Part 1 (2/2)

Of my former wordes, easy it is to be gathered, that _Number_ hath a treble state: One, in the Creator: an other in euery Creature (in respect of his complete const.i.tution:) and the third, in Spirituall and Angelicall Myndes, and in the Soule of m. In the first and third state, _Number_, is termed _Number Numbryng_. But in all Creatures, otherwise, _Number_, is termed _Nuber Numbred_. And in our Soule, Nuber beareth such a swaye, and hath such an affinitie therwith: that some of the old _Philosophers_ taught, _Mans Soule, to be a Number mouyng it selfe_. And in dede, in vs, 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_ therfore, is the discretion discerning, and distincting of thinges. But in G.o.d 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 Conseruation of them in being: And, where and when he will lacke an _Vnit_: there and then, that particular thyng shalbe _Discreated_. Here I stay. But our Seuerallyng, distinctyng, and _Numbryng_, createth nothyng: but of Mult.i.tude considered, maketh certaine and distinct determination. And albeit these thynges be waighty and truthes of great importance, yet (by the infinite goodnes of the Almighty _Ternarie_,) Artificiall Methods and easy wayes are made, by which the zelous Philosopher, may wyn nere this Riuerish _Ida_, this Mountayne of Contemplation: and more then Contemplation. And also, though _Number_, be a thyng so Immateriall, so diuine, and aeternall: yet by degrees, by litle and litle, stretchyng forth, and applying some likenes of it, as first, to thinges Spirituall: and then, bryngyng it lower, to thynges sensibly perceiued: as of a momentanye sounde iterated: then to the least thynges that may be seen, numerable: And at length, (most grossely,) to a mult.i.tude of any corporall thynges seen, or felt: and so, of these grosse and sensible thynges, we are trayned to learne a certaine Image or likenes of numbers: and to vse Arte in them to our pleasure and proffit. So grosse is our conuersation, and dull is our apprehension: while mortall Sense, in vs, ruleth the common wealth of our litle world. Hereby we say, Three Lyons, are three: or a _Ternarie_. Three Egles, are three, or a _Ternarie_.

Which * _Ternaries_, are eche, the _Vnion_, _knot_, and _Vniformitie_, of three discrete and distinct _Vnits_. That is, we may in eche _Ternarie_, thrise, seuerally pointe, and shew a part, _One_, _One_, and _One_. Where, in Numbryng, we say One, two, Three. But how farre, these visible Ones, do differre from our Indiuisible Vnits (in pure _Arithmetike_, princ.i.p.ally considered) no man is ignorant. Yet from these grosse and materiall thynges, may we be led vpward, by degrees, so, informyng our rude Imagination, toward the cceiuyng of _Numbers_, absolutely (:Not supposing, nor admixtyng any thyng created, Corporall or Spirituall, to support, conteyne, or represent those _Numbers_ imagined:) that at length, we may be hable, to finde the number of our owne name, gloriously exemplified and registred in the booke of the _Trinitie_ most blessed and aeternall.

But farder vnderstand, that vulgar Practisers, haue Numbers, otherwise, in sundry Considerations: and extend their name farder, then to Numbers, whose least part is an _Vnit_. For the common Logist, Reckenmaster, or Arithmeticien, in hys vsing of Numbers: of an Vnit, imagineth lesse partes: and calleth them _Fractions_. As of an _Vnit_, he maketh an halfe, and thus noteth it, . and so of other, (infinitely diuerse) partes of an _Vnit_. Yea and farder, hath, _Fractions of Fractions. &c_.

And, forasmuch, as, _Addition_, _Substraction_, _Multiplication_, _Diuision_ and _Extraction of Rotes_, are the chief, and sufficient partes of _Arithmetike_:

[Arithmetike.]

which is, the _Science that demonstrateth the properties, of Numbers, and all operatis, in numbers to be performed_:

[Note.]

”How often, therfore, these fiue sundry sortes of Operations, do, for the most part, of their execution, differre from the fiue operations of like generall property and name, in our Whole numbers practisable, So often, (for a more distinct doctrine) we, vulgarly account and name it, an other kynde of _Arithmetike_.” And by this reason:

[1.]

the Consideration, doctrine, and working, in whole numbers onely: where, of an _Vnit_, is no lesse part to be allowed: is named (as it were) an _Arithmetike_ by it selfe. And so of the _Arithmetike of Fractions_.

[2.]

In lyke sorte, the necessary, wonderfull and Secret doctrine of Proportion, and proportionalytie hath purchased vnto it selfe a peculier maner of handlyng and workyng: and so may seme an other forme of _Arithmetike_.

[3.]

Moreouer, the _Astronomers_, for spede and more commodious calculation, haue deuised a peculier maner of orderyng nubers, about theyr circular motions, by s.e.xagenes, and s.e.xagesmes. By Signes, Degrees and Minutes &c. which commonly is called the _Arithmetike_ of _Astronomical_ or _Phisicall Fractions_. That, haue I briefly noted, by the name of _Arithmetike Circular_. Bycause it is also vsed in circles, not _Astronomicall. &c._

[4.]

