do you judge, when you assert, that the line, in which I have supposed them to concur, cannot make the same right line with those two, that form so small an angle betwixt them?  You must surely have some idea of a right line, to which this line does not agree.  Do you therefore mean that it takes not the points in the same order and by the same rule, as is peculiar and essential to a right line?  If so, I must inform you, that besides that in judging after this manner you allow, that extension is composed of indivisible points (which, perhaps, is more than you intend) besides this, I say, I must inform you, that neither is this the standard from which we form the idea of a right line; nor, if it were, is there any such firmness in our senses or imagination, as to determine when such an order is violated or preserved.  The original standard of a right line is in reality nothing but a certain general appearance; and it is evident right lines may be made to concur with each other, and yet correspond to this standard, though corrected by all the means either practicable or imaginable.

To whatever side mathematicians turn, this dilemma still meets them.  If they judge of equality, or any other proportion, by the accurate and exact standard, viz. the enumeration of the minute indivisible parts, they both employ a standard, which is useless in practice, and actually establish the indivisibility of extension, which they endeavour to explode.  Or if they employ, as is usual, the inaccurate standard, derived from a comparison of objects, upon their general appearance, corrected by measuring and juxtaposition; their first principles, though certain and infallible, are too coarse to afford any such subtile inferences as they commonly draw from them.  The first principles are founded on the imagination and senses:  The conclusion, therefore, can never go beyond, much less contradict these faculties.

This may open our eyes a little, and let us see, that no geometrical demonstration for the infinite divisibility of extension can have so much force as what we naturally attribute to every argument, which is supported by such magnificent pretensions.  At the same time we may learn the reason, why geometry falls of evidence in this single point, while all its other reasonings command our fullest assent and approbation.  And indeed it seems more requisite to give the reason of this exception, than to shew, that we really must make such an exception, and regard all the mathematical arguments for infinite divisibility as utterly sophistical.  For it is evident, that as no idea of quantity is infinitely divisible, there cannot be imagined a more glaring absurdity, than to endeavour to prove, that quantity itself admits of such a division; and to prove this by means of ideas, which are directly opposite in that particular.  And as this absurdity is very glaring in itself, so there is no argument founded on it. which is not attended with a new absurdity, and involves not an evident contradiction.