P R E F A C E .

things that I publish now, and not to detract from the merit of those who, without having seen anything of what I had written, may have found themselves treating similar matters: as indeed happened to two excellent geometersIn the 17th century, "geometer" was a common term for a mathematician., Messrs. Newton and Leibniz, regarding the problem of the shape of lenses for focusing rays when one of the surfaces is given.

One might ask why I have delayed so long in bringing this work to light. The reason is that I had written it rather carelessly in the language in which it is seenreferring to French, the language of the original publication, rather than Latin which was the standard for scientific works at the time., with the intention of translating it into Latin, doing so to give closer attention to the subject matter. After which I proposed to provide it along with another Treatise on DioptricsDioptrics is the branch of optics that deals with the refraction of light through lenses., where I explain the effects of telescopes, and what else pertains to that science. But the pleasure of novelty having ceased, I have postponed the execution of this design from time to time, and I do not know when I might yet have completed it, being often distracted either by business or by some new study. Considering this, I finally judged that it was better to let this writing appear as it is, rather than to let it run the risk, by waiting longer, of remaining lost.

One will see in it those kinds of demonstrations, which