[Note the worde, Vnit, to expresse the Greke Monas, & not Vnitie: as we haue all, commonly, till now, vsed.]
Of _Mathematicall_ thinges, are two principall kindes: namely, _Number_, and _Magnitude_.
_Number_, we define, to be, a certayne Mathematicall Sũme, of _Vnits_. And, an _Vnit_, is that thing Mathematicall, Indiuisible, by participation of some likenes of whose property, any thing, which is in deede, or is counted One, may resonably be called One. We account an _Vnit_, a thing _Mathematicall_, though it be no Number, and also indiuisible: because, of it, materially, Number doth consist: which, principally, is a thing _Mathematicall_.
_Magnitude_ is a thing _Mathematicall_, by participation of some likenes of whose nature, any thing is iudged long, broade, or thicke. “A thicke _Magnitude_ we call a _Solide_, or a _Body_. What _Magnitude_ so euer, is Solide or Thicke, is also broade, & long. A broade magnitude, we call a _Superficies_ or a Plaine. Euery playne magnitude, hath also length. A long magnitude, we terme a _Line_. A _Line_ is neither thicke nor broade, but onely long: Euery certayne Line, hath two endes:
The endes of a line, are _Pointes_ called. A _Point_, is a thing _Mathematicall_, indiuisible, which may haue a certayne determined situation.” If a Poynt moue from a determined situation, the way wherein it moued, 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 Mathematicall: though it be no Magnitude, and indiuisible: 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 _Mathematicall_, which is diuisible for euer, in partes diuisible, long, broade or thicke. Therefore though a Poynt be no _Magnitude_, yet _Terminatiuely_, we recken it a thing _Mathematicall_ (as I sayd) by reason it is properly the end, and bound of a line. Neither _Number_, nor _Magnitude_, haue 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_. 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 perceaue? yea, who doth not wonderfully wõder at it? For, neither pure _Element_, nor _Aristoteles, Quinta Essentia_, is hable to serue 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: _Omnia quæcun[que] a primæua rerum natura constructa sunt, Numerorum videntur ratione formata. Hoc enim fuit principale in animo Conditoris Exemplar_. That is: +_All thinges (which from the very first originall being of thinges, haue 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_.+ O comfortable allurement, O rauishing perswasion, to deale with a Science, whose Subiect, is so Auncient, so pure, so excellent, so surmounting all creatures, so vsed 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 vs, by all possible meanes, (to the perfection of the Science) learned, we may both winde and draw our selues into the inward and deepe search and vew, of all creatures distinct vertues, natures, properties, and _Formes_: And also, farder, arise, clime, ascend, and mount vp (with Speculatiue winges) in spirit, to behold in the Glas of Creation, the _Forme of Formes_, the _Exemplar Number_ of all thinges _Numerable_: both visible and inuisible, mortall and immortall, Corporall and Spirituall. Part of this profound and diuine Science, had _Ioachim_ the Prophesier atteyned vnto: by _Numbers Formall, Naturall_, and _Rationall_, forseyng, concludyng, and forshewyng great particular euents, long before their comming. His bookes yet remainyng, hereof, are good profe: And the noble Earle of _Mirandula_, (besides that,) a sufficient witnesse: that _Ioachim, in his prophesies, proceded by no other way, then by Numbers Formall_. And this Earle hym selfe, in Rome,