There have been many objections drawn from the mathematics against the indivisibility of the parts of extension: though at first sight that science seems rather favourable to the present doctrine; and if it be contrary in its DEMONSTRATIONS, it is perfectly conformable in its definitions.

My present business then must be to defend the definitions, and refute the demonstrations.
A surface is DEFINed to be length and breadth without depth: A line to be length without breadth or depth: A point to be what has neither length, breadth nor depth.

It is evident that all this is perfectly unintelligible upon any other supposition than that of the composition of extension by indivisible points or atoms.

How else coued any thing exist without length, without breadth, or without depth?
Two different answers, I find, have been made to this argument; neither of which is in my opinion satisfactory.

The first is, that the objects of geometry, those surfaces, lines and points, whose proportions and positions it examines, are mere ideas in the mind; I and not only never did, but never can exist in nature.