Part 6 (1/2)

[* _Note this Corollary._]

* This, my Demonstrati is more generall, then onely in Square Pyramis or Cone: Consider well. Thus, haue I, both Mathematically and Mechanically, ben very long in wordes: yet (I trust) nothing tedious to them, who, to these thinges, are well affected. And verily I am forced (auoiding prolixitie) to omit sundry such things, easie to be practised: which to the Mathematicien, would be a great Threasure: and to the Mechanicien, no small gaine.

[* The great Commodities following of these new Inuentions.]

* Now may you, +Betwene two lines giuen, finde two middle proportionals, in Continuall proportion: by the hollow Parallelipipedon, and the hollow Pyramis, or Cone.+ Now, any Parallelipipedon rectangle being giuen: thre right lines may be found, proportionall in any proportion a.s.signed, of which, shal be produced a Parallelipipedon, aequall to the Parallelipipedon giuen. Hereof, I noted somwhat, vpon the 36.

proposition, of the 11. boke of _Euclide_. Now, all those thinges, which _Vitruuius_ in his Architecture, specified hable to be done, by dubbling of the Cube: Or, by finding of two middle proportionall lines, betwene two lines giuen, may easely be performed. Now, that Probleme, which I noted vnto you, in the end of my Addition, vpon the 34. of the 11. boke of _Euclide_, is proued possible. Now, may any regular body, be Transformed into an other, &c. Now, any regular body: any Sphere, yea any Mixt Solid: and (that more is) Irregular Solides, may be made (in any proporti a.s.signed) like vnto the body, first giuen. Thus, of a _Manneken_, (as the _Dutch_ Painters terme it) in the same _Symmetrie_, may a Giant be made: and that, with any gesture, by the Manneken vsed: and contrarywise. Now, may you, of any Mould, or Modell of a s.h.i.+p, make one, of the same Mould (in any a.s.signed proportion) bigger or lesser.

Now, may you, of any * Gunne, or little peece of ordinauce, make an other, with the same _Symmetrie_ (in all pointes) as great, and as little, as you will. Marke that: and thinke on it. Infinitely, +may you apply this, so long sought for, and now so easily concluded: and withall, so willingly and frankly communicated to such, as faithfully deale with vertuous studies.+

[Such is the Fruite of the Mathematicall Sciences and Artes.]

Thus, can the Mathematicall minde, deale Speculatiuely in his own Arte: and by good meanes, Mount aboue the cloudes and sterres: And thirdly, he can, by order, Descend, to frame Naturall thinges, to wonderfull vses: and when he list, retire home into his owne Centre: and there, prepare more Meanes, to Ascend or Descend by: and, all, to the glory of G.o.d, and our honest delectation in earth.

Although, the Printer, hath looked for this Praeface, a day or two, yet could I not bring my pen from the paper, before I had giuen you comfortable warning, and brief instructions, of some of the Commodities, by _Statike_, hable to be reaped: In the rest, I will therfore, be as brief, as it is possible: and with all, describing them, somwhat accordingly. And that, you shall perceiue, by this, which in order commeth next. For, wheras, it is so ample and wonderfull, that, an whole yeare long, one might finde fruitfull matter therin, to speake of: and also in practise, is a Threasure endeles: yet will I glanse ouer it, with wordes very few.

This do I call +Anthropographie+. Which is an Art restored, and of my preferment to your Seruice. I pray you, thinke of it, as of one of the chief pointes, of Humane knowledge. Although it be, but now, first Cfirmed, with this new name: yet the matter, hath from the beginning, ben in consideration of all perfect Philosophers. +Anthropographie, is the description of the Number, Measure, Waight, figure, Situation, and colour of euery diuerse thing, conteyned in the perfect body of MAN: with certain knowledge of the Symmetrie, figure, waight, Characterization, and due locall motion, of any parcell of the sayd body, a.s.signed: and of Nubers, to the sayd parcell appertainyng.+ This, is the one part of the Definition, mete for this place: Sufficient to notifie, the particularitie, and excellency of the Arte: and why it is, here, ascribed to the Mathematicals. Yf the description of the heauenly part of the world, had a peculier Art, called _Astronomie:_ If the description of the earthly Globe, hath his peculier arte, called _Geographie_. If the Matching of both, hath his peculier Arte, called _Cosmographie:_ Which is the Descripti of the whole, and vniuersall frame of the world: Why should not the description of

[MAN is the Lesse World.]

