E1P15D
Demonstration — Part I
Latin
Præter Deum nulla datur neque concipi potest substantia (per 14 propositionem) hoc est (per definitionem 3) res quæ in se est et per se concipitur. Modi autem (per definitionem 5) sine substantia nec esse nec concipi possunt; quare hi in sola divina natura esse et per ipsam solam concipi possunt. Atqui præter substantias et modos nil datur (per axioma 1). Ergo nihil sine Deo esse neque concipi potest. Q.E.D.
English (Elwes 1883)
Besides God, no substance is granted or can be conceived (by Prop. xiv.), that is (by Def. iii.) nothing which is in itself and is conceived through itself. But modes (by Def. v.) can neither be, nor be conceived without substance; wherefore they can only be in the divine nature, and can only through it be conceived. But substances and modes form the sum total of existence (by Ax. i.), therefore, without God nothing can be, or be conceived. Q.E.D.
Modern English
Besides God, no substance exists or can be conceived (E1P14), that is, nothing that is in itself and conceived through itself (E1D3). But modes (E1D5) cannot exist or be conceived without substance; so they can only exist in the divine nature and be conceived through it alone. And besides substances and modes there is nothing (E1A1). Therefore nothing can exist or be conceived without God. Q.E.D.