... 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 mateniall, compounded, divisible, corruptible, and changeable. Things Supernaturall, are of the minde onely comprehended. Things Naturall of the sense exterior ar hable to be perceived. In thinges Naturall, probabilitie and conjecture hath place. But in things Supernaturall, chief demostration, & most sure Science is to be had. By which properties and comparisons of these two, more easily may be described the state, condition, nature and property of those thinges which, we before termed of a third thing being: which, by a peculiar 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 things 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 subsistyng, a mervaylous newtralitie have these thinges Mathematicall, and also a stratinge participion betwene thinges supernaturall, immortall, intellectual, simple and indivisible, and thyriges naturall, mortall, sensible, compounded and divisible. Probabilitie and sensible profe may well serve in thinges naturall, and is commendable. In Mathematicall reasoninges, a probable Argument is nothyng regarded, nor yet 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.

Of Mathernaticall thinges are two phincipall kindes, namely: Number, and Magnitude. Number, we define to be a certayne Mathernaticall Sume of Units. And, an Unit is that thing Mathernaticall, Indivisible, by participation of some likenes of whose property, any thing, which is indeede or is counted [as] One, may resonably be called One. We account an Unit a thing Mathematicall though it be no Number, and also indivisible. Because, of it, materially, Number doth consist: which, principally, is a thing Mathernaticall. Magnitude is a thing Mathematicall, by participation of some likenes of whose nature, any thing is judged long, broade, or thicke. A thicke Magnitude we call a Solide, or a Body. What Magnitude so ever is Solide or Thicke, is also broade & long. A broade magnitude we call a Superficies or a Plaine. Every playne magnitude, hath also length. A long Magnitude, we terme a Line. A Line is neither thicke nor broade, but onely long. Every certayne Line hath two endes: The endes of a line, are Pointes called. A Point is a thing Mathernaticall, indivisible, which may have a certayne determined situation. If a Poynt move from a determined situation, the way wherein it moved is also a Line, mathematically produced. Whereupon, of the auncient Mathematiciens, a Line is called the race or course of a Point. A Poynt we define, by the name of a thing Mathernaticall: though it be no Magnitude, and indivisible: because it is the propre ende and bound of a Line, which is a true Magnitude. And Magnitude we may define to be that thing Mathernaticall, which is divisible for ever: in partes divisible, long, broade or thicke. Therefore, Though a Poymbe no Magnitude, yet Terminatively we recken it a thing Mathernaticall (as I sayd) by reason it is properly the end, and bound of a line.

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 Geomaetrie. But that name contenteth me not: whereof a word or two hereafter shall be sayd. 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 Aristoteles, Quinta Essentia, is liable to serve for Number, as his propre matter. Nor yet the punitie and simplenes of Substance Spirituall or Angelicall, will be found propre enough thereto. And therefore the great & godly Philosopoher Anitius Boetius, sayd: Omnia quacunq, a primava rerum natura constructa sunt, Numerorum videntur ratione formata. Hoc enim Juit principale in animo Conditoris Exemplar. That is: All things (whichfrom the veryfirst 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 orpatterne in the minde ofthe Creator. O comfortable Allurement, 0 ravishing perswasion, to deale with a Science, whose Subject, is so Auncient, so pure, so excellent, so surmounting all creatures, so used of the Almighty and incomprehensible wisdome of the Creator, in the distinct creation of all creatures, in all their distinct partes, properties, natures, and vertues; by order, and most absolute number, brought from Nothing to the Formalitie of their being and state. By Numbers propertie therefore, of us by all possible meanes (to the perfection of the Science) learned, we may both winde and draw our selves into the inward and deepe search and vew, of all creatures distinct vertues, natures, properties, and Formes. And also, farder, anise, clime, ascend and mount up (with Speculative winges) in spirit, to behold in the Glas of Creation, the Forme of Formes, the Exemplar of all thinges Numerable, both visible and invisible, mortall and immortall, Corporall and Spirituall. Part of this profound and divine Science had Joachim the Prophesier atteyned unto: by Numbers Formall, Naturall, and Rationall, forseyng, concludyng, and forshewyng great particular events, long before their comining. His bookes yet remainyng hereof, are good prose. And the noble Earle of Mirandula, (besides that,) a sufficient witnesse: that Ioachim, in his prophesies, proceded by no other way than by Numbers Formall. And this Earle hym selfe, in Rome, set up 900 Conclusions, in all kinde of Sciences, openly to be disputed of And among the rest, in his Conclusions Mathernaticall, (in the eleventh Conclusion) hath in Latin, this English sentence: By Numbers, a way is had, to the searchyng out and understanding of every thing, hable to be knowen. For the verifying ofwhich Conclusion, 1promise to aunswere to the 74 Questions, under written, by the way offumbers. Which Conclusions I omit here to rehearse: as well avoidyng superfluous prolixitie as bycause loannes Picus, workes, are commonly had. But, in any case, I would that those Conclusions were red diligently, and perceived of such as are earnest Observers and Considerers of the constant law of numbers which is planted in thyngs Naturall and Supernaturall, and is prescribed to all Creatures, inviolably to be kept. For, so, besides many other thinges in those Conclusions to be marked, it would apeare how sincerely, & within my boundes I disclose the wonderfull mysteries by numbers to be atteyned unto.

Of my former wordes, easy it is to be gathered that Number hath a treble state: One, in the Creator; an other in every Creature (in respect of his complete constitution); and the third,in Spirituall and Angelicall Myndes, and in the Soule of man. In the first and third state, Number, is termed Number Numbryng. But in all Creatures, otherwise, Number, is termed Number Numbred. And in our Soule, Number beareth such a swaye, and hath such an affinitie therewith: that some of the old Philosophers taught, Man's Soule to be a Number movyng it selfe. And in dede, in us, though it be a very Accident yet such an Accident it is, that before all Creatures it had perfect beyng in the Creator, Sempiternally. Number Numbryng therefore, is the discretion discerning, and distincting of thinges. But in God the Creator this discretion, in the beginnyng, produced orderly and distinctly all thinges. For his Numbryng then was his Creatyng of all thinges. And his Continuall Numbryng of all thinges is the conservation of them in beffig. And where and when he will lacke an Unit, there and then that particular thyng shalbe Discreated. Here I stay....