Francis Vieta, a Frenchman, a most distinguished man, and on account of his remarkable skill in Mathematical Science the honour of the French nation, first of all with singular genius and with industry hitherto unattempted undertook the restoration of the analytic art, of which subject we are here treating, which after the learned age of the Greeks for a long time had become antiquated and remained uncultivated : and by various treatises which he eloquently and ingeniously wrote in the working out of this line of argument, left a record to posterity of this noble design of his mind. But while he seriously laboured at the restoration of the old Analysis, which he had proposed to himself, he seems not so much to have transmitted to us a restoration of that science, as a new and original method, worked out and illustrated by his own discoveries. This, having been enunciated in general terms, must be explained a little more at length ; so that having shown what was first effected by Vieta in promoting his design, it may be more clear, what was afterwards performed by our very learned author Thomas Harriot, who followed him in these analytical investigations. And at the end of the volume, on page 180, is the following explanatory note : AD MATHIMATICIS STUDIOSOS. ‘Ex omnibus _Thoma Harrioti_ fcriptis Mathematicis,quòd opus hoc Analyticum primum in publicum emiflum fit, haud inconfulto factum eft. Nam, quùm reliqua eius opera, multiplici inuentorum nouitate excellentia, eodem omnino quo tractatus ifte (Logiftices fpeciofsæ exemplis omnimodis totus compofitus) ftilo Logiftico, hactenùs inufitato, confcripta fint, eâ certè ratione fit, vt prodromus hic tractatus, vltra proprium ipfius inæftimabilem vfum, reliquis _Harrioti_ fcriptis, de quorum editione iam ferio cogitatur, pro neceffario preparamento fiue introductorio opportunè inferuire poffit. De quâ quidem accefforiâ operis huius vtilitate rerum Mathematicarum ftudiofos paucis his præmonuiffe operæprecium efle duximus.’ [Which being interpreted reads as follows in English] TO STUDENTS OF MATHEMATICS. It is not without good reason that, of all Thomas Harriot’s Mathematical writings, this on Analysis has been published first. For whereas all his remaining works, remarkable for their manifold novelties of discovery, are written precisely in the same, hitherto unusual, logical style as this treatise (which consists entirely of varied specimens of beautiful reasoning); this was certainly done that this preliminary treatise, besides its own inestimable utility, might suitably serve as a necessary preparation or introduction to the study of Harriot’s remaining works, the publication of which is now under serious consideration. Of this accessory use of this treatise we have thought it worth while to remind mathematical students in these brief remarks.