The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara Part 9

Now end I, with +Archemastrie+. Which name, is not so new, as this Arte is rare. For an other Arte, vnder this, a degree (for skill and power) hath bene indued with this English name before. And yet, this, may serue for our purpose, sufficiently, at this present. +This Arte, teacheth to bryng to actuall experience sensible, all worthy conclusions by all the Artes Mathematicall purposed, & by true Naturall Philosophie concluded: & both addeth to them a farder scope, in the termes of the same Artes, & also by hys propre Method, and in peculier termes, procedeth, with helpe of the foresayd Artes, to the performance of complet Experi?ces, which of no particular Art, are hable (Formally) to be challenged.+ If you remember, how we considered _Architecture_, in respect of all common handworkes: some light may you haue, therby, to vnderstand the Souerainty and propertie of this Science. _Science_ I may call it, rather, then an Arte: for the excellency and Mastershyp it hath, ouer so many, and so mighty Artes and Sciences. And bycause it procedeth by _Experiences_, and searcheth forth the causes of Conclusions, by _Experiences_: and also putteth the Conclusions them selues, in _Experience_, it is named of some, _Scientia Experimentalis_.

The +_Experimentall Science_+. _Nicolaus Cusa.n.u.s_ termeth it so, in hys _Experimentes Statikall_, And an other _Philosopher_,

[R. B.]

of this land Natiue (the floure of whose worthy fame, can neuer dye nor wither) did write therof largely, at the request of _Clement the sixt_.

The Arte carrieth with it, a wonderfull Credit: By reason, it certefieth, sensibly, fully, and completely to the vtmost power of Nature, and Arte. This Arte, certifieth by _Experience_ complete and absolute: and other Artes, with their Argumentes, and Demonstrations, persuade: and in wordes, proue very well their Conclusions. *

But wordes, and Argumentes, are no sensible certifying: nor the full and finall frute of Sciences practisable. And though some Artes, haue in them, _Experiences_, yet they are not complete, and brought to the vttermost, they may be stretched vnto, and applyed sensibly. As for example: the Naturall Philosopher disputeth and maketh goodly shew of reason: And the Astronomer, and the Opticall Mechanicien, put some thynges in _Experience_: but neither, all, that they may: nor yet sufficiently, and to the vtmost, those, which they do, There, then, the _Archemaster_ steppeth in, and leadeth forth on, the _Experiences_, by order of his doctrine _Experimentall_, to the chief and finall power of Naturall and Mathematicall Artes. Of two or three men, in whom, this Description of _Archemastry_ was _Experimentally_, verified, I haue read and hard: and good record, is of their such perfection. So that, this Art, is no fantasticall Imagination: as some Sophister, might, _c.u.m suis Insolubilibus_, make a florish: and da.s.sell your Imagination: and dash your honest desire and Courage, from beleuing these thinges, so vnheard of, so meruaylous, & of such Importance. Well: as you will. I haue forewarned you. I haue done the part of a frende: I haue discharged my Duety toward G.o.d: for my small Talent, at hys most mercyfull handes receiued. To this Science, doth the _Science Alnirangiat_, great Seruice. Muse nothyng of this name. I chaunge not the name, so vsed, and in Print published by other: beyng a name, propre to the Science. Vnder this, commeth _Ars Sintrillia_, by _Artephius_, briefly written. But the chief Science, of the Archemaster, (in this world) as yet knowen, is an other (as it were) OPTICAL Science: wherof, the name shall be told (G.o.d w.i.l.l.yng) when I shall haue some, (more iust) occasion, therof, to Discourse.

Here, I must end, thus abruptly (Gentle frende, and vnfayned louer of honest and necessary verities.) For, they, who haue (for your sake, and vertues cause) requested me, (an old forworne Mathematicien) to take pen in hand: (through the confidence they reposed in my long experience: and tryed sincerity) for the declaryng and reportyng somewhat, of the frute and commodity, by the +Artes Mathematicall, to be atteyned vnto+: euen they, Sore agaynst their willes, are forced, for sundry causes, to satisfie the workemans request, in endyng forthwith: He, so feareth this, so new an attempt, & so costly: And in matter so slenderly (hetherto) among the common Sorte of Studentes, considered or estemed.

And where I was willed, somewhat to alledge, why, in our vulgare Speche, this part of the Princ.i.p.all Science of _Geometrie_, called _Euclides Geometricall Elementes_, is published, to your handlyng: being vnlatined people, and not Vniuersitie Scholers: Verily, I thinke it nedelesse.

[1.]

For, the Honour, and Estimation of the +Vniuersities, and Graduates+, is, hereby, nothing diminished. Seing, from, and by their Nurse Children, you receaue all this Benefite: how great soeuer it be.

[2.]

Neither are their Studies, hereby, any whit hindred. No more, then the Italian _Vniuersities_, as _Academia Bononiensis_, _Ferrariensis_, _Florentina_, _Mediolanensis_, _Patauina_, _Papiensis_, _Perusina_, _Pisana_, _Romana_, _Senensis_, or any one of them, finde them selues, any deale, disgraced, or their Studies any thing hindred, by _Frater Lucas de Burgo_, or by _Nicolaus Tartalea_, who in vulgar Italian language, haue published, not onely _Euclides Geometrie_, but of _Archimedes_ somewhat: and in Arithmetike and Practicall Geometrie, very large volumes, all in their vulgar speche. Nor in Germany haue the famous _Vniuersities_, any thing bene discontent with _Albertus Durerus_, his Geometricall Inst.i.tutions in Dutch: or with _Gulielmus Xylander_, his learned translation of the first sixe bookes of _Euclide_, out of the Greke into the high Dutch. Nor with _Gualterus H.

