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 nũbers, about theyr circular motions, by Sexagenes, and Sexagesmes. 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, Nũbers are become, as Lynes, Playnes and Solides: some tymes _Rationall_, some tymes _Irrationall_. And haue propre and peculier characters, (as ²√. ³√. and so of other. Which is to signifie _Rote Square, Rote Cubik: and so forth_:) & propre and peculier fashions in the fiue principall 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_ nũbers, diuersly knit, by signes, of More & Lesse: as thus ²√12 + ³√15. Or thus ⁴√19 + ³√12 - ²√2. &c. And some tyme with whole numbers, or fractions of whole Number, amõg them: as 20 + ²√24. ³√16 + 33 - ²√10. ⁴√44 + 12¼ + ³√9. 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 spokẽ, is vntrue: as _Euclides_ tenth booke may teach you. Therfore to call them, generally, _Radicall Numbers_, (by reason of the signe √. 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 _Æquation_: commonly called the _Rule of Coss._ or _Algebra_. The Latines termed it,