The first is of a point: Σημεῖον, &c. “_Signum est, cujus est pars nulla_,” that is to say, _a mark is that of which there is no part_. Which definition, not only to a candid, but also to a rigid construer, is sound and useful. But to one that neither will interpret candidly, nor can interpret accurately, is neither useful nor true. Theologers say the soul hath no part, and that an angel hath no part, yet do not think that soul or angel is a point. A mark or as some put instead of it ϛίγμη, which is a mark with a hot iron, is visible; if visible, then it hath quantity, and consequently may be divided into parts innumerable. That which is indivisible is no quantity; and if a point be not quantity, seeing it is neither substance nor quality, it is nothing. And if Euclid had meant it so in his definition, as you pretend he did, he might have defined it more briefly, but ridiculously, thus, _a point is nothing_. Sir Henry Savile was better pleased with the candid interpretation of Proclus, that would have it understood respectively to the matter of geometry. But what meaneth this _respectively to the matter of geometry_? It meaneth this, that no argument in any geometrical demonstration should be taken from the division, quantity, or any part of a point; which is as much as to say, a point is that whose quantity is not drawn into the demonstration of any geometrical conclusion; or, which is all one, whose quantity is not considered. An accurate interpreter might make good the definition thus, _a point is that which is undivided_; and this is properly the same with _cujus non est pars_: for there is a great difference between _undivided_ and _indivisible_, that is, between _cujus non est pars_, and _cujus non potest esse pars_. Division is an act of the understanding; the understanding is therefore that which maketh parts, and there is no part where there is no consideration but of one. And consequently Euclid’s definition of a point is accurately true, and the same with mine, which is, that _a point is that body whose quantity is not considered_. And _considered_ is that, as I have defined it chap. I. at the end of the third article, which is not put to account in demonstration. Euclid therefore seemeth not to be of your opinion, that say a point is nothing. But why then doth he never use this definition in the demonstration of any proposition? Whether he useth it expressly or no, I remember not; but the sixteenth proposition of the third book without the force of this definition is undemonstrated.