The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara Part 7

[=Anthemius.=]

what with his * Burning Gla.s.ses: by which he fired their other s.h.i.+ppes a far-of: what, with his other pollicies, deuises, and engines, he so manfully acquit him selfe: that all the Force, courage, and pollicie of the Romaines (for a great season) could nothing preuaile, for the winning of Syracusa. Wherupon, the Romanes named _Archimedes_, _Briareus_, and _Centima.n.u.s_. _Zonaras_ maketh mention of one _Proclus_, who so well had perceiued _Archimedes_ Arte of _Menadrie_, and had so well inuented of his owne, that with his Burning Gla.s.ses,

[Burning Gla.s.ses.]

being placed vpon the walles of Bysance, he multiplied so the heate of the Sunne, and directed the beames of the same against his enemies Nauie with such force, and so sodeinly (like lightening) that he burned and destroyed both man and s.h.i.+p. And _Dion_specifieth of _Priscus_, a _Geometricien_ in Bysance, who inuented and vsed sondry Engins, of Force multiplied: Which was cause, that the _Emperour Seuerus_ pardoned him, his life, after he had wonne Bysance: Bycause he honored the Arte, wytt, and rare industrie of _Priscus_. But nothing inferior to the inuention of these engines of Force, was the inuention of Gunnes.

[Gunnes.]

Which, from an English man, had the occasion and order of first inuenting: though in an other land, and by other men, it was first executed. And they that should see the record, where the occasion and order generall, of Gunning, is first discoursed of, would thinke: that, "small thinges, slight, and cmon: comming to wise mens consideration, and industrious mens handling, may grow to be of force incredible."

+Hypogeiodie, is an Arte Mathematicall, demonstratyng, how, vnder the Sphaericall Superficies of the earth, at any depth, to any perpendicular line a.s.signed (whose distance from the perpendicular of the entrance: and the Azimuth, likewise, in respect of the said entrance, is knowen) certaine way may be praescribed and gone: And how, any way aboue the Superficies of the earth designed, may vnder earth, at any depth limited, be kept: goyng alwayes, perpendicularly, vnder the way, on earth designed: And, contrarywise, Any way, (straight or croked,) vnder the earth, beyng giuen: vppon the vtface, or Superficies of the earth, to Lyne out the same: So, as, from the Centre of the earth, perpendiculars drawen to the Sphaericall Superficies of the earth, shall precisely fall in the Correspondent pointes of those two wayes. This, with all other Cases and circ.u.mstances herein, and appertenances, this Arte demonstrateth.+ This Arte, is very ample in varietie of Conclusions: and very profitable sundry wayes to the Common Wealth. The occasion of my Inuenting this Arte, was at the request of two Gentlemen, who had a certaine worke (of gaine) vnder ground: and their groundes did ioyne ouer the worke: and by reason of the crokednes, diuers depthes, and heithes of the way vnder ground, they were in doubt, and at controuersie, vnder whose ground, as then, the worke was. The name onely (before this) was of me published, _De Itinere Subterraneo_: The rest, be at G.o.ds will. For Pioners, Miners, Diggers for Mettalls, Stone, Cole, and for secrete pa.s.sages vnder ground, betwene place and place (as this land hath diuerse) and for other purposes, any man may easily perceaue, both the great fruite of this Arte, and also in this Arte, the great aide of Geometrie.

