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preparabit cogitationem, vt ad supera conuertamus: qu, nunc, contra qum decet, ad inferiora deijcimus. &c. Qum maxim igitur prcipiendum est, vt qui prclarissimam hanc habitt Civitatem, nullo modo, Geometriam spernant. Nam & qu prter ipsius propositum, quodam modo esse videntur, haud exigua sunt. &c._ It must nedes be confessed (saith _Plato_) +_That =[Geometrie]= is learned, for the knowyng of that,
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which is euer: and not of that, which, in tyme, both is bred and is brought to an ende. &c. Geometrie is the knowledge of that which is euerlastyng. It will lift vp therfore (O Gentle Syr) our mynde to the Veritie: and by that meanes, it will prepare the Thought, to the Philosophicall loue of wisdome: that we may
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turne or conuert, toward heauenly thinges =[both mynde and thought]= which now, otherwise then becommeth vs, we cast down on base or inferior things. &c. Chiefly, therfore, Commaundement must be giuen, that such as do inhabit this most honorable Citie, by no meanes, despise Geometrie. For euen those thinges =[done by it]= which, in manner, seame to be, beside the
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purpose of Geometrie: are of no small importance. &c._+ And besides the manifold vses of _Geometrie_, in matters appertainyng to warre, he addeth more, of second vnpurposed frute, and commoditye, arrising by _Geometrie_: saying: _Scimus quin etiam, ad Disciplinas omnes facilius per discendas, interesse omnino, attigerit ne Geometriam aliquis, an non. &c. Hanc ergo Doctrinam, secundo loco discendam Iuuenibus statuamus._
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That is. +_But, also, we know, that for the more easy learnyng of all Artes, it importeth much, whether one haue any knowledge in Geometrie, or no. &c. Let vs therfore make an ordinance or decree, that this Science, of young men shall be learned in the second place._+ This was _Diuine Plato_ his Iudgement, both of the purposed, chief,
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and perfect vse of _Geometrie_: and of his second, dependyng, deriuatiue commodities. And for vs, Christen men, a thousand thousand mo occasions are, to haue nede of the helpe of * [I. D. * Herein, I would gladly shake of, the earthly name, of Geometrie.] _Megethologicall_ Contemplations: wherby, to trayne our Imaginations and Myndes, by litle and litle, to forsake
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and abandon, the grosse and corruptible Obiectes, of our vtward senses: and to apprehend, by sure doctrine demonstratiue, Things Mathematicall. And by them, readily to be holpen and conducted to conceiue, discourse, and conclude of things Intellectual, Spirituall, ternall, and such as concerne our Blisse euerlasting: which, otherwise (without Speciall priuiledge of Illumination, or Reuelation fr heauen) No mortall mans
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wyt (naturally) is hable to reach vnto, or to Compasse. And, veryly, by my small Talent (from aboue) I am hable to proue and testifie, that the litterall Text, and order of our diuine Law, Oracles, and Mysteries, require more skill in Numbers, and Magnitudes: then (commonly) the expositors haue vttered: but rather onely (at the most) so warned: &
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shewed their own want therin. (To name any, is nedeles: and to note the places, is, here, no place: But if I be duely asked, my answere is ready.) And without the litterall, Grammaticall, Mathematicall or Naturall verities of such places, by good and certaine Arte, perceiued, no Spirituall sense (propre to those places, by Absolute _Theologie_) will thereon depend.
