E1P13D

Demonstration — Part I

Latin

Si enim divisibilis esset, partes in quas divideretur vel naturam substantiæ absolute infinitæ retinebunt vel non. Si primum, dabuntur ergo plures substantiæ ejusdem naturæ, quod (per propositionem 5) est absurdum. Si secundum ponatur, ergo (ut supra) poterit substantia absolute infinita desinere esse, quod (per propositionem 11) est etiam absurdum.

English (Elwes 1883)

If it could be divided, the parts into which it was divided would either retain the nature of absolutely infinite substance, or they would not. If the former, we should have several substances of the same nature, which (by Prop. v.) is absurd. If the latter, then (by Prop. vii.) substance absolutely infinite could cease to exist, which (by Prop. xi.) is also absurd.

Modern English

Suppose substance is divisible. Then the parts into which it is divided will either keep the nature of absolutely infinite substance or not. Suppose they do. Then several substances of the same nature would exist, which is absurd (E1P5). Suppose instead they do not. Then (as above) an absolutely infinite substance could cease to be, which is also absurd (E1P11).

Depends on (3)

Propositions