that several theorems undoubtedly true are discovered by methods
in which infinitesimals are made use of, which could never have
been if their existence included a contradiction in it; I answer
that upon a thorough examination it will not be found that in any
instance it is necessary to make use of or conceive infinitesimal parts
of finite lines, or even quantities less than the minimum sensible; nay,
it will be evident this is never done, it being impossible.

133. IF THE DOCTRINE WERE ONLY AN HYPOTHESIS IT SHOULD BE RESPECTED
FOR ITS CONSEQUENCES.--By what we have premised, it is plain that very
numerous and important errors have taken their rise from those false
Principles which were impugned in the foregoing parts of this treatise;
and the opposites of those erroneous tenets at the same time appear to be
most fruitful Principles, from whence do flow innumerable consequences
highly advantageous to true philosophy. as well as to religion.
Particularly Matter, or the absolute existence of corporeal objects, has
been shown to be that wherein the most avowed and pernicious enemies of
all knowledge, whether human or divine, have ever placed their chief
strength and confidence. And surely, if by distinguishing the real
existence of unthinking things from their being perceived, and allowing
them a subsistance of their own out of the minds of spirits, no one thing
is explained in nature, but on the contrary a great many inexplicable
difficulties arise; if the supposition of Matter is barely precarious, as
not being grounded on so much as one single reason; if its consequences
cannot endure the light of examination and free inquiry, but screen
themselves under the dark and general pretence of "infinites being
incomprehensible"; if withal the removal of this Matter be not attended
with the least evil consequence; if it be not even missed in the world,
but everything as well, nay much easier conceived without it; if, lastly,
both Sceptics and Atheists are for ever silenced upon supposing only