nature of the said external body; thus so long as the mind conceives things, which increase or help the power of activity in our body, the body is affected in modes which increase or help its power of activity (III. Post. i.); consequently (III. xi.) the mind's power of thinking is for that period increased or helped. Thus (III. vi., ix.) the mind, as far as it can, endeavours to imagine such things. Q.E.D.
Modern English
For as long as the human body is affected in a way that involves the nature of some external body, the human mind will regard that external body as present (E2P17), and consequently (E2P7), for as long as the human mind regards an external body as present, that is (E2P17), imagines it, the human body is affected in a way that involves the nature of that external body. So for as long as the mind imagines things that increase or help the power of activity of our body, the body is affected in ways that increase or help its power of activity (E3Post1), and consequently (E3P11) the mind's power of thinking is for that period increased or helped. The mind therefore (E3P6) strives, as much as it can, to imagine such things. Q.E.D.