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varios errare colores. Cruleus, pluuiam denunciat, igneus Euros. Sin macul 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,
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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
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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. Yet, this one thyng may I, (iustly) say. In _Nauigation_, none ought to haue greater care, to be skillfull, then our English Pylotes. And perchaunce, Some, would more attempt: And
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other Some, more willingly would be aydyng, it they wist certainely, What Priuiledge, God had endued this Iland with, by reason of Situation, most commodious for _Nauigation_, to Places most Famous & Riche. And though, [* Anno. S. H. G.] (of * Late) a young Gentleman, a Courragious Capitaine, was in a great readynes, with good hope, and great causes
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of persuasion, to haue ventured, for a Discouerye, (either _Westerly_, by _Cape de Paramantia_: or _Esterly_, aboue _Noua Zemla_, and the _Cyremisses_) and was, at the very nere tyme of Attemptyng, called and employed otherwise (both then, and since,) in great good seruice to his Countrey, as the Irish Rebels haue * tasted: [* Anno. ] Yet, I say, (though
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the same Gentleman, doo not hereafter, deale therewith) Some one, or other, should listen to the Matter: and by good aduise, and discrete Circumspection, by little, and little, wynne to the sufficient knowledge of that +Trade+ and +Voyage+: Which, now, I would be sory, (through Carelesnesse, want of Skill, and Courrage,) should remayne Vnknowne and vnheard of. Seyng, also, we
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are herein, halfe Challenged, by the learned, by halfe request, published. Therof, verely, might grow Commoditye, to this Land chiefly, and to the rest of the Christen Common wealth, farre passing all riches and worldly Threasure. +Thaumaturgike, is that Art Mathematicall, which giueth certaine order to make straunge workes, of the sense to be perceiued, and of men greatly to
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be wondred at.+ By sundry meanes, this _Wonder-worke_ is wrought. Some, by _Pneumatithmie_. As the workes of _Ctesibius_ and _Hero_, Some by waight. wherof _Timus_ speaketh. Some, by Stringes strayned, or Springs, therwith Imitating liuely Motions. Some, by other meanes, as the Images of Mercurie: and the brasen hed, made by _Albertus Magnus_, which dyd seme to speake. _Boethius_ was
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excellent in these feates. To whom, _Cassiodorus_ writyng, sayth. +_Your purpose is to know profound thynges: and to shew meruayles. By the disposition of your Arte, Metals do low: Diomedes of brasse, doth blow a Trumpet loude: a brasen Serpent hisseth: byrdes made, sing swetely. Small thynges we rehearse of you, who can Imitate the heauen. &c._+ Of the straunge
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Selfmouyng, which, at Saint Denys, by Paris, [* Anno. ] * I saw, ones or twise (_Orontius_ beyng then with me, in Company) it were to straunge to tell. But some haue written it. And yet, (I hope) it is there, of other to be sene. And by _Perspectiue_ also straunge thinges, are done. As partly (before) I gaue you
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to vnderstand in _Perspectiue_. As, to see in the Ayre, a loft, the lyuely Image of an other man, either walkyng to and fro: or standyng still. Likewise, to come into an house, and there to see the liuely shew of Gold, Siluer or precious stones: and commyng to take them in your hand, to finde nought but Ayre. Hereby,
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haue some men (in all other matters counted wise) fouly ouershot th selues: misdeaming of the meanes. Therfore sayd _Claudius Clestinus_. [De his qu Mundo mirabiliter eueniunt. cap. .] _Hodie magn literatur viros & magna reputationis videmus, opera quedam quasi miranda, supra Natur putare: de quibus in Perspectiua doctus causam faciliter reddidisset._ That is. +_Now a dayes, we see some
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men, yea of great learnyng and reputation, to Iudge certain workes as meruaylous, aboue the power of Nature: Of which workes, one that were skillfull in Perspectiue might easely haue giuen the Cause._+ Of _Archimedes Sphre_, _Cicero_ witnesseth. [Tusc. .] Which is very straunge to thinke on. +_For when Archimedes_+ (sayth he) +_did fasten in a Sphre, the mouynges of