Riffius_, his Geometricall Volume: very diligently translated into the high Dutch tounge, and published. Nor yet the _Vniuersities_ of Spaine, or Portugall, thinke their reputation to be decayed: or suppose any their Studies to be hindred by the Excellent _P. Nonnius_, his Mathematicall workes, in vulgare speche by him put forth. Haue you not, likewise, in the French tounge, the whole Mathematicall Quadriuie? and yet neither Paris, Orleance, or any of the other Vniuersities of Fraunce, at any time, with the Translaters, or Publishers offended: or any mans Studie thereby hindred?

[3.]

And surely, the Common and Vulgar Scholer (much more, the Gramarian) before his comming to the _Vniuersitie_, shall (or may) be, now (according to _Plato_ his Counsell) sufficiently instructed in _Arithmetike_ and _Geometrie_, for the better and easier learning of all maner of _Philosophie_, _Academicall_, or _Peripateticall_. And by that meanes, goe more cherefully, more skilfully, and spedily forwarde, in his Studies, there to be learned. And, so, in lesse time, profite more, then (otherwise) he should, or could do.

[4.]

Also many good and pregnant Englishe wittes, of young Gentlemen, and of other, who neuer intend to meddle with the profound search and Studie of Philosophie (in the _Vniuersities_ to be learned) may neuerthelesse, now, with more ease and libertie, haue good occasion, vertuously to occupie the sharpnesse of their wittes: where, els (perchance) otherwise, they would in fond exercises, spend (or rather leese) their time: neither seruing G.o.d: nor furdering the Weale, common or priuate.

[5.]

And great Comfort, with good hope, may the _Vniuersities_ haue, by reason of this _Englishe_ +Geometrie, and Mathematicall Praeface+, that they (hereafter) shall be the more regarded, esteemed, and resorted vnto. For, when it shall be knowen and reported, that of the _Mathematicall Sciences_ onely, such great Commodities are ensuing (as I haue specified): and that in dede, some of you vnlatined Studentes, can be good witnesse, of such rare fruite by you enioyed (thereby): as either, before this, was not heard of: or els, not so fully credited: "Well, may all men coniecture, that farre greater ayde, and better furniture, to winne to the Perfection of all Philosophie,

[Vniuersities.]

may in the Vniuersities be had: being the Storehouses & Threasory of all Sciences,

and all Artes, necessary for the best, and most n.o.ble State of Common Wealthes."

[6.]

Besides this, how many a Common Artificer, is there, in these Realmes of England and Ireland, that dealeth with Numbers, Rule, & c.u.mpa.s.se: Who, with their owne Skill and experience, already had, will be hable (by these good helpes and informations) to finde out, and deuise, new workes, straunge Engines, and Instrumentes: for sundry purposes in the Common Wealth? or for priuate pleasure? and for the better maintayning of their owne estate? I will not (therefore) fight against myne owne shadowe. For, no man (I am sure) will open his mouth against this Enterprise. No m (I say) who either hath Charitie toward his brother (and would be glad of his furtherance in vertuous knowledge): or that hath any care & zeale for the bettering of the Cmon state of this Realme. Neither any, that make accompt, what the wiser sort of men (Sage and Stayed) do thinke of them. To none (therefore) will I make any _Apologie,_ for a vertuous acte doing: and for cmending, or setting forth, Profitable Artes to English men, in the English toung. "But, vnto G.o.d our Creator, let vs all be thankefull: for that, +_As he, of his Goodnes, by his Powre, and in his wisedome,

hath Created all thynges, in Number, Waight, and Measure_+: So, to vs, of hys great Mercy, he hath reuealed Meanes, whereby, to atteyne the sufficient and necessary knowledge of the foresayd hys three princ.i.p.all Instrumentes: Which Meanes, I haue abundantly proued vnto you, to be the _Sciences_ and _Artes Mathematicall_."

And though I haue ben pinched with straightnes of tyme: that, no way, I could so pen downe the matter (in my Mynde) as I determined: hopyng of conuenient laysure: Yet. if vertuous zeale, and honest Intent prouoke and bryng you to the readyng and examinyng of this Compendious treatise, I do not doute, but, as the veritie therof (accordyng to our purpose) will be euident vnto you: So the pith and force therof, will persuade you: and the wonderfull frute therof, highly pleasure you. And that you may the easier perceiue, and better remember, the princ.i.p.all pointes, whereof my Preface treateth,

[The Ground platt of this Praeface in a Table.]

I will giue you the +Groundplatt+ of my whole discourse, in a Table annexed: from the first to the last, somewhat Methodically contriued.

If Hast, hath caused my poore pen, any where, to stumble: You will, (I am sure) in part of recompence, (for my earnest and sincere good will to pleasure you), Consider the rockish huge mountaines, and the perilous vnbeaten wayes, which (both night and day, for the while) it hath toyled and labored through, to bryng you this good Newes, and Comfortable profe, of Vertues frute.

So, I Commit you vnto G.o.ds Mercyfull direction, for the rest: hartely besechyng hym, to prosper your Studyes, and honest Intentes: to his Glory, & the Commodity of our Countrey. _Amen_.

_Written at my poore House At Mortlake._

_Anno. 1570. February. 9._

[Decoration]