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[] No man, therfore, can doute, but toward the atteyning of knowledge incomparable, and Heauenly Wisedome: Mathematicall Speculations, both of Numbers and Magnitudes: are meanes, aydes, and guides: ready, certaine, and necessary. From henceforth, in this my Preface, will I frame my talke, to _Plato_ his fugitiue Scholers: or, rather, to such, who well can, (and also wil,) vse their
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vtward senses, to the glory of God, the benefite of their Countrey, and their owne secret contentation, or honest preferment, on this earthly Scaffold. To them, I will orderly recite, describe & declare a great Number of Artes, from our two Mathematicall fountaines, deriued into the fieldes of _Nature_. Wherby, such Sedes, and Rotes, as lye depe hyd in the
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grod of _Nature_, are refreshed, quickened, and prouoked to grow, shote vp, floure, and giue frute, infinite, and incredible. And these Artes, shalbe such, as vpon Magnitudes properties do depende, more, then vpon Number. And by good reason we may call them Artes, and Artes Mathematicall Deriuatiue: for (at this tyme) I Define [An Arte.] +An Arte, to be a
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Methodicall cplete Doctrine, hauing abundancy of sufficient, and peculier matter to deale with, by the allowance of the Metaphisicall Philosopher: the knowledge whereof, to humaine state is necessarye.+ And that I account, [Art Mathematicall Deriuatiue.] +An Art Mathematicall deriuatiue, which by Mathematicall demonstratiue Method, in Nbers, or Magnitudes, ordreth and confirmeth his doctrine, as much & as perfectly, as the
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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
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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
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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 th 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. [+.+]
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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 qutities 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,
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Rule, Squire, Yarde, Ell, Perch, Pole, Line, Gaging rod, (or such like instrument) to the Length, Plaine, or Solide measured, [.] * to be certified, either of the length, perimetry, or distance lineall: and this is called, _Mecometrie_. Or [.] * to be certified of the content of any plaine Superficies: whether it be in ground Surueyed, Borde, or Glasse
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measured, or such like thing: which measuring, is named _Embadometrie_. [.] * 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
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is called _Gaging_. And the generall name of these Solide measures, is _Stereometrie_. [+.+] 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 [.] * how Farre, a thing seene (on land or water) is from the measurer: and this
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may be called _Apomecometrie_: [.] Or, how High or depe, aboue or vnder the leuel of the measurers stding, any thing is, which is sene on land or water, called _Hypsometrie_. [.] * Or, it informeth the measurer, how Broad any thing is, which is in the measurers vew: so it be on Land or Water, situated: and may be
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called _Platometrie_. Though I vse here to condition, the thing measured, to be on Land, or Water Situated: [Note.] yet, know for certaine, that the sundry heigthe of Cloudes, blasing Starres, and of the Mone, may (by these meanes) haue their distances from the earth: and, of the blasing Starres and Mone, the Soliditie (aswell as distances) to be measured:
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But because, neither these things are vulgarly taught: nor of a common practiser so ready to be executed: I, rather, let such measures be reckened incident to some of our other Artes, dealing with thinges on high, more purposely, then this vulgar Land measuring Geometrie doth: as in _Perspectiue_ and _Astronomie, &c._ Of these Feates (farther applied) is Sprong the
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Feate of _Geodesie_, or Land Measuring: more cunningly to measure & Suruey Land, Woods, and Waters, a farre of. More cunningly, I say: But God knoweth (hitherto) in these Realmes of England and Ireland (whether through ignorance or fraude, I can not tell, in euery particular) [Note.] how great wrong and iniurie hath (in my time) bene committed by vntrue
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measuring and surueying of Land or Woods, any way. And, this I am sure: that the Value of the difference, betwene the truth and such Surueyes, would haue bene hable to haue fod (for euer) in eche of our two Vniuersities, an excellent Mathematicall Reader: to eche, allowing (yearly) a hundred Markes of lawfull money of this realme: which, in