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the Sonne, Mone, and of the fiue other Planets, he did, as the God, which (in Timus of Plato) did make the world. That, one turnyng, should rule motions most vnlike in slownes, and swiftnes._+ But a greater cause of meruayling we haue by _Claudianus_ report hereof. Who affirmeth this _Archimedes worke_, to haue ben of Glasse. And discourseth of
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it more at large: which I omit. The Doue of wood, which the _Mathematicien Archytas_ did make to flye, is by _Agellius_ spoken of. Of _Ddalus_ straunge Images, _Plato_ reporteth. _Homere_ of _Vulcans Selfmouers_, (by secret wheles) leaueth in writyng. _Aristotle_, in hys _Politikes_, of both, maketh mention. Meruaylous was the workemanshyp, of late dayes, performed by good skill of
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_Trochilike. &c._ For in Noremberge, A flye of Iern, beyng let out of the Artificers hand, did (as it were) fly about by the gestes, at the table, and at length, as though it were weary, retourne to his masters hand agayne. Moreouer, an Artificiall Egle, was ordred, to fly out of the same Towne, a mighty way, and that
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a loft in the Ayre, toward the Emperour comming thether: and followed hym, beyng come to the gate of the towne. * [* ] Thus, you see, what, Arte Mathematicall can performe, when Skill, will, Industry, and Hability, are duely applyed to profe. [A Digression.] And for these, and such like marueilous Actes and Feates, Naturally, Mathematically, and Mechanically, wrought
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and contriued: [Apologeticall.] ought any honest Student, and Modest Christian Philosopher, be counted, & called a +Coniurer+? Shall the folly of Idiotes, and the Mallice of the Scornfull, so much preuaile, that He, who seeketh no worldly gaine or glory at their handes: But onely, of God, the threasor of heauenly wisedome, & knowledge of pure veritie: Shall he (I
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say) in the meane space, be robbed and spoiled of his honest name and fame? He that seketh (by S. Paules aduertisement) in the Creatures Properties, and wonderfull vertues, to finde iuste cause, to glorifie the ternall, and Almightie Creator by: Shall that man, be (in hugger mugger) condemned, as a Companion of the Helhoundes, and a Caller, and Coniurer
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of wicked and damned Spirites? He that bewaileth his great want of time, sufficient (to his contentation) for learning of Godly wisdome, and Godly Verities in: and onely therin setteth all his delight: Will that m leese and abuse his time, in dealing with the Chiefe enemie of Christ our Redemer: the deadly foe of all mankinde: the subtile and
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impudent peruerter of Godly Veritie: the Hypocriticall Crocodile: the Enuious Basiliske, continually desirous, in the twinke of an eye, to destroy all Mankinde, both in Body and Soule, ternally? Surely (for my part, somewhat to say herein) I haue not learned to make so brutish, and so wicked a Bargaine. Should I, for my xx. or xxv. yeares Studie: for
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two or three thousand Markes spending: seuen or eight thousand Miles going and trauailing, onely for good learninges sake: And that, in all maner of wethers: in all maner of waies and passages: both early and late: in daunger of violence by man: in daunger of destruction by wilde beastes: in hunger: in thirst: in perilous heates by day, with
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toyle on foote: in daungerous dampes of colde, by night, almost bereuing life: (as God knoweth): with lodginges, oft times, to small ease: and somtime to lesse securitie. And for much more (then all this) done & suffred, for Learning and attaining of Wisedome: Should I (I pray you) for all this, no otherwise, nor more warily: or (by Gods
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mercifulnes) no more luckily, haue fished, with so large, and costly, a Nette, so long time in drawing (and that with the helpe and aduise of Lady Philosophie, & Queene Theologie): but at length, to haue catched, and drawen vp, * a Frog? [* A prouerb. Fayre fisht, and caught a Frog.] Nay, a Deuill? For, so, doth the Common
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peuish Pratler Imagine and Iangle: And, so, doth the Malicious skorner, secretly wishe, & brauely and boldly face down, behinde my backe. Ah, what a miserable thing, is this kinde of Men? How great is the blindnes & boldnes, of the Multitude, in thinges aboue their Capacitie? What a Land: what a People: what Maners: what Times are these? Are
