P12: No attribute of a substance can be truly conceived from which it follows that the substance can be divided.

Dem.: For the parts into which a substance so conceived would be divided either will retain the nature of the substance or will not. If the first {viz. they retain the nature of the substance}, then (by P8) each part will have to be infinite, and (by P7) its own cause, and (by P5) each part will have to consist of a different attribute. And so many substances will be able to be formed from one, which is absurd (by P6). Furthermore, the parts (by P2) would have nothing in common with their whole, and the whole (by D4 and P10) could both be and be conceived without its parts, which is absurd, as no one will be able to doubt.

But if the second is asserted, viz. that the parts will not retain the nature of substance, then since the whole substance would be divided into equal parts, it would lose the nature of substance, and would cease to be, which (by P7) is absurd.