+Hydragogie, demonstrateth the possible leading of Water, by Natures lawe, and by artificiall helpe, from any head (being a Spring, standing, or running Water) to any other place a.s.signed.+ Long, hath this Arte bene in vse: and much thereof written: and very marueilous workes therein, performed: as may yet appeare, in Italy: by the Ruynes remaining of the Aqueductes. In other places, of Riuers leading through the Maine land, Nauigable many a Mile. And in other places, of the marueilous forcinges of Water to Ascend. which all, declare the great skill, to be required of him, who should in this Arte be perfecte, for all occasions of waters possible leading. To speake of the allowance of the Fall, for euery hundred foote: or of the Ventills (if the waters labour be farre, and great) I neede not: Seing, at hand (about vs) many expert men can sufficiently testifie, in effecte, the order: though the Demonstration of the Necessitie thereof, they know not: Nor yet, if they should be led, vp and downe, and about Mountaines, from the head of the Spring: and then, a place being a.s.signed: and of them, to be demaunded, how low or high, that last place is, in respecte of the head, from which (so crokedly, and vp and downe) they be come: Perhaps, they would not, or could not, very redily, or nerely a.s.soyle that question. _Geometrie_ therefore, is necessary to _Hydragogie_. Of the sundry wayes to force water to ascend, eyther by _Tympane_, _Kettell mills_, _Skrue_, _Ctesibike_, or such like: in _Vitruuius_, _Agricola_, (and other,) fully, the maner may appeare. And so, thereby, also be most euident, how the Artes, of _Pneumat.i.thmie_, _Helicosophie_, _Statike_, _Trochilike_, and _Menadrie_, come to the furniture of this, in Speculation, and to the Commoditie of the Common Wealth, in practise.

+Horometrie, is an Arte Mathematicall, which demstrateth, how, at all times appointed, the precise vsuall denominati of time, may be knowen, for any place a.s.signed.+ These wordes, are smoth and plaine easie Englishe, but the reach of their meaning, is farther, then you woulde lightly imagine. Some part of this Arte, was called in olde time, _Gnomonice_: and of late, _Horologiographia_: and in Englishe, may be termed, _Dialling_. Auncient is the vse, and more auncient, is the Inuention. The vse, doth well appeare to haue bene (at the least) aboue two thousand and three hundred yeare agoe:

[4. Reg. 20.]

in * King _Achaz_ Diall, then, by the Sunne, shewing the distinction of time. By Sunne, Mone, and Sterres, this Dialling may be performed, and the precise Time of day or night knowen. But the demonstratiue delineation of these Dialls, of all sortes, requireth good skill, both of _Astronomie_, and _Geometrie_ Elementall, Sphaericall, Phaenomenall, and Conikall. Then, to vse the groundes of the Arte, for any regular Superficies, in any place offred: and (in any possible apt position therof) theron, to describe (all maner of wayes) how, vsuall howers, may be (by the _Sunnes_ shadow) truely determined: will be found no sleight Painters worke. So to Paint, and prescribe the Sunnes Motion, to the breadth of a heare. In this Feate (in my youth) I Inuented a way, +How in any Horizontall, Murall, or aequinoctiall Diall, &c. At all howers (the Sunne s.h.i.+ning) the Signe and Degree ascendent, may be knowen.+ Which is a thing very necessary for the Rising of those fixed Sterres: whose Operation in the Ayre, is of great might, euidently. I speake no further, of the vse hereof. Bur forasmuch as, Mans affaires require knowledge of Times & Momentes, when, neither Sunne, Mone, or Sterre, can be sene: Therefore, by Industrie Mechanicall, was inuented, first, how, by Water, running orderly, the Time and howers might be knowen: whereof, the famous _Ctesibius_, was Inuentor: a man, of _Vitruuius_, to the Skie (iustly) extolled. Then, after that, by Sand running, were howers measured: Then, by _Trochilike_ with waight: And of late time, by _Trochilike_ with Spring: without waight. All these, by Sunne or Sterres direction (in certaine time) require ouersight and reformation, according to the heauenly aequinoctiall Motion: besides the inaequalitie of their owne Operation. There remayneth (without parabolicall meaning herein) among the Philosophers,

[A perpetuall Motion.]

a more excellent, more commodious, and more marueilous way, then all these: of hauing the motion of the Primouant (or first aequinoctiall motion,) by Nature and Arte, Imitated: which you shall (by furder search in waightier studyes) hereafter, vnderstand more of. And so, it is tyme to finish this Annotation, of Tymes distinction, vsed in our common, and priuate affaires: The commoditie wherof, no man would want, that can tell, how to bestow his tyme.

