[Art Mathematicall Deriuatiue.] +An Art Mathematicall deriuatiue, which by Mathematicall demonstratiue Method, in Nũbers, or Magnitudes, ordreth and confirmeth his doctrine, as much & as perfectly, as the matter subiect will admit.+ And for that, I entend to vse the name and propertie of a [A Mechanitien.] _Mechanicien_, otherwise, then (hitherto) it hath ben vsed, I thinke it good, (for distinction sake) to giue you also a brief description, what I meane therby. +A Mechanicien, or a Mechanicall workman is he, whose skill is, without knowledge of Mathematicall demonstration, perfectly to worke and finishe any sensible worke, by the Mathematicien principall or deriuatiue, demonstrated or demonstrable.+ Full well I know, that he which inuenteth, or maketh these demonstrations, is generally called _A speculatiue Mechanicien_: which differreth nothyng from a _Mechanicall Mathematicien_. So, in respect of diuerse actions, one man may haue the name of sundry artes: as, some tyme, of a Logicien, some tymes (in the same matter otherwise handled) of a Rethoricien. Of these trifles, I make, (as now, in respect of my Preface,) small account: to fyle thẽ for the fine handlyng of subtile curious disputers. In other places, they may commaunde me, to giue good reason: and yet, here, I will not be vnreasonable. [+1.+] First, then, from the puritie, absolutenes, and Immaterialitie of Principall _Geometrie_, is that kinde of _Geometrie_ deriued, which vulgarly is counted _Geometrie_: and is the +Arte of Measuring sensible magnitudes, their iust quãtities and contentes.+ [Geometrie vulgar.] This, teacheth to measure, either at hand: and the practiser, to be by the thing Measured: and so, by due applying of Cumpase, Rule, Squire, Yarde, Ell, Perch, Pole, Line, Gaging rod, (or such like instrument) to the Length, Plaine, or Solide measured, [1.] * to be certified, either of the length, perimetry, or distance lineall: and this is called, _Mecometrie_. Or [2.] * to be certified of the content of any plaine Superficies: whether it be in ground Surueyed, Borde, or Glasse measured, or such like thing: which measuring, is named _Embadometrie_. [3.] * Or els to vnderstand the Soliditie, and content of any bodily thing: as of Tymber and Stone, or the content of Pits, Pondes, Wells, Vessels, small & great, of all fashions. Where, of Wine, Oyle, Beere, or Ale vessells, &c, the Measuring, commonly, hath a peculier name: and is called _Gaging_. And the generall name of these Solide measures, is _Stereometrie_. [+2.+] Or els, this _vulgar Geometrie_, hath consideration to teach the practiser, how to measure things, with good distance betwene him and the thing measured: and to vnderstand thereby, either [1.] * how Farre, a thing seene (on land or water) is from the measurer: and this may be called _Apomecometrie_: [2.]