Practise hath led _Numbers_ farder, and hath framed them, to take vpon them, the shew of _Magnitudes_ propertie: Which is _Incommensurabilitie_ and _Irrationalitie_. (For in pure _Arithmetike_, an _Vnit_, is the common Measure of all Numbers.) And, here, Nubers are become, as Lynes, Playnes and Solides: some tymes _Rationall_, some tymes _Irrationall_.

And haue propre and peculier characters, (as v. v. and so of other.

Which is to signifie _Rote Square, Rote Cubik: and so forth_:) & propre and peculier fas.h.i.+ons in the fiue princ.i.p.all partes: Wherfore the practiser, estemeth this, a diuerse _Arithmetike_ from the other.

Practise bryngeth in, here, diuerse compoundyng of Numbers: as some tyme, two, three, foure (or more) _Radicall_ nubers, diuersly knit, by signes, of More & Lesse: as thus v12 + v15. Or thus 4v19 + v12 - v2.

&c. And some tyme with whole numbers, or fractions of whole Number, amg them: as 20 + v24. v16 + 33 - v10. 4v44 + 12 + v9. And so, infinitely, may hap the varietie. After this: Both the one and the other hath fractions incident: and so is this _Arithmetike_ greately enlarged, by diuerse exhibityng and vse of Compositions and mixtynges. Consider how, I (beyng desirous to deliuer the student from error and Cauillation) do giue to this _Practise_, the name of the _Arithmetike of Radicall numbers_: Not, of _Irrationall_ or _Surd Numbers_: which other while, are Rationall: though they haue the Signe of a Rote before them, which, _Arithmetike_ of whole Numbers most vsuall, would say they had no such Roote: and so account them _Surd Numbers_: which, generally spok?, is vntrue: as _Euclides_ tenth booke may teach you. Therfore to call them, generally, _Radicall Numbers_, (by reason of the signe v.

prefixed,) is a sure way: and a sufficient generall distinction from all other ordryng and vsing of Numbers: And yet (beside all this) Consider: the infinite desire of knowledge, and incredible power of mans Search and Capacitye: how, they, ioyntly haue waded farder (by mixtyng of speculation and practise) and haue found out, and atteyned to the very chief perfection (almost) of _Numbers_ Practicall vse. Which thing, is well to be perceiued in that great Arithmeticall Arte of _aequation_: commonly called the _Rule of Coss._ or _Algebra_. The Latines termed it, _Regulam Rei & Census_, that is, the +_Rule of the thyng and his value_+. With an apt name: comprehendyng the first and last pointes of the worke. And the vulgar names, both in Italian, Frenche and Spanish, depend (in namyng it,) vpon the signification of the Latin word, _Res_: +_A thing_+: vnleast they vse the name of _Algebra_. And therin (commonly) is a dubble error. The one, of them, which thinke it to be of _Geber_ his inuentyng: the other of such as call it _Algebra_. For, first, though _Geber_ for his great skill in Numbers, Geometry, Astronomy, and other maruailous Artes, mought haue semed hable to haue first deuised the sayd Rule: and also the name carryeth with it a very nere likenes of _Geber_ his name: yet true it is, that a _Greke_ Philosopher and Mathematicien, named _Diophantus_, before _Geber_ his tyme, wrote 13. bookes therof (of which, six are yet extant: and I had them to *vse,

[* Anno. 1550.]

of the famous Mathematicien, and my great frende, _Petrus Montaureus_:) And secondly, the very name, is _Algiebar_, and not _Algebra_: as by the Arabien _Auicen_, may be proued: who hath these precise wordes in Latine, by _Andreas Alpagus_ (most perfect in the Arabik tung) so translated. _Scientia faciendi Algiebar & Almachabel. i. Scientia inueniendi numerum ignotum, per additionem Numeri, & diuisionem & aequationem_. Which is to say: +_The Science of workyng Algiebar and Almachabel_+, that is, the +_Science of findyng an vnknowen number, by Addyng of a Number, & Diuision & aequation_+. Here haue you the name: and also the princ.i.p.all partes of the Rule, touched. To name it, _The rule, or Art of aequation_, doth signifie the middle part and the State of the Rule. This Rule, hath his peculier Characters:

[5.]

and the princ.i.p.al partes of _Arithmetike_, to it appertayning, do differre from the other _Arithmeticall operations_. This _Arithmetike, hath Nubers_ Simple, Cpound, Mixt: and Fractions, accordingly. This Rule, and _Arithmetike of Algiebar_, is so profound, so generall and so (in maner) conteyneth the whole power of Numbers Application practicall: that mans witt, can deale with nothyng, more proffitable about numbers: nor match, with a thyng, more mete for the diuine force of the Soule, (in humane Studies, affaires, or exercises) to be tryed in. Perchaunce you looked for, (long ere now,) to haue had some particular profe, or euident testimony of the vse, proffit and Commodity of Arithmetike vulgar, in the Common lyfe and trade of men. Therto, then, I will now frame my selfe: But herein great care I haue, least length of sundry profes, might make you deme, that either I did misdoute your zelous mynde to vertues schole: or els mistrust your hable witts, by some, to gesse much more. A profe then, foure, fiue, or six, such, will I bryng, as any reasonable man, therwith may be persuaded, to loue & honor, yea learne and exercise the excellent Science of _Arithmetike_.

<script>