+Zographie, is an Arte Mathematicall, which teacheth and demonstrateth, how, the Intersection of all visuall Pyramides, made by any playne a.s.signed, (the Centre, distance, and lightes, beyng determined) may be, by lynes, and due propre colours, represented.+ A notable Arte, is this: and would require a whole Volume, to declare the property thereof: and the Commodities ensuyng. Great skill of _Geometrie_, _Arithmetike_, _Perspectiue_, and _Anthropographie_, with many other particular Artes, hath the _Zographer_, nede of, for his perfection. For, the most excellent Painter, (who is but the propre Mechanicien, & Imitator sensible, of the Zographer) hath atteined to such perfection, that Sense of Man and beast, haue iudged thinges painted, to be things naturall, and not artificiall: aliue, and not dead. This Mechanicall Zographer (commonly called the Painter) is meruailous in his skill: and seemeth to haue a certaine diuine power: As, of frendes absent, to make a frendly, present comfort: yea, and of frendes dead, to giue a continuall, silent presence: not onely with vs, but with our posteritie, for many Ages. And so procedyng, Consider, How, in Winter, he can shew you, the liuely vew of Sommers Ioy, and riches: and in Sommer, exhibite the countenance of Winters dolefull State, and nakednes. Cities, Townes, Fortes, Woodes, Armyes, yea whole Kingdomes (be they neuer so farre, or greate) can he, with ease, bring with him, home (to any mans Iudgement) as Paternes liuely, of the thinges rehea.r.s.ed. In one little house, can he, enclose (with great pleasure of the beholders,) the portrayture liuely, of all visible Creatures, either on earth, or in the earth, liuing: or in the waters lying, Creping, slyding, or swimming: or of any foule, or fly, in the ayre flying. Nay, in respect of the Starres, the Skie, the Cloudes: yea, in the shew of the very light it selfe (that Diuine Creature) can he match our eyes Iudgement, most nerely. What a thing is this? thinges not yet being, he can represent so, as, at their being, the Picture shall seame (in maner) to haue Created them. To what Artificer, is not Picture, a great pleasure and Commoditie? Which of them all, will refuse the Direction and ayde of Picture? The Architect, the Goldsmith, and the Arras Weauer: of Picture, make great account. Our liuely Herbals, our portraitures of birdes, beastes, and fishes: and our curious Anatomies, which way, are they most perfectly made, or with most pleasure, of vs beholden? Is it not, by Picture onely? And if Picture, by the Industry of the Painter, be thus commodious and meruailous: what shall be thought of _Zographie_, the Scholemaster of Picture, and chief gouernor? Though I mencion not _Sculpture_, in my Table of Artes Mathematicall: yet may all men perceiue, How, that _Picture_ and _Sculpture_, are Sisters germaine: and both, right profitable, in a Comm wealth. and of _Sculpture_, aswell as of Picture, excellent Artificers haue written great bokes in commendation. Witnesse I take, of _Georgio Vasari_, _Pittore Aretino_: of _Pomponius Gauricus_: and other. To these two Artes, (with other,) is a certaine od Arte, called _Althalmasat_, much beholdyng: more, then the common _Sculptor_, _Entayler_, _Keruer_, _Cutter_, _Grauer_, _Founder_, or _Paynter (&c)_ know their Arte, to be commodious.

[An objection.]

+Architecture+, to many may seme not worthy, or not mete, to be reckned among the _Artes Mathematicall_. To whom, I thinke good, to giue some account of my so doyng. Not worthy, (will they say,) bycause it is but for building, of a house, Pallace, Church, Forte, or such like, grosse workes. And you, also, defined the _Artes Mathematicall_, to be such, as dealed with no Materiall or corruptible thing: and also did demonstratiuely procede in their faculty, by Number or Magnitude. First,

[The Answer.]

you see, that I count, here, _Architecture_, among those _Artes Mathematicall_, which are Deriued from the Princ.i.p.als: and you know, that such, may deale with Naturall thinges, and sensible matter. Of which, "some draw nerer, to the Simple and absolute Mathematicall Speculation, then other do.