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they become Deuils, them selues: and, by false witnesse bearing against their Neighbour, would they also, become Murderers? Doth God, so long geue them respite, to reclaime them selues in, from this horrible slaundering of the giltlesse: contrary to their owne Consciences: and yet will they not cease? Doth the Innocent, forbeare the calling of them, Iuridically to aunswere him,
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according to the rigour of the Lawes: and will they despise his Charitable pacience? As they, against him, by name, do forge, fable, rage, and raise slaunder, by Worde & Print: Will they prouoke him, by worde and Print, likewise, to Note their Names to the World: with their particular deuises, fables, beastly Imaginations, and vnchristen-like slaunders? Well: Well. O
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(you such) my vnkinde Countrey men. O vnnaturall Countrey men. O vnthankfull Countrey men. O Brainsicke, Rashe, Spitefull, and Disdainfull Countrey men. Why oppresse you me, thus violently, with your slaundering of me: Contrary to Veritie: and contrary to your owne Consciences? And I, to this hower, neither by worde, deede, or thought, haue bene, any way, hurtfull, damageable, or
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iniurious to you, or yours? Haue I, so long, so dearly, so farre, so carefully, so painfully, so daungerously sought & trauailed for the learning of Wisedome, & atteyning of Vertue: And in the end (in your iudgemt) am I become, worse, then when I beg? Worse, th a Mad man? A dangerous Member in the Common Wealth: and no
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Member of the Church of Christ? Call you this, to be Learned? Call you this, to be a Philosopher? and a louer of Wisedome? To forsake the straight heauenly way: and to wallow in the broad way of damnation? To forsake the light of heauenly Wisedome: and to lurke in the dungeon of the Prince of darkenesse? To forsake the
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Veritie of God, & his Creatures: and to fawne vpon the Impudent, Craftie, Obstinate Lier, and continuall disgracer of Gods Veritie, to the vttermost of his power? To forsake the Life & Blisse ternall: and to cleaue vnto the Author of Death euerlasting? that Murderous Tyrant, most gredily awaiting the Pray of Mans Soule? Well: I thanke God and our
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Lorde Iesus Christ, for the Comfort which I haue by the Examples of other men, before my time: To whom, neither in godlines of life, nor in perfection of learning, I am worthy to be compared: and yet, they sustained the very like Iniuries, that I do: or rather, greater. Pacient _Socrates_, his _Apologie_ will testifie: _Apuleius_ his _Apologies_, will
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declare the Brutishnesse of the Multitude. _Ioannes Picus_, Earle of Mirandula, his _Apologie_ will teach you, of the Raging slaunder of the Malicious Ignorant against him. _Ioannes Trithemius_, his _Apologie_ will specifie, how he had occasion to make publike Protestation: as well by reason of the Rude Simple: as also, in respect of such, as were counted to be of
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the wisest sort of men. Many could I recite: But I deferre the precise and determined handling of this matter: being loth to detect the Folly & Mallice of my Natiue Countrey men. * [* ] Who, so hardly, can disgest or like any extraordinary course of Philosophicall Studies: not falling within the Cumpasse of their Capacitie: or where they
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are not made priuie of the true and secrete cause, of such wonderfull Philosophicall Feates. These men, are of fower sortes, chiefly. The first, I may name, _Vaine pratling busie bodies_: The second, _Fond Frendes_: The third, _Imperfectly zelous_: and the fourth, _Malicious Ignorant_. To eche of these (briefly, and in charitie) I will say a word or two, and
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so returne to my Prface. [.] _Vaine pratling busie bodies_, vse your idle assemblies, and conferences, otherwise, then in talke of matter, either aboue your Capacities, for hardnesse: or contrary to your Consciences, in Veritie. [.] _Fonde Frendes_, leaue of, so to commend your vnacquainted frend, vpon blinde affection: As, because he knoweth more, then the common Student: that, therfore,
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he must needes be skilfull, and a doer, in such matter and maner, as you terme _Coniuring_. Weening, thereby, you aduaunce his fame: and that you make other men, great marueilers of your hap, to haue such a learned frend. Cease to ascribe Impietie, where you pretend Amitie. For, if your tounges were true, then were that your frend, _Vntrue_,