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dede, would seme requisit, here, to be had (though by other wayes prouided for) as well, as, the famous Vniuersitie of Paris, hath two Mathematicall Readers: and eche, two hundreth French Crownes yearly, of the French Kinges magnificent liberalitie onely. Now, againe, to our purpose returning: Moreouer, of the former knowledge Geometricall, are growen the Skills of _Geographie_, _Chorographie_, _Hydrographie_,
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and _Stratarithmetrie_. +Geographie+ teacheth wayes, by which, in sdry formes, (as _Sphrike_, _Plaine_ or other), the Situation of Cities, Townes, Villages, Fortes, Castells, Mountaines, Woods, Hauens, Riuers, Crekes, & such other things, vp the outface of the earthly Globe (either in the whole, or in some principall mber and portion therof ctayned) may be described and designed, in cmensurations Analogicall
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to Nature and veritie: and most aptly to our vew, may be represented. Of this Arte how great pleasure, and how manifolde commodities do come vnto vs, daily and hourely: of most men, is perceaued. While, some, to beautifie their Halls, Parlers, Chambers, Galeries, Studies, or Libraries with: other some, for thinges past, as battels fought, earthquakes, heauenly fyringes, &
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such occurentes, in histories mentioned: therby liuely, as it were, to vewe the place, the region adioyning, the distance from vs: and such other circumstances. Some other, presently to vewe the large dominion of the Turke: the wide Empire of the Moschouite: and the litle morsell of ground, where Christendome (by profession) is certainly knowen. Litle, I say, in respecte
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of the rest. &c. Some, either for their owne iorneyes directing into farre landes: or to vnderstand of other mens trauailes. To conclude, some, for one purpose: and some, for an other, liketh, loueth, getteth, and vseth, Mappes, Chartes, & Geographicall Globes. Of whose vse, to speake sufficiently, would require a booke peculier. +Chorographie+ seemeth to be an vnderling, and
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a twig, of _Geographie_: and yet neuerthelesse, is in practise manifolde, and in vse very ample. This teacheth Analogically to describe a small portion or circuite of ground, with the contentes: not regarding what commensuration it hath to the whole, or any parcell, without it, contained. But in the territory or parcell of ground which it taketh in hand to
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make description of, it leaueth out (or vndescribed) no notable, or odde thing, aboue the ground visible. Yea and sometimes, of thinges vnder ground, geueth some peculier marke: or warning: as of Mettall mines, Cole pittes, Stone quarries. &c. Thus, a Dukedome, a Shiere, a Lordship, or lesse, may be described distinctly. But marueilous pleasant, and profitable it is, in
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the exhibiting to our eye, and commensuration, the plat of a Citie, Towne, Forte, or Pallace, in true Symmetry: not approching to any of them: and out of Gunne shot. &c. Hereby, the _Architect_ may furnishe him selfe, with store of what patterns he liketh: to his great instruction: euen in those thinges which outwardly are proportioned: either simply in
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them selues: or respectiuely, to Hilles, Riuers, Hauens, and Woods adioyning. Some also, terme this particular description of places, _Topographie_. +Hydrographie+, deliuereth to our knowledge, on Globe or in Plaine, the perfect Analogicall description of the Ocean Sea coastes, through the whole world: or in the chiefe and principall partes thereof: with the Iles and chiefe particular places of daungers,
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conteyned within the boundes, and Sea coastes described: as, of Quicksandes, Bankes, Pittes, Rockes, Races, Countertides, Whorlepooles. &c. This, dealeth with the Element of the water chiefly: as _Geographie_ did principally take the Element of the Earthes description (with his appertenances) to taske. And besides thys, _Hydrographie_, requireth a particular Register of certaine Landmarkes (where markes may be had) from
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the sea, well hable to be skried, in what point of the Seacumpase they appeare, and what apparent forme, Situation, and bignes they haue, in respecte of any daungerous place in the sea, or nere vnto it, assigned: And in all Coastes, what Mone, maketh full Sea: and what way, the Tides and Ebbes, come and go, the _Hydrographer_ ought
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to recorde. The Soundinges likewise: and the Chanels wayes: their number, and depthes ordinarily, at ebbe and flud, ought the _Hydrographer_, by obseruation and diligence of _Measuring_, to haue certainly knowen. And many other pointes, are belonging to perfecte _Hydrographie_, and for to make a _Rutter_, by: of which, I nede not here speake: as of the describing, in any