And though, the _Architect_ procureth, enformeth, & directeth, the _Mechanicien_, to handworke, & the building actuall, of house, Castell, or Pallace, and is chief Iudge of the same: yet, with him selfe (as chief _Master_ and _Architect_,) remaineth the Demonstratiue reason and cause, of the Mechaniciens worke: in Lyne, plaine, and Solid: by _Geometricall_, _Arithmeticall_, _Opticall_, _Musicall_, _Astronomicall_, _Cosmographicall_" (& to be brief) by all the former Deriued _Artes Mathematicall_, and other Naturall Artes, hable to be confirmed and stablished. If this be so: then, may you thinke, that _Architecture_, hath good and due allowance, in this honest Company of _Artes Mathematicall_ Deriuatiue. I will, herein, craue Iudgement of two most perfect _Architectes_: the one, being _Vitruuius_, the Romaine: who did write ten bookes thereof, to the Emperour _Augustus_ (in whose daies our Heauenly Archemaster, was borne): and the other, _Leo Baptista Albertus_, a Florentine: who also published ten bookes therof.

_Architectura_ (sayth _Vitruuius_) _est Scientia pluribus disciplinis & varijs eruditionibus ornata: cuius Iudicio probantur omnia, quae ab caeteris Artificibus perficiuntur opera._ That is. +Architecture, is a Science garnished with many doctrines & diuerse instructions: by whose Iudgement, all workes, by other workmen finished, are Iudged.+ It followeth. _Ea nascitur ex Fabrica, & Ratiocinatione. &c. Ratiocinatio autem est, quae, res fabricatas, Solertia ac ratione proportionis, demonstrare at[que] explicare potest. +Architecture, groweth of Framing, and Reasoning. &c. Reasoning, is that, which of thinges framed, with forecast, and proportion: can make demonstration, and manifest declaration.+_ Againe. _c.u.m, in omnibus enim rebus, tum maxime etiam in Architectura, haec duo insunt: quod significatur, & quod significat.

Significatur proposita res, de qua dicitur: hanc autem Significat Demonstratio, rationibus doctrinarum explicata. +Forasmuch as, in all thinges: therefore chiefly in Architecture, these two thinges are: the thing signified: and that which signifieth. The thing propounded, whereof we speake, is the thing Signified. But Demonstration, expressed with the reasons of diuerse doctrines, doth signifie the same thing.+_ After that. _Vt literatus sit, peritus Graphidos, eruditus Geometriae, & Optices non ignarus: instructus Arithmetica: historias complures nouerit, Philosophos diligenter audiuerit: Musicam sciuerit: Medicinae non sit ignarus, responsa Iurisperitoru nouerit: Astrologiam, Caeli[que]

rationes cognitas habeat. +An Architect+_ (sayth he) +_ought to vnderstand Languages, to be skilfull of Painting, well instructed in Geometrie, not ignorant of Perspectiue, furnished with Arithmetike, haue knowledge of many histories, and diligently haue heard Philosophers, haue skill of Musike, not ignorant of Physike, know the aunsweres of Lawyers, and haue Astronomie, and the courses Caelestiall, in good knowledge._+ He geueth reason, orderly, wherefore all these Artes, Doctrines, and Instructions, are requisite in an excellent _Architect_.

And (for breuitie) omitting the Latin text, thus he hath. +_Secondly, it is behofefull for an Architect to haue the knowledge of Painting: that he may the more easilie fas.h.i.+on out, in patternes painted, the forme of what worke he liketh. And Geometrie, geueth to Architecture many helpes: and first teacheth the Vse of the Rule, and the c.u.mpa.s.se: wherby (chiefly and easilie) the descriptions of Buildinges, are despatched in Groundplats: and the directions of Squires, Leuells, and Lines.