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both to God, and his Soueraigne. Such _Frendes_ and _Fondlinges_, I shake of, and renounce you: Shake you of, your Folly. [.] _Imperfectly zelous_, to you, do I say: that (perhaps) well, do you Meane: But farre you misse the Marke: If a Lambe you will kill, to feede the flocke with his bloud. Sheepe, with Lambes bloud, haue no
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naturall sustenaunce: No more, is Christes flocke, with horrible slaunders, duely dified. Nor your faire pretense, by such rashe ragged Rhetorike, any whit, well graced. But such, as so vse me, will finde a fowle Cracke in their Credite. Speake that you know: And know, as you ought: Know not, by Heare say, when life lieth in daunger. Search to
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the quicke, & let Charitie be your guide. [.] _Malicious Ignorant_, what shall I say to thee? _Prohibe linguam tuam a malo. A detractione parcite lingu. +Cause thy toung to refraine fr euill. Refraine your toung from slaunder.+_ Though your tounges be sharpned, Serpent like, & Adders poyson lye in your lippes: [Psal. .] yet take heede, and thinke, betimes,
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with your selfe, _Vir linguosus non stabilietur in terra. Virum violentum venabitur malum, donec prcipitetur._ For, sure I am, _Quia faciet Dominus Iudicium afflicti: & vindictam pauperum._ Thus, I require you, my assured frendes, and Countrey men (you Mathematiciens, Mechaniciens, and Philosophers, Charitable and discrete) to deale in my behalf, with the light & vntrue tounged, my enuious Aduersaries, or
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Fond frends. And farther, I would wishe, that at leysor, you would consider, how _Basilius Magnus_, layeth _Moses_ and _Daniel_, before the eyes of those, which count all such Studies Philosophicall (as mine hath bene) to be vngodly, or vnprofitable. Waye well _S. Stephen_ his witnesse of _Moses_. [Act. . C.] _Eruditus est Moses omni Sapientia gyptior: & erat potens
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in verbis & operibus suis. +Moses was instructed in all maner of wisedome of the gyptians: and he was of power both in his wordes, and workes.+_ You see this Philosophicall Power & Wisedome, which _Moses_ had, to be nothing misliked of the Holy Ghost. Yet _Plinius_ hath recorded, _Moses_ to be a wicked _Magicien_. And that (of force) must
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be, either for this Philosophicall wisedome, learned, before his calling to the leading of the Children of _Israel_: or for those his wonders, wrought before King _Pharao_, after he had the conducting of the _Israelites_. As concerning the first, you perceaue, how _S. Stephen_, at his Martyrdome (being full of the Holy Ghost) in his Recapitulation of the olde Testament,
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hath made mention of _Moses_ Philosophie: with good liking of it: And _Basilius Magnus_ also, auoucheth it, to haue bene to _Moses_ profitable (and therefore, I say, to the Church of God, necessary). But as ccerning _Moses_ wonders, done before King _Pharao_: God, him selfe, sayd: _Vide vt omnia ostenta, qu posui in manu tua, facias coram Pharaone. +See that
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thou do all those wonders before Pharao, which I haue put in thy hand.+_ Thus, you euidently perceaue, how rashly, _Plinius_ hath slaundered _Moses_, [Lib. . Cap. .] of vayne fraudulent _Magike_, saying: _Est & alia Magices Factio, a Mose, Iamne, & Iotape, Iudis pendens: sed multis millibus annorum post Zoroastrem. &c._ [.] Let all such, therefore, who, in Iudgement
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and Skill of Philosophie, are farre Inferior to _Plinie_, take good heede, least they ouershoote them selues rashly, in [] Iudging of _Philosophers straunge Actes_: and the Meanes, how they are done. [.] But, much more, ought they to beware of forging, deuising, and imagining monstrous feates, and wonderfull workes, when and where, no such were done: no, not any
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sparke or likelihode, of such, as they, without all shame, do report. [.] And (to conclude) most of all, let them be ashamed of Man, and afraide of the dreadfull and Iuste Iudge: both Folishly or Maliciously to deuise: and then, deuilishly to father their new fond Monsters on me: Innocent, in hand and hart: for trespacing either against the
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lawe of God, or Man, in any my Studies or Exercises, Philosophicall, or Mathematicall: As in due time, I hope, will be more manifest. 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.
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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
