An Introduction to the Doctrine of _Plains_ and _Solids_, which is an _Analytical_ Treatise, concerning the solution of _Plains_ and _Solids_, which has been seen (as the Advertiser affirms) before Monsieur _Des Cartes_ had publish'd any thing upon this Subject. A Treatise _De Contactibus Sphaericis_, where he hath demonstrated in _Solids_, what Mr. _Viet_, Master of Requests, had but demonstrated in _Plains_. Another Treatise, wherein he establisheth and demonstrateth the two Books of _Apollonius Pergaeus_, of _Plains_. And a General Method for the dimension of _Curve Lines_, &c. Besides, having a perfect knowledge in Antiquity, he was consulted from all parts upon the difficulties that did emerg therein: he hath explained abundance of obscure places, that are {16} found in the Antients. There have been lately printed some of his Observations upon _Athenaeus_; and he that hath interpreted _Benedetto Castelli_, of the Measure of running waters, hath thence inserted in his Work a very handsome one upon an Epistle of _Synesius_, which was so difficult, that the Jesuit _Petavius_, who hath commented upon this Author, acknowledges, that he could not understand it. He hath also made many Observations upon _Theon of Smyrne_, and upon other Antient Authors: but most part of them are not found but scattered in his Epistles, because he did not write much upon these kinds of Subjects, but to satisfie the curiosity of his friends. All these Mathematical Works, and all these curious searches in Antiquity, did not hinder this great _Virtuoso_ from discharging the duties of his place with much assiduity, and with so much ability, that he hath had the reputation of one of the greatest _Civilians_ of his Age. But that, which is most of all surprizing to many, is, that with all that strength of understanding, which was requisite to make good these rare qualities, lately mentioned, he had so polite and delicate parts, that he composed _Latin_, _French_, and _Spanish_ Verses with the same elegancy, as if he had lived in the time of _Augustus_, and passed the greatest part of his life at the Courts of _France_ and _Spain_. More particulars will perhaps be mention'd of the Works of this Rare person, when all things, that he hath publish'd, shall be recovered, and when liberty shall be obtained of his Worthy Son, to impart unto the World the rest of his Writings, hitherto unpublished. * * * * * _LONDON,_ Printed with Licence, By _John Martyn_, and _James Allestry_, Printers to the _Royal-Society_. {17} * * * * * _Num._ 2. PHILOSOPHICAL _TRANSACTIONS._ * * * * * _Munday_, _April_ 3. 1665. * * * * * The Contents.