Likewise, by Perspectiue, the Lightes of the heauen, are well led, in the buildinges: from certaine quarters of the world. By Arithmetike, the charges of Buildinges are summed together: the measures are expressed, and the hard questions of Symmetries, are by Geometricall Meanes and Methods discoursed on. &c. Besides this, of the Nature of thinges (which in Greke is called f?s??????a) Philosophie doth make declaration. Which, it is necessary, for an Architect, with diligence to haue learned: because it hath many and diuers naturall questions: as specially, in Aqueductes. For in their courses, leadinges about, in the leuell ground, and in the mountinges, the naturall Spirites or breathes are ingendred diuers wayes: The hindrances, which they cause, no man can helpe, but he, which out of Philosophie, hath learned the originall causes of thinges. Likewise, who soeuer shall read Ctesibius, or Archimedes bookes, (and of others, who haue written such Rules) can not thinke, as they do: vnlesse he shall haue receaued of Philosophers, instructions in these thinges. And Musike he must nedes know: that he may haue vnderstanding, both of Regular and Mathematicall Musike: that he may temper well his Balistes, Catapultes, and Scorpions. &c. Moreouer, the Brasen Vessels, which in Theatres, are placed by Mathematicall order, in ambries, vnder the steppes: and the diuersities of the soundes (which y^e Grecians call ??e?a) are ordred according to Musicall Symphonies & Harmonies: being distributed in y^e Circuites, by Diatessaron, Diapente, and Diapason. That the conuenient voyce, of the players sound, wh? it came to these preparations, made in order, there being increased: with y^t increasing, might come more cleare & pleasant, to y^e eares of the lokers on. &c. And of Astronomie, is know? y^e East, West, South, and North. The fas.h.i.+on of the heauen, the aequinox, the Solsticie, and the course of the sterres. Which thinges, vnleast one know: he can not perceiue, any thyng at all, the reason of Horologies. Seyng therfore this ample Science, is garnished, beautified and stored, with so many and sundry skils and knowledges: I thinke, that none can iustly account them selues Architectes, of the suddeyne. But they onely, who from their childes yeares, ascendyng by these degrees of knowledges, beyng fostered vp with the atteynyng of many Languages and Artes, haue wonne to the high Tabernacle of Architecture. &c. And to whom Nature hath giuen such quicke Circ.u.mspection, sharpnes of witt, and Memorie, that they may be very absolutely skillfull in Geometrie, Astronomie, Musike, and the rest of the Artes Mathematicall: Such, surmount and pa.s.se the callyng, and state, of Architectes:

[A Mathematicien.]

and are become Mathematiciens. &c. And they are found, seldome. As, in tymes past, was Aristarchus Samius: Philolaus, and Archytas, Tarentynes: Apollonius Pergeus: Eratosthenes Cyreneus: Archimedes, and Scopas, Syracusians. Who also, left to theyr posteritie, many Engines and Gnomonicall workes: by numbers and naturall meanes, inuented and declared._+

Thus much, and the same wordes (in sense) in one onely Chapter of this Incparable _Architect Vitruuius_, shall you finde. And if you should, but take his boke in your hand, and slightly loke thorough it, you would say straight way:

[Vitruuius.]

This is _Geometrie_, _Arithmetike_, _Astronomie_, _Musike_, _Anthropographie_, _Hydragogie_, _Horometrie_. _&c_. and (to cclude) the Storehouse of all workms.h.i.+p. Now, let vs listen to our other Iudge, our Florentine, _Leo Baptista_: and narrowly consider, how he doth determine of _Architecture_. _Sed ante[que] vltra progrediar. &c. +But before I procede any further +_(sayth he) +_I thinke, that I ought to expresse, what man I would haue to bee allowed an Architect. For, I will not bryng in place a Carpenter: as though you might Compare him to the Chief Masters of other Artes. For the hand of the Carpenter, is the Architectes Instrument._+

[VVho is an Architect.]