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termes, procedeth, with helpe of the foresayd Artes, to the performance of complet Experices, 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
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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 Cusanus_ termeth it so, in hys _Experimentes
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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
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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
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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
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_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, _Cum suis Insolubilibus_,
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make a florish: and dassell 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 God: for my small Talent, at hys most mercyfull handes receiued.
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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
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it were) OPTICAL Science: wherof, the name shall be told (God willyng) 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:
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(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
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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 Principall Science of _Geometrie_, called _Euclides Geometricall Elementes_, is published, to your handlyng: being vnlatined people, and not Vniuersitie Scholers: Verily, I thinke it nedelesse. [.] For,
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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. [.] 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
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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
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thing bene discontent with _Albertus Durerus_, his Geometricall Institutions 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
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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
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Publishers offended: or any mans Studie thereby hindred? [.] 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,
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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. [.] 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
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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 God: nor furdering the Weale, common or priuate. [.] And great Comfort, with good hope, may the _Vniuersities_ haue, by reason of
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this _Englishe_ +Geometrie, and Mathematicall Prface+, 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
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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
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most noble State of Common Wealthes. [.] Besides this, how many a Common Artificer, is there, in these Realmes of England and Ireland, that dealeth with Numbers, Rule, & Cumpasse: 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
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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
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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
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men, in the English toung. But, vnto God 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
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foresayd hys three principall 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
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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 principall pointes, whereof my
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Preface treateth, [The Ground platt of this Prface 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
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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 Gods Mercyfull direction, for the rest: hartely besechyng hym, to prosper your Studyes, and honest
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Intentes: to his Glory, & the Commodity of our Countrey. _Amen_. _Written at my poore House At Mortlake._ _Anno. . February. ._ [Decoration] [Transcribers Note: The Groundplat was printed in the form of a stemma, or tree, on an oversized fold-out page. The layout was impossible to reproduce for this e-text, so the information has been rearranged in nested-list form.