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place, vpon Globe or Plaine, the . pointes of the Compase, truely: (wherof, scarsly foure, in England, haue right knowledge: bycause, the lines therof, are no straight lines, nor Circles.) Of making due proiection of a Sphere in plaine. Of the Variacion of the Compas, from true Northe: And such like matters (of great importance, all) I leaue to speake
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of, in this place: bycause, I may seame (al ready) to haue enlarged the boundes, and duety of an Hydographer, much more, then any man (to this day) hath noted, or prescribed. Yet am I well hable to proue, all these thinges, to appertaine, and also to be proper to the Hydrographer. The chief vse and ende of this Art,
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is the Art of Nauigation: but it hath other diuerse vses: euen by them to be enioyed, that neuer lacke sight of land. +Stratarithmetrie+, is the Skill, (appertainyng to the warre,) by which a man can set in figure, analogicall to any _Geometricall_ figure appointed, any certaine number or summe of men: of such a figure capable: (by reason of
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the vsuall spaces betwene Souldiers allowed: and for that, of men, can be made no Fractions. Yet, neuertheles, he can order the giuen summe of men, for the greatest such figure, that of them, c be ordred) and certifie, of the ouerplus: (if any be) and of the next certaine summe, which, with the ouerplus, will admit a figure exactly
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proportionall to the figure assigned. By which Skill, also, of any army or company of men: (the figure & sides of whose orderly standing, or array, is knowen) he is able to expresse the iust number of men, within that figure conteined: or (orderly) able to be conteined. [* Note.] * And this figure, and sides therof, he is hable
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to know: either beyng by, and at hand: or a farre of. Thus farre, stretcheth the description and property of _Stratarithmetrie_: sufficient for this tyme and place. [The difference betwene Stratarithmetrie and Tacticie.] It differreth from the Feate _Tacticall_, _De aciebus instruendis._ bycause, there, is necessary the wisedome and foresight, to what purpose he so ordreth the men: and Skillfull
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hability, also, for any occasion, or purpose, to deuise and vse the aptest and most necessary order, array and figure of his Company and Summe of men. By figure, I meane: as, either of a _Perfect Square_, _Triangle_, _Circle_, _Ouale_, _long square_, (of the Grekes it is called _Eteromekes_) _Rhombe_, _Rhombod_, _Lunular_, _Ryng_, _Serpentine_, and such other Geometricall figures: Which,
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in warres, haue ben, and are to be vsed: for commodiousnes, necessity, and auauntage &c. And no small skill ought he to haue, that should make true report, or nere the truth, of the numbers and Summes, of footemen or horsemen, in the Enemyes ordring. A farre of, to make an estimate, betwene nere termes of More and Lesse, is
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not a thyng very rife, among those that gladly would do it. [I. D. Frende, you will finde it hard, to performe my description of this Feate. But by Chorographie, you may helpe your selfe some what: where the Figures knowne (in Sides and Angles) are not Regular: And where, Resolution into Triangles can serue. &c. And yet you will
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finde it strange to deale thus generally with Arithmeticall figures: and, that for Battayle ray. Their contentes, differ so much from like Geometricall Figures.] Great pollicy may be vsed of the Capitaines, (at tymes fete, and in places conuenient) as to vse Figures, which make greatest shew, of so many as he hath: and vsing the aduauntage of the three
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kindes of vsuall spaces: (betwene footemen or horsemen) to take the largest: or when he would seme to haue few, (beyng many:) contrarywise, in Figure, and space. The Herald, Purseuant, Sergeant Royall, Capitaine, or who soeuer is carefull to come nere the truth herein, besides the Iudgement of his expert eye, his skill of Ordering _Tacticall_, the helpe of his
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Geometricall instrument: Ring, or Staffe Astronomicall: (commodiously framed for cariage and vse) He may wonderfully helpe him selfe, by perspectiue Glasses. In which, (I trust) our posterity will proue more skillfull and expert, and to greater purposes, then in these dayes, can (almost) be credited to be possible. Thus haue I lightly passed ouer the Artificiall Feates, chiefly dependyng vpon
