onsieur _Auzout_'s Considerations, in a Letter to
the Publisher of these _Transactions_._

_SIR_,

Together with my most hearty thanks for the favour you were pleased to do
me, in sending me an _Epitome_ of what had been by the ingenious Monsieur
_Auzout_ animadverted on a description, I had made of an _Engine_ for
_grinding spherical Glasses_, I thought my self obliged, both for your
satisfaction, and my own Vindication, to return you my present thoughts
upon those Objections. The chief of which seems to be against the very
_Proposition_ it self: For it appears, that the _Objector_ is somewhat
unsatisfied, that I should propound a thing in _Theory_, without having
first tried the _Practicableness_ of it. But first, I could wish that this
worthy Person had rectified my mistakes, not by speculation, but by
experiments. Next, I have this to answer, that (though I did not tell the
_Reader_ so much, to the end that he might have the more freedom to examine
and judg of the contrivance, yet) it was not meer _Theory_ I propounded,
but somewhat of _History_ and _matter of Fact_: For, I had made trials, as
many as my leisure would permit, not without some good success; but not
having time and opportunity enough to prosecute them, I thought it would
not be unacceptable to such, as enjoyed both, to have a description of a
way altogether _New_, and _Geometrically_ true, and seemingly, not
unpracticable, whereof they might make use, or not, as they should see
reason. But nothing surprised me so much, as, that he is pleased (after he
had declared it a fault, to write this _Theory_, without having reduced it
to practice) to lay it, as he seems to do, in one place of his book, _p._
22 upon the _Royal Society_. Truly, _Sir_, I should think my self most
injurious to that _Noble Company_, had I not endeavoured, even in the
beginning of my Book, to prevent such a misconstruction. And therefore I
cannot but make this interpretation of what Monsieur _Auzout_ saith in this
particular, that either he had not so {65} much of the Language wherein I
have written, as to understand all what was said by me, or, that he had not
read my _Dedication_ to the _Royal Society_, which if he had done, he would
have found, how careful I was, that that _Illustrious Society_ should not
be prejudiced by my _Errors_, that could be so little advantaged by my
_Actions_. And indeed, for any man to look upon the matters published by
their Order or Licence, as if th