+_But I will appoint the Architect to be "that man, who hath the skill, (by a certaine and meruailous meanes and way,) both in minde and Imagination to determine and also in worke to finish: what workes so euer, by motion of waight, and cuppling and framyng together of bodyes, may most aptly be Commodious for the worthiest Vses of Man." And that he may be able to performe these thinges, he hath nede of atteynyng and knowledge of the best, and most worthy thynges. &c. The whole Feate of Architecture in buildyng, consisteth in Lineamentes, and in Framyng. And the whole power and skill of Lineamentes, tendeth to this: that the right and absolute way may be had, of Coaptyng and ioyning Lines and angles: by which, the face of the buildyng or frame, may be comprehended and concluded. And it is the property of Lineamentes, to prescribe vnto buildynges, and euery part of them, an apt place, & certaine nuber: a worthy maner, and a semely order: that, so, y^e whole forme and figure of the buildyng, may rest in the very Lineamentes. &c. And we may prescribe in mynde and imagination the whole formes, *

[* The Immaterialitie of perfect Architecture.]

all material stuffe beyng secluded. Which point we shall atteyne, by Notyng and forepointyng the angles, and lines, by a sure and certaine direction and connexion. Seyng then, these thinges, are thus:_+

[What, Lineament is.]

+_Lineamente, shalbe the certaine and constant prescribyng, conceiued in mynde: made in lines and angles: and finished with a learned minde and wyt._+ "We thanke you Master _Baptist_, that you haue so aptly brought your Arte, and phrase therof, to haue some Mathematicall perfection:

[Note.]

by certaine order, nuber, forme, figure, and _Symmetrie_ mentall:" all naturall & sensible stuffe set a part. Now, then, it is euident, (Gentle reader) how aptely and worthely, I haue preferred _Architecture_, to be bred and fostered vp in the Dominion of the pereles _Princesse_, _Mathematica_: and to be a naturall Subiect of hers. And the name of _Architecture_, is of the princ.i.p.alitie, which this Science hath, aboue all other Artes. And _Plato_ affirmeth, the _Architect_ to be _Master_ ouer all, that make any worke. Wherupon, he is neither Smith, nor Builder: nor, separately, any Artificer: but the Hed, the Prouost, the Directer, and Iudge of all Artificiall workes, and all Artificers. For, the true _Architect_, is hable to teach, Demonstrate, distribute, describe, and Iudge all workes wrought. And he, onely, searcheth out the causes and reasons of all Artificiall thynges. Thus excellent, is _Architecture_: though few (in our dayes) atteyne thereto: yet may not the Arte, be otherwise thought on, then in very dede it is worthy. Nor we may not, of auncient Artes, make new and imperfect Definitions in our dayes: for scarsitie of Artificers: No more, than we may pynche in, the Definitions of _Wisedome_, or _Honestie_, or of _Frendeshyp_ or of _Iustice_. No more will I consent, to Diminish any whit, of the perfection and dignitie, (by iust cause) allowed to absolute _Architecture_. Vnder the Direction of this Arte, are thre princ.i.p.all, necessary _Mechanicall Artes_. Namely, _Howsing_, _Fortification_, and _Naupegie_. _Howsing_, I vnderstand, both for Diuine Seruice, and Mans common vsage: publike, and priuate. Of _Fortification_ and _Naupegie_, straunge matter might be told you: But perchaunce, some will be tyred, with this Bederoll, all ready rehea.r.s.ed: and other some, will nycely nip my grosse and homely discoursing with you: made in post hast: for feare you should wante this true and frendly warnyng, and tast giuyng, of the _Power Mathematicall_. Lyfe is short, and vncertaine: Tymes are perilouse: &c. And still the Printer awayting, for my pen staying: All these thinges, with farder matter of Ingratefulnes, giue me occasion to pa.s.se away, to the other Artes remainyng, with all spede possible.

