"All thinges which are, & have beyng, are found under a triple diversitie generall. For, either, they are demed Supernaturall, Naturall, or of a third being. Thinges Supernaturall are immateriall, simple, indivisible, incorruptible, & unchangeable. Things Naturall are materiall, compounded, divisible, corruptible, and changeable. Thinges Supernaturall, are, of the minde onely, comprehended: Things Naturall, of the sense exterior, are able to be perceived. In thinges Naturall, probabilitie and conjecture hath place: But in things Supernaturall, chief demonstration, & most sure Science is to be had. By which properties & comparasons of these two, more easily may be described the state, condition, nature and property of those thinges, which, we before termed of a third being: which, by a peculier name also, are called Thynges Mathematicall. For, these, beyng (in a maner) middle, betwene thinges supernaturall and naturall, are not so absolute and excellent, as thinges supernatural: Nor yet so base and grosse, as things naturall: But are thinges immateriall: and neverthelesse, by materiall things hable somewhat to be signified. And though their particular Images, by Art, are aggregable and divisible, yet the generall Formes, notwithstandyng, are constant, unchangeable, untransformable, and incorruptible. Neither of the sense can they, at any tyme, be perceived or judged. Nor yet, for all that, in the royall mynde of man, first conceived. But, surmountyng the imperfection of conjecture, weenyng and opinion, and commyng short of high intellectuall conception, are the Mercurial fruite of Dianœticall discourse, in perfect imagination subsistyng. A mervaylous neutralitie have these thinges Mathematicall, and also a strange participation betwene thinges supernaturall, immortall, intellectual, simple and indivisible: and thynges naturall, mortall, sensible, compounded and divisible. Probabilitie and sensible prose, may well serve in thinges naturall: and is commendable: In Mathematicall reasoninges, a probable Argument, is nothyng regarded: nor yet the testimony of sense, any whit credited: But onely a perfect demonstration, of truthes certaine, necessary, and invincible: universally and necessaryly concluded: is allowed as sufficient for an Argument exactly and purely Mathematical. ... Neither Number, nor Magnitude, have any Materialitie. First, we will consider of Number, and of the Science Mathematicall, to it appropriate, called Arithmetike: and afterward of Magnitude, and his Science, called Geometrie. ...How Immateriall and free from all matter, Number is, who doth not perceave? yea, who doth not wonderfully wonder at it? For, neither pure Element, nor Aristotele's Quinta Essentia, is hable to serve for Number, as his propre matter. Nor yet the puritie and simplenes of Substance Spirituall or Angelicall, will be found propre enough thereto. And therefore the great & godly Philosopher Anitius Boetius, sayd... All thinges (which from the very first originall being of thinges, have bene framed and made) do appeare to be Formed by the reason of Numbers. For this was the principall example or patterne in the minde of the Creator."