and I communicated it in the year 1678 to the learned persons who then
composed the Royal Academy of Science, to the membership of which the
King had done me the honour of calling, me. Several of that body who
are still alive will remember having been present when I read it, and
above the rest those amongst them who applied themselves particularly
to the study of Mathematics; of whom I cannot cite more than the
celebrated gentlemen Cassini, Römer, and De la Hire. And, although I
have since corrected and changed some parts, the copies which I had
made of it at that time may serve for proof that I have yet added
nothing to it save some conjectures touching the formation of Iceland
Crystal, and a novel observation on the refraction of Rock Crystal. I
have desired to relate these particulars to make known how long I have
meditated the things which now I publish, and not for the purpose of
detracting from the merit of those who, without having seen anything
that I have written, may be found to have treated of like matters: as
has in fact occurred to two eminent Geometricians, Messieurs Newton
and Leibnitz, with respect to the Problem of the figure of glasses for
collecting rays when one of the surfaces is given.

One may ask why I have so long delayed to bring this work to the
light. The reason is that I wrote it rather carelessly in the Language
in which it appears, with the intention of translating it into Latin,
so doing in order to obtain greater attention to the thing. After
which I proposed to myself to give it out along with another Treatise
on Dioptrics, in which I explain the effects of Telescopes and those
things which belong more to that Science. But the pleasure of novelty
being past, I have put off from time to time the execution of this
design, and I know not when I shall ever come to an end if it, being
often turned aside either by business or by some new study.
Considering which I have finally judged that it was better worth while