+The Arte of Nauigation, demonstrateth how, by the shortest good way, by the aptest Directi, & in the shortest time, a sufficient s.h.i.+p, betwene any two places (in pa.s.sage Nauigable,) a.s.signed: may be cducted: and in all stormes, & naturall disturbances chauncyng, how, to vse the best possible meanes, whereby to recouer the place first a.s.signed.+ What nede, the _Master Pilote_, hath of other Artes, here before recited, it is easie to know: as, of _Hydrographie_, _Astronomie_, _Astrologie_, and _Horometrie_. Presupposing continually, the common Base, and foundacion of all: namely _Arithmetike_ and _Geometrie_. So that, he be hable to vnderstand, and Iudge his own necessary Instrumentes, and furniture Necessary: Whether they be perfectly made or no: and also can, (if nede be) make them, hym selfe.

As Quadrantes, The Astronomers Ryng, The Astronomers staffe, The Astrolabe vniuersall. An Hydrographicall Globe. Charts Hydrographicall, true, (not with parallell Meridians). The Common Sea Compas: The Compas of variacion: The Proportionall, and Paradoxall Compa.s.ses

[Anno. 1559.]

(of me Inuented, for our two Moscouy Master Pilotes, at the request of the Company) Clockes with spryng: houre, halfe houre, and three houre Sandgla.s.ses: & sundry other Instrum?tes: And also, be hable, on Globe, or Playne to describe the Paradoxall Compa.s.se: and duely to vse the same, to all maner of purposes, whereto it was inuented. And also, be hable to Calculate the Planetes places for all tymes.

Moreouer, with Sonne Mone or Sterre (or without) be hable to define the Longitude & Lat.i.tude of the place, which he is in: So that, the Longitude & Lat.i.tude of the place, from which he sayled, be giuen: or by him, be knowne. whereto, appertayneth expert meanes, to be certified euer, of the s.h.i.+ps way. &c. And by foreseing the Rising, Settyng, Nonestedyng, or Midnightyng of certaine tempestuous fixed Sterres: or their Coniunctions, and Anglynges with the Planetes, &c. he ought to haue expert coniecture of Stormes, Tempestes, and Spoutes: and such lyke Meteorologicall effectes, daungerous on Sea. For (as _Plato_ sayth,) _Mutationes, opportunitates[que] temporum presentire, non minus rei militari, quam Agriculturae, Nauigationi[que] conuenit. +To foresee the alterations and opportunities of tymes, is conuenient, no lesse to the Art of Warre, then to Husbandry and Nauigation.+_ And besides such cunnyng meanes, more euident tokens in Sonne and Mone, ought of hym to be knowen: such as (the Philosophicall Poete) _Virgilius_ teacheth, in hys _Georgikes_. Where he sayth,

[Sidenote: Georgic. 1.]

_Sol quo[que] & exoriens & quum se condet in vndas, Signa dabit, Solem certissima signa sequuntur. &c.

-------- Nam saepe videmus, Ipsius in vultu varios errare colores.

Caeruleus, pluuiam denunciat, igneus Euros.

Sin maculae incipient rutilo immiscerier igni, Omnia tum pariter vento, nimbis[que] videbis Feruere: non illa quisquam me nocte per altum Ire, ne[que] a terra moueat conuellere funem. &c.

Sol tibi signa dabit. Solem quis dicere falsum Audeat? -------- &c._

And so of Mone, Sterres, Water, Ayre, Fire, Wood, Stones, Birdes, and Beastes, and of many thynges els, a certaine Sympathicall forewarnyng may be had: sometymes to great pleasure and proffit, both on Sea and Land. Sufficiently, for my present purpose, it doth appeare, by the premisses, how _Mathematicall_, the _Arte_ of _Nauigation_, is: and how it nedeth and also vseth other _Mathematicall Artes_: And now, if I would go about to speake of the manifold Commodities, commyng to this Land, and others, by Shypps and _Nauigation_, you might thinke, that I catch at occasions, to vse many wordes, where no nede is.