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Size markings (see note at beginning of e-text) are relative within each paragraph.] _J. DEE_ +Here haue you (according to my promisse) the Groundplat of+ +my MATHEMATICALL Prface: annexed to _Euclide_ (now first)+ published in our Englishe tounge. An. . Febr. . +Sciences, and Artes Mathematicall, are, either+ +Principall, which are two, onely,+ +Arithmetike.+ +Simple+, Which dealeth with Numbers onely:
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and demonstrateth all their properties and appertenances: where, an Vnit, is Indiuisible. +Mixt+, Which with aide of Geometrie principall, demonstrateth some Arithmeticall Conclusion, or Purpose. +Geometrie.+ +Simple+, Which dealeth with Magnitudes, onely: and demonstrateth all their properties, passions, and appertenances: whose Point, is Indiuisible. +Mixt+, Which with aide of Arithmetike principall, demonstrateth some Geometricall purpose, as +EVCLIDES ELEMENTES+. +The vse
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whereof, is either,+ In thinges Supernaturall, ternall, & Diuine: By Application, _Ascending_. In thinges Mathematicall: without farther Application. In thinges Naturall: both Substtiall, & Accidentall, Visible, & Inuisible. &c. By Application: _Descending_. The like Vses and Applications are, (though in a degree lower) in the +Artes Mathematicall Deriuatiue+. +Deriuatiue fr the Principalls: of which, some haue+ +The names of the
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Principalls: as,+ +_Arithmetike_, vulgar: which considereth+ --Arithmetike of most vsuall whole numbers: And of Fractions to them appertaining. --Arithmetike of Proportions. --Arithmetike Circular. --Arithmetike of Radicall Nbers: Simple, Compound, Mixt: And of their Fractions. --Arithmetike of Cossike Nbers: with their Fractions: And the great Arte of Algiebar. +_Geometrie_, vulgar: which teacheth Measuring+ +At hand+ All Lengthes.--+Mecometrie.+ All Plaines: As, Land,
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Borde, Glasse, &c.--+Embadometrie.+ All Solids: As, Timber, Stone, Vessels, &c.--+Stereometrie.+ +With distce+ from the thing Measured, as, +How farre+, from the Measurer, any thing is: of him sene, on Land or Water: called +Apomecometrie+. +How high or deepe+, from the leuell of the Measurers standing, any thing is: Seene of hym, on Land or Water: called +Hypsometrie+. +How broad+, a
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thing is, which is in the Measurers view: so it be situated on Land or Water: called +Platometrie+. +Of which are growen the Feates & Artes of+ +Geodesie+: more cunningly to Measure and Suruey Landes, Woods, Waters. &c. +Geographie.+ +Chorographie.+ +Hydrographie.+ +Stratarithmetrie.+ +Propre names as+, +Perspectiue,+--Which demonstrateth the maners and properties of all Radiations: Directe, Broken, and Reflected. +Astronomie,+--Which demonstrateth
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the Distances, Magnitudes, and all Naturall motions, Apparences, and Passions, proper to the Planets and fixed Starres: for any time, past, present, and to come: in respecte of a certaine Horizon, or without respecte of any Horizon. +Musike,+--Which demonstrateth by reason, and teacheth by sense, perfectly to iudge and order the diuersitie of Soundes, hie or low. +Cosmographie,+--Which, wholy and
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perfectly maketh description of the Heauenlym and also Elementall part of the World: and of these partes, maketh homologall application, and mutuall collation necessary. +Astrologie,+--Which reasonably demonstrateth the operations and effectes of the naturall beames of light, and secrete Influence of the Planets, and fixed Starres, in euery Element and Elementall body: at all times, in any Horizon assigned. +Statike,+--Which
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demonstrateth the causes of heauines and lightnes of all thinges: and of the motions and properties to heauines and lightnes belonging. +Anthropographie,+ Which describeth the Nber, Measure, Waight, Figure, Situation, and colour of euery diuers thing contained in the perfecte body of MAN: and geueth certaine knowledge of the Figure, Symmetrie, Waight, Characterization, & due Locall motion of any percell
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of the said body assigned: and of numbers to the said percell appertaining. +Trochilike,+--Which demonstrateth the properties of all Circular motions: Simple and Compound. +Helicosophie,+--Which demonstrateth the designing of all Spirall lines: in Plaine, on Cylinder, Cone, Sphre, Conod, and Sphroid: and their properties. +Pneumatithmie,+--Which demonstrateth by close hollow Geometricall figures (Regular and Irregular) the straunge properties (in motion or
