Page:Philosophical Transactions - Volume 004.djvu/18

 si favor tuus accedat, non ipsam methodum tantum, sed & alia, quæ simul observavi, brevi, Deo bene juvante, censura tuae submittere.

We come next to speak of the last part of the Book, to wit, his Miscellanea, and because it fails in here somewhat properly, we therefore first mention his fourth Chap. De Maximis & Minimis, from which he derives this Proposition;

If any Magnitude (or Number, as the whole) be divided into such parts, that are to each other as a Number to a Number, the Product of those powers of the parts, that are of the same degree, as the parts themselves denominate, if the greatest of all Products of the like powers of the parts of the same magnitude when otherwise divided.

Concerning the Proposition the Author saith thus; Liceret hujus Propositionis Usum prolixius extendere ad determinandas nempe maximas & minima applicatarum in Curvis, tangentes, & similia; verum cum hanc materiam nuper in Exercitatione sua Geometrica; feliciter aggressus sit Vir Clarissimus Michael Angelus Riccius, doctrina & humanitate singulari, orbi literato notissimus, & justi operis spem faciat; frustra nunc pluribus insisterem, cum meliora & prefectiora ab ipso propediem expectari debeant.

That exercitation of Riccio hath been lately re-printed for Moses Pitts, Book-seller in Little-Britain, (and is annexed to Mercators Logarithmotechnia) wherein the Author Riccio promiseth a new Rank of Conical Solids, which cut, do exhibit those Infinite Parabolas and Ellipses, whereby all Æquations may be easily resolved and determined. But the Learned and Modest Slusius in a private Letter concerning these matters, and Riccio's before-mention'd Geometrical Exercitation, saith somewhat more. Diu est etiam ex quo eandem materiam aggressus fueram, qua Methodo, videbis in Miscellaneorum meorum'' Cap. 4. ubi Propositionem universalem demonstravi, ex qua omnia deduci possunt; non tamen deduxi, ne viro amico, qui hanc materiam jam occuparat & a quo multa ac præclara expectari possunt, occasionem bene merendi de Rep. literaria præriperem.''

Concerning the rest of the Miscellanies; Our Author in the 1. Chapt. treates De Infinitis Spiralibus, & spatiorum, ab iis & Rh