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vulgar _Geometrie_: & commonly and generally reckened vnder the name of _Geometrie_. But there are other (very many) _Methodicall Artes_, which, declyning from the purity, simplicitie, and Immateriality, of our Principall Science of _Magnitudes_: do yet neuertheles vse the great ayde, direction, and Method of the sayd principall Science, and haue propre names, and distinct: both from the Science of
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_Geometrie_, (from which they are deriued) and one from the other. As +Perspectiue, Astronomie, Musike, Cosmographie, Astrologie, Statike, Anthropographie, Trochilike, Helicosophie, Pneumatithmie, Menadrie, Hypogeiodie, Hydragogie, Horometrie, Zographie, Architecture, Nauigation, Thaumaturgike+ and +Archemastrie+. I thinke it necessary, orderly, of these to giue some peculier descriptions: and withall, to touch some of their commodious vses, and so to make this Preface, to
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be a little swete, pleasant Nosegaye for you: to comfort your Spirites, beyng almost out of courage, and in despayre, (through brutish brute) Weenyng that _Geometrie_, had but serued for buildyng of an house, or a curious bridge, or the roufe of Westminster hall, or some witty pretty deuise, or engyn, appropriate to a Carpenter, or a Ioyner &c. That
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the thing is farre otherwise, then the world, (commonly) to this day, hath demed, by worde and worke, good profe wilbe made. Among these Artes, by good reason, +Perspectiue+ ought to be had, ere of _Astronomicall Apparences_, perfect knowledge can be atteyned. And bycause of the prerogatiue of _Light_, beyng the first of _Gods Creatures_: and the eye, the light
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of our body, and his Sense most mighty, and his organ most Artificiall and _Geometricall_: At _Perspectiue_, we will begyn therfore. +Perspectiue, is an Art Mathematicall, which demonstrateth the maner, and properties, of all Radiations Direct, Broken, and Reflected.+ This Description, or Notation, is brief: but it reacheth so farre, as the world is wyde. It concerneth all Creatures, all
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Actions, and passions, by Emanation of beames perfourmed. Beames, or naturall lines, (here) I meane, not of light onely, or of colour (though they, to eye, giue shew, witnes, and profe, wherby to ground the Arte vpon) but also of other _Formes_, both _Substantiall_, and _Accidentall_, the certaine and determined actiue Radiall emanations. By this Art (omitting to speake of
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the highest pointes) we may vse our eyes, and the light, with greater pleasure: and perfecter Iudgement: both of things, in light seen, & of other: which by like order of Lightes Radiations, worke and produce their effectes. We may be ashamed to be ignorant of the cause, why so sundry wayes our eye is deceiued, and abused: as, while
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the eye weeneth a rod Globe or Sphere (beyng farre of) to be a flat and plaine Circle, and so likewise iudgeth a plaine Square, to be rod: supposeth walles parallels, to approche, a farre of: rofe and floure parallels, the one to bend downward, the other to rise vpward, at a little distance from you. Againe, of thinges being
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in like swiftnes of mouing, to thinke the nerer, to moue faster: and the farder, much slower. Nay, of two thinges, wherof the one (incomparably) doth moue swifter then the other, to deme the slower to moue very swift, & the other to stand: what an error is this, of our eye? Of the Raynbow, both of his Colours, of
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the order of the colours, of the bignes of it, the place and heith of it, (&c) to know the causes demonstratiue, is it not pleasant, is it not necessary? of two or three Sonnes appearing: of Blasing Sterres: and such like thinges: by naturall causes, brought to passe, (and yet neuertheles, of farder matter, Significatiue) is it not commodious
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for man to know the very true cause, & occasion Naturall? Yea, rather, is it not, greatly, against the Souerainty of Mans nature, to be so ouershot and abused, with thinges (at hand) before his eyes? as with a Pecockes tayle, and a Doues necke: or a whole ore, in water, holden, to seme broken. Thynges, farre of, to seeme
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nere: and nere, to seme farre of. Small thinges, to seme great: and great, to seme small. One man, to seme an Army. Or a man to be curstly affrayed of his owne shaddow. Yea, so much, to feare, that, if you, being (alone) nere a certaine glasse, and proffer, with dagger or sword, to foyne at the glasse, you
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shall suddenly be moued to giue backe (in maner) by reason of an Image, [ A marueilous Glasse.] appearing in the ayre, betwene you & the glasse, with like hand, sword or dagger, & with like quicknes, foyning at your very eye, likewise as you do at the Glasse. Straunge, this is, to heare of: but more meruailous to behold,
