Diuine _Plato_, the great Master of many worthy Philosophers, and the constant auoucher, and pithy perswader of _Vnum_, _Bonum_, and _Ens_: in his Schole and Academie, sundry times (besides his ordinary Scholers) was visited of a certaine kinde of men, allured by the noble fame of _Plato_, and the great commendation of hys profound and profitable doctrine. But when such Hearers, after long harkening to him, perceaued, that the drift of his discourses issued out, to conclude, this _Vnum_, _Bonum_, and _Ens_, to be Spirituall, Infinite, Æternall, Omnipotent, &c. Nothyng beyng alledged or expressed, How, worldly goods: how, worldly dignitie: how, health, Strẽgth or lustines of body: nor yet the meanes, how a merueilous sensible and bodyly blysse and felicitie hereafter, might be atteyned: Straightway, the fantasies of those hearers, were dampt: their opinion of _Plato_, was clene chaunged: yea his doctrine was by them despised: and his schole, no more of them visited. Which thing, his Scholer, _Aristotle_, narrowly cõsidering, founde the cause therof, to be, “For that they had no forwarnyng and information, in generall,” whereto his doctrine tended. For, so, might they haue had occasion, either to haue forborne his schole hauntyng: (if they, then, had misliked his Scope and purpose) or constantly to haue continued therin: to their full satisfaction: if such his finall scope & intent, had ben to their desire. Wherfore, _Aristotle_, euer, after that, vsed in brief, to forewarne his owne Scholers and hearers, “both of what matter, and also to what ende, he tooke in hand to speake, or teach.” While I consider the diuerse trades of these two excellent Philosophers (and am most sure, both, that _Plato_ right well, otherwise could teach: and that _Aristotle_ mought boldely, with his hearers, haue dealt in like sorte as _Plato_ did) I am in no little pang of perplexitie: Bycause, that, which I mislike, is most easy for me to performe (and to haue _Plato_ for my exãple.) And that, which I know to be most commendable: and (in this first bringyng, into common handling, the _Artes Mathematicall_) to be most necessary: is full of great difficultie and sundry daungers. Yet, neither do I think it mete, for so straunge matter (as now is ment to be published) and to so straunge an audience, to be bluntly, at first, put forth, without a peculiar Preface: Nor (Imitatyng _Aristotle_) well can I hope, that accordyng to the amplenes and dignitie of the _State Mathematicall_, I am able, either playnly to prescribe the materiall boundes: or precisely to expresse the chief purposes, and most wonderfull applications therof. And though I am sure, that such as did shrinke from _Plato_ his schole, after they had perceiued his finall conclusion, would in these thinges haue ben his most diligent hearers (so infinitely mought their desires, in fine and at length, by our _Artes Mathematicall_ be satisfied) yet,