De lineis insecabilibus

Are there indivisible lines? And, generally, is there a simple unit in every class of quanta?

§ 1. Some people maintain this thesis on the following grounds: —

(i) If we recognize the validity of the predicates * big ‘ and ‘ great ‘, we must equally recognize the validity of their opposites, * little ‘ and ‘ small ‘. Now that which admits practically an infinite number of divisions, is * big * not * little ‘ (or ‘great* not ‘small’). Hence, the ‘little’ quantum and the ‘ small ‘ quantum will clearly admit only a finite number of divisions. But if the divisions are finite in number, there must be a simple magnitude. Hence in all classes of quanta there will be found a simple unit, since in all of them the predicates ‘ little ‘ and * small * apply.

(ii) Again, if there is an Idea of line, and if the Idea is first of the things called by its name: — then, since the parts are by nature prior to their whole, the Ideal Line must be indivisible. And, on the same principle, the Ideal Square, the Ideal Triangle, and all the other Ideal Figures — and, generalizing, the Ideal Plane and the Ideal Solid — must be without parts: for otherwise it will result that there are elements prior to each of them.