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stay) of the Water, Ayre, Smoke, and Fire, in their Continuitie, and as they are ioyned to the Elementes next them. +Menadrie,+--Which demonstrateth, how, aboue Natures Vertue, and power simple: Vertue and force, may be multiplied: and so to directe, to lift, to pull to, and to put or cast fro, any multiplied, or simple determined Vertue, Waight, or Force:
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naturally, not, so, directible, or moueable. +Hypogeiodie,+--Which demonstrateth, how, vnder the Sphricall Superficies of the Earth, at any depth, to any perpendicular line assigned (whose distance from the perpendicular of the entrance: and the Azimuth likewise, in respecte of the sayd entrance, is knowen) certaine way, may be prescribed and gone, &c. +Hydragogie,+--Which demonstrateth the possible leading of water by
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Natures law, and by artificiall helpe, from any head (being Spring, standing, or running water) to any other place assigned. +Horometrie,+--Which demonstrateth, how, at all times appointed, the precise, vsuall denomination of time, may be knowen, for any place assigned. +Zographie,+--Which demonstrateth and teacheth, how, the Intersection of all visuall Pyramids, made by any plaine assigned (the Center, distance, and
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lightes being determined) may be, by lines, and proper colours represented. +Architecture,+--Which is a Science garnished with many doctrines, and diuers Instructions: by whose iudgement, all workes by other workmen finished, are iudged. +Nauigation,+--Which demonstrateth, how, by the Shortest good way, by the aptest direction, and in the shortest time: a sufficient Shippe, betwene any two places (in passage nauigable)
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assigned, may be conducted: and in all stormes and naturall disturbances chauncing, how to vse the best possible meanes, to recouer the place first assigned. +Thaumaturgike,+--Which geueth certaine order to make straunge workes, of the sense to be perceiued: and of men greatly to be wondred at. +Archemastrie,+--Which teacheth to bring to actuall experience sensible, all worthy conclusions, by all
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the Artes Mathematicall purposed: and by true Naturall philosophie, concluded: And both addeth to them a farder Scope, in the termes of the same Artes: and also, by his proper Method, and in peculiar termes, procedeth, with helpe of the forsayd Artes, to the performance of complete Experiences: which, of no particular Arte, are hable (Formally) to be challenged. +
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Imprinted by _Iohn Day_.+ An. . Feb. . * * * * * * * * * * * * * * Errors and Anomalies: Unless otherwise noted, spelling and punctuation are unchanged. Errors are listed below, with the original form, if changed, shown in [brackets]. Unusual words include fatch (probably used as a variant of fetch) and the mathematical
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terms sexagene and sexagesme. How, worldly goods: how, worldly dignitie [_o in second worldly invisible_] his most diligent hearers (so infinitely mought [hearers) so] the boundes, and duety of an Hydrographer [Hydographer] of the Grekes it is called _Eteromekes_ [_text unchanged: correct form is Heteromekes_] [_accent unchanged_] in our worldly affaires [wordly] fall to worke.. [_Some text readers may not
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display the oversized-asterisk symbol._] _Emptying the first._ [Emptyting] , , [ ... ] of the suddeyne [snddeyne] that the right and absolute way may be had [he had] Georgic I: [_The quoted segments, each ending in &c., are -; -; -._] Additional Notes: The Greek letter (eta) was consistently printed as if it were the ou-ligature . The Latin -que
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was written as an abbreviation resembling -q;. It is shown here as [que]. Mathematical symbols seen in the section accompanying the diagrams could not be reproduced. The following substitutions were made: --The curly P used for Pounds is shown as {P}. --The potestas symbol, used to represent x (the unknown), is shown as {x}. --All roots were expressed as the
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root sign combined with symbols for the power of (doubled for power of , or fourth root) and . They are shown as . Euclid: The following Propositions were identified by number. .: (How) to find a fourth (line) proportional to three given straight lines. .: In equal parallelepipedal solids the bases are reciprocally proportional to the heights; and those
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