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then these my wordes can signifie. And neuerthelesse by demonstration Opticall, the order and cause therof, is certified: euen so, as the effect is consequent. Yea, thus much more, dare I take vpon me, toward the satisfying of the noble courrage, that longeth ardently for the wisedome of Causes Naturall: as to let him vnderstand, that, in London, he may
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with his owne eyes, haue profe of that, which I haue sayd herein. A Gentleman, (which, for his good seruice, done to his Countrey, is famous and honorable: [S. W. P.] and for skill in the Mathematicall Sciences, and Languages, is the Od man of this land. &c.) euen he, is hable: and (I am sure) will, very willingly, let
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the Glasse, and profe be sene: and so I (here) request him: for the encrease of wisedome, in the honorable: and for the stopping of the mouthes malicious: and repressing the arrogancy of the ignorant. Ye may easily gesse, what I meane. This Art of _Perspectiue_, is of that excellency, and may be led, to the certifying, and executing of
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such thinges, as no man would easily beleue: without Actuall profe perceiued. I speake nothing of _Naturall Philosophie_, which, without _Perspectiue_, can not be fully vnderstanded, nor perfectly atteined vnto. Nor, of _Astronomie_: which, without _Perspectiue_, can not well be grounded: Nor _Astrologie_, naturally Verified, and auouched. That part hereof, which dealeth with Glasses (which name, Glasse, is a generall
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name, in this Arte, for any thing, from which, a Beame reboundeth) is called _Catoptrike_: and hath so many vses, both merueilous, and proffitable: that, both, it would hold me to long, to note therin the principall conclusions, all ready knowne: And also (perchaunce) some thinges, might lacke due credite with you: And I, therby, to leese my labor: and
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you, to slip into light Iudgement, [* ] Before you haue learned sufficiently the powre of Nature and Arte. Now, to procede: +Astronomie, is an Arte Mathematicall, which demonstrateth the distance, magnitudes, and all naturall motions, apparences, and passions propre to the Planets and fixed Sterres: for any time past, present and to come: in respect of a certaine Horizon,
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or without respect of any Horizon.+ By this Arte we are certified of the distance of the Starry Skye, and of eche _Planete_ from the Centre of the Earth: and of the greatnes of any Fixed starre sene, or _Planete_, in respect of the Earthes greatnes. As, we are sure (by this Arte) that the Solidity, Massines and Body of
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the _Sonne_, conteineth the quantitie of the whole Earth and Sea, a hundred thre score and two times, lesse by one eight parte of the earth. But the Body of the whole earthly globe and Sea, is bigger then the body of the Mone, three and forty times lesse by of the Mone. Wherfore the _Sonne_ is bigger then the
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_Mone_, times, lesse, by / that is, precisely / bigger then the _Mone_. And yet the vnskillfull man, would iudge them a like bigge. Wherfore, of Necessity, the one is much farder from vs, then the other. The _Sonne_, when he is fardest from the earth (which, now, in our age, is, when he is in the . degree, of
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Cancer) is, Semidiameters of the Earth, distante. And the _Mone_ when she is fardest from the earth, is Semidiameters of the earth and The nerest, that the _Mone_ commeth to the earth, is Semidiameters 52 The distance of the Starry Skye is, fr vs, in Semidiameters of the earth 20081 Twenty thousand fourescore, one, and almost a halfe. Subtract from
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this, the _Mones_ nerest distance, from the Earth: and therof remaineth Semidiameters of the earth 20029 Twenty thousand nine and twenty and a quarter. [Note.] So thicke is the heauenly Palace, that the _Planetes_ haue all their exercise in, and most meruailously perfourme the Commadement and Charge to them giuen by the omnipotent Maiestie of the king of kings. This
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is that, which in _Genesis_ is called _Ha Rakia_. Consider it well. The Semidiameter of the earth, cteineth of our common miles / three thousand, foure hundred thirty six and foure eleuenth partes of one myle: Such as the whole earth and Sea, round about, is . One and twenty thousand six hundred of our myles. Allowyng for euery degree
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of the greatest circle, thre score myles. Now if you way well with your selfe but this litle parcell of frute _Astronomicall_, as concerning the bignesse, Distances of _Sonne_, _Mone_, _Sterry Sky_, and the huge massines of _Ha Rakia_, will you not finde your Consciences moued, with the kingly Prophet, to sing the confession of Gods Glory, and say, +_The
