E1P12D
Demonstration — Part I
Latin
Partes enim in quas substantia sic concepta divideretur, vel naturam substantiæ retinebunt vel non. Si primum, tum (per 8 propositionem) unaquæque pars debebit esse infinita et (per propositionem 6) causa sui et (per propositionem 5) constare debebit ex diverso attributo adeoque ex una substantia plures constitui poterunt, quod (per propositionem 6) est absurdum. Adde quod partes (per propositionem 2) nihil commune cum suo toto haberent et totum (per definitionem 4 et propositionem 10) absque suis partibus et esse et concipi posset, quod absurdum esse nemo dubitare poterit. Si autem secundum ponatur quod scilicet partes naturam substantiæ non retinebunt, ergo cum tota substantia in æquales partes esset divisa, naturam substantiæ amitteret et esse desineret, quod (per propositionem 7) est absurdum.
English (Elwes 1883)
The parts into which substance as thus conceived would be divided either will retain the nature of substance, or they will not. If the former, then (by Prop. viii.) each part will necessarily be infinite, and (by Prop. vi.) self--caused, and (by Prop. v.) will perforce consist of a different attribute, so that, in that case, several substances could be formed out of one substance, which (by Prop. vi.) is absurd. Moreover, the parts (by Prop. ii.) would have nothing in common with their whole, and the whole (by Def. iv. and Prop. x.) could both exist and be conceived without its parts, which everyone will admit to be absurd. If we adopt the second alternative--namely, that the parts will not retain the nature of substance--then, if the whole substance were divided into equal parts, it would lose the nature of substance, and would cease to exist, which (by Prop. vii.) is absurd.
Modern English
The parts into which a substance so conceived would be divided will either keep the nature of substance or not.
Suppose they do. Then each part would have to be infinite (E1P8), be *causa sui* (E1P6), and consist of a different attribute (E1P5), so several substances could be formed from one, which is absurd (E1P6). Add to this that the parts would have nothing in common with their whole (E1P2), and the whole could exist and be conceived without its parts (E1D4)(E1P10), which no one can doubt is absurd.
Suppose instead they do not keep the nature of substance. Then, when the whole substance was divided into equal parts, it would lose the nature of substance and cease to be, which is absurd (E1P7).