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
to publish this writing, such as it is, than to let it run the risk,
by waiting longer, of remaining lost.

There will be seen in it demonstrations of those kinds which do not
produce as great a certitude as those of Geometry, and which even
differ much therefrom, since whereas the Geometers prove their
Propositions by fixed and incontestable Principles, here the
Principles are verified by the conclusions to be drawn from them; the
nature of these things not allowing of this being done otherwise.

It is always possible to attain thereby to a degree of probability
which very often is scarcely less than complete proof. To wit, when
things which have been demonstrated by the Principles that have been
assumed correspond perfectly to the phenomena which experiment has
brought under observation; especially when there are a great number of
them, and further, principally, when one can imagine and foresee new
phenomena which ought to follow from the hypotheses which one employs,
and when one finds that therein the fact corresponds to our prevision.
But if all these proofs of probability are met with in that which I
propose to discuss, as it seems to me they are, this ought to be a
very strong confirmation of the success of my inquiry; and it must be
ill if the facts are not pretty much as I represent them. I would
believe then that those who love to know the Causes of things and who
are able to admire the marvels of Light, will find some satisfaction
in these various speculations regarding it, and in the new explanat