E4P39D
Demonstration — Part IV
Latin
Corpus humanum indiget ut conservetur plurimis aliis corporibus (per postulatum 4 partis II). At id quod formam humani corporis constituit, in hoc consistit quod ejus partes motus suos certa quadam ratione sibi invicem communicent (per definitionem ante lemma 4, quam vide post propositionem 13 partis II). Ergo quæ efficiunt ut motus et quietis ratio quam corporis humani partes ad invicem habent, conservetur, eadem humani corporis formam conservant et consequenter efficiunt (per postulata 3 et 6 partis II) ut corpus humanum multis modis affici et ut idem corpora externa multis modis afficere possit adeoque (per propositionem præcedentem) bona sunt. Deinde quæ efficiunt ut corporis humani partes aliam motus et quietis rationem obtineant, eadem (per eandem definitionem partis II) efficiunt ut corpus humanum aliam formam induat hoc est (ut per se notum et in fine præfationis hujus partis monuimus) ut corpus humanum destruatur et consequenter ut omnino ineptum reddatur ne possit pluribus modis affici ac proinde (per propositionem præcedentem) mala sunt. Q.E.D.
English (Elwes 1883)
The human body needs many other bodies for its preservation (II. Post. iv.). But that which constitutes the specific reality (forma) of a human body is, that its parts communicate their several motions one to another in a certain fixed proportion (Def. before Lemma iv. after II. xiii.). Therefore, whatsoever brings about the preservation of the proportion between motion and rest, which the parts of the human body mutually possess, preserves the specific reality of the human body, and consequently renders the human body capable of being affected in many ways and of affecting external bodies in many ways; consequently it is good (by the last Prop.). Again, whatsoever brings about a change in the aforesaid proportion causes the human body to assume another specific character, in other words (see Preface to this Part towards the end, though the point is indeed self--evident), to be destroyed, and consequently totally incapable of being affected in an increased numbers of ways; therefore it is bad. Q.E.D.
Modern English
The human body requires many other bodies for its preservation (E2Post4). What constitutes the specific form of a human body consists in this: that its parts communicate their motions to one another in a certain definite proportion (E2L4). Therefore whatever brings about the preservation of the proportion of motion and rest that the parts of the human body maintain relative to one another also preserves the form of the human body, and consequently (E2Post3) enables the human body to be affected in many ways and to affect external bodies in many ways — and so (E4P38) it is good.
Conversely, whatever causes the parts of the human body to obtain a different proportion of motion and rest (E2L4) thereby causes the human body to take on a different form, that is, (as is self-evident, and as we noted toward the end of the preface to this Part), to be destroyed. The body is therefore rendered wholly unfit to be affected in more ways, and so (E4P38) it is bad. Q.E.D.