E2P15D
Demonstration — Part II
Latin
Idea quæ esse formale humanæ mentis constituit, est idea corporis (per propositionem 13 hujus) quod (per postulatum 1) ex plurimis valde compositis individuis componitur. At cujuscunque individui corpus componentis datur necessario (per corollarium propositionis 8 hujus) in Deo idea; ergo (per propositionem 7 hujus) idea corporis humani ex plurimis hisce partium componentium ideis est composita. Q.E.D.
English (Elwes 1883)
The idea constituting the actual being of the human mind is the idea of the body (II. xiii.), which (Post. i.) is composed of a great number of complex individual parts. But there is necessarily in God the idea of each individual part whereof the body is composed (II. viii. Coroll.); therefore (II. vii.), the idea of the human body is composed of these numerous ideas of its component parts. Q.E.D.
Modern English
The idea that constitutes the formal being of the human mind is the idea of the body (E2P13), which (by Postulate 1) is composed of a great many highly composite individuals. (E2Post1) But in God there is necessarily an idea of each individual part composing the body (by the Corollary of Proposition 8 of this Part) (E2P8C); therefore (by Proposition 7 of this Part) (E2P7) the idea of the human body is composed of these many ideas of its component parts. Q.E.D.