him, who is the Lesse world: and, fr the beginning, called _Microcosmus_ (that is. _The Lesse World._) And for whose sake, and seruice, all bodily creatures els, were created: Who, also, partic.i.p.ateth with Spirites, and Angels: and is made to the Image and similitude of _G.o.d_: haue his peculier Art? and be called the _Arte of Artes_: rather, then, either to want a name, or to haue to base and impropre a name? You must of sundry professions, borow or challenge home, peculier partes hereof: and farder procede: as, G.o.d, Nature, Reason and Experience shall informe you. The Anatomistes will restore to you, some part: The Physiognomistes, some: The Chyromantistes some. The Metaposcopistes, some: The excellent, _Albert Durer_, a good part: the Arte of Perspectiue, will somwhat, for the Eye, helpe forward: _Pythagoras_, _Hipocrates_, _Plato_, _Galenus_, _Meletius_, & many other (in certaine thinges) will be Contributaries. And farder, the Heauen, the Earth, and all other Creatures, will eche shew, and offer their Harmonious seruice, to fill vp, that, which wanteth hereof: and with your own Experience, concluding: you may Methodically register the whole, for the posteritie: Whereby, good profe will be had, of our Harmonious, and

[Micro Cosmus.]

Microcosmicall const.i.tution.

The outward Image, and vew hereof: to the Art of _Zographie_ and Painting, to Sculpture, and Architecture: (for Church, House, Fort, or s.h.i.+p) is most necessary and profitable: for that, it is the chiefe base and foundation of them.

[* Lib. 3. Cap. 1.]

Looke in * _Vitruuius_, whether I deale sincerely for your behoufe, or no. Looke in _Albertus Durerus_, _De Symmetria humani Corporis_. Looke in the 27. and 28. Chapters, of the second booke, _De occulta Philosophia_. Consider the _Arke_ of _Noe_. And by that, wade farther.

Remember the _Delphicall Oracle NOSCE TEIPSVM_ +_(Knowe thy selfe)_+ so long agoe p.r.o.nounced: of so many a Philosopher repeated: and of the _Wisest_ attempted: And then, you will perceaue, how long agoe, you haue bene called to the Schole, where this Arte might be learned. Well. I am nothing affrayde, of the disdayne of some such, as thinke Sciences and Artes, to be but Seuen. Perhaps, those Such, may, with ignorance, and shame enough, come short of them Seuen also: and yet neuerthelesse they can not prescribe a certaine number of Artes: and in eche, certaine vnpa.s.sable boundes, to G.o.d, Nature, and mans Industrie. New Artes, dayly rise vp: and there was no such order taken, that,

All Artes, should in one age, or in one land, or of one man, be made knowen to the world. Let vs embrace the giftes of G.o.d, and wayes to wisedome, in this time of grace, from aboue, continually bestowed on them, who thankefully will receiue them: _Et bonis Omnia Cooperabuntur in bonum._

+Trochilike, is that Art Mathematicall, which demonstrateth the properties of all Circular motions, Simple and Compounde.+ And bycause the frute hereof, vulgarly receiued, is in Wheles, it hath the name of _Trochilike:_ as a man would say, _Whele Art_. By this art, a Whele may be geuen which shall moue ones about, in any tyme a.s.signed. Two Wheles may be giuen, whose turnynges about in one and the same tyme, (or equall tymes), shall haue, one to the other, any proportion appointed. By Wheles, may a straight line be described: Likewise, a Spirall line in plaine, Conicall Section lines, and other Irregular lines, at pleasure, may be drawen. These, and such like, are princ.i.p.all Conclusions of this Arte: and helpe forward many pleasant and profitable Mechanicall workes:

[Saw Milles.]

As Milles, to Saw great and very long Deale bordes, no man being by.

Such haue I seene in Germany: and in the Citie of Prage: in the kingdome of Bohemia: Coyning Milles, Hand Milles for Corne grinding: And all maner of Milles, and Whele worke: By Winde, Smoke, Water, Waight, Spring, Man or Beast, moued. Take in your hand, _Agricola De re Metallica:_ and then shall you (in all Mines) perceaue, how great nede is, of Whele worke. By Wheles, straunge workes and incredible, are done: as will, in other Artes hereafter, appeare. A wonderfull example of farther possibilitie, and present commoditie, was sene in my time, in a certaine Instrument: which by the Inuenter and Artificer (before) was solde for xx. Talentes of Golde: and then had (by misfortune) receaued some iniurie and hurt: And one _Ianellus_ of _Cremona_ did mend the same, and presented it vnto the Emperour _Charles_ the fifth.

_Hieronymus Carda.n.u.s_, can be my witnesse, that therein, was one Whele, which moued, and that, in such rate, that, in 7000. yeares onely, his owne periode should be finished. A thing almost incredible: But how farre, I keepe me within my boundes: very many men (yet aliue) can tell.