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Heauens declare the glory of God, and the Firmament =[Ha Rakia]= sheweth forth the workes of his handes_+. And so forth, for those fiue first staues, of that kingly Psalme. Well, well, It is time for some to lay hold on wisedome, and to Iudge truly of thinges: and notso to expound the Holy word, all by Allegories: as to
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Neglect the wisedome, powre and Goodnes of God, in, and by his Creatures, and Creation to be seen and learned. By parables and Analogies of whose natures and properties, the course of the Holy Scripture, also, declareth to vs very many Mysteries. The whole Frame of Gods Creatures, (which is the whole world,) is to vs, a bright glasse: from
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which, by reflexion, reboundeth to our knowledge and perceiuerance, Beames, and Radiations: representing the Image of his Infinite goodnes, Omnipotcy, and wisedome. And we therby, are taught and persuaded to Glorifie our Creator, as God: and be thankefull therfore. Could the Heathenistes finde these vses, of these most pure, beawtifull, and Mighty Corporall Creatures: and shall we, after that the
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true _Sonne_ of rightwisenesse is risen aboue the _Horizon_, of our temporall _Hemisphrie_, and hath so abundantly streamed into our hartes, the direct beames of his goodnes, mercy, and grace: Whose heat All Creatures feele: Spirituall and Corporall: Visible and Inuisible. Shall we (I say) looke vpon the _Heauen_, _Sterres_, and _Planets_, as an Oxe and an Asse doth: no
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furder carefull or inquisitiue, what they are: why were they Created, How do they execute that they were Created for? Seing, All Creatures, were for our sake created: and both we, and they, Created, chiefly to glorifie the Almighty Creator: and that, by all meanes, to vs possible. _Nolite ignorare_ (saith _Plato in Epinomis_) _Astronomiam, Sapientissim quiddam esse._ +_Be ye
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not ignorant, Astronomie to be a thyng of excellent wisedome._+ _Astronomie_, was to vs, from the beginning commended, and in maner commaunded by God him selfe. In asmuch as he made the _Sonne_, _Mone_, and _Sterres_, to be to vs, for _Signes_, and knowledge of Seasons, and for Distinctions of Dayes, and yeares. Many wordes nede not. But I wish,
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euery man should way this word, _Signes_. And besides that, conferre it also with the tenth Chapter of _Hieremie_. And though Some thinke, that there, they haue found a rod: Yet Modest Reason, will be indifferent Iudge, who ought to be beaten therwith, in respect of our purpose. Leauing that: I pray you vnderstand this: that without great diligence of
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Obseruation, examination and Calculation, their periods and courses (wherby _Distinction_ of Seasons, yeares, and New Mones might precisely be knowne) could not exactely be certified. Which thing to performe, is that _Art_, which we here haue Defined to be _Astronomie_. Wherby, we may haue the distinct Course of Times, dayes, yeares, and Ages: aswell for Considerati of Sacred Prophesies, accomplished
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in due time, foretold: as for high Mysticall Solemnities holding: And for all other humaine affaires, Conditions, and couenantes, vpon certaine time, betwene man and man: with many other great vses: Wherin, (verely), would be great incertainty, Confusion, vntruth, and brutish Barbarousnes: without the wonderfull diligence and skill of this Arte: continually learning, and determining Times, and periodes of Time,
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by the Record of the heauenly booke, wherin all times are written: and to be read with an _Astronomicall staffe_, in stede of a festue. +Musike+, of Motion, hath his Originall cause: Therfore, after the motions most swift, and most Slow, which are in the Firmament, of Nature performed: and vnder the _Astronomers Consideration_: now I will Speake of an
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other kinde of _Motion_, producing sound, audible, and of Man numerable. _Musike_ I call here that _Science_, which of the Grekes is called _Harmonice_. Not medling with the Controuersie betwene the auncient _Harmonistes_, and _Canonistes_. +Musike is a Mathematicall Science, which teacheth, by sense and reason, perfectly to iudge, and order the diuersities of soundes, hye and low.+ _Astronomie_ and
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_Musike_ are Sisters, saith _Plato_. As, for _Astronomie_, the eyes: So, for _Harmonious Motion_, the eares were made. But as _Astronomie_ hath a more diuine Contemplation, and cmodity, then mortall eye can perceiue: So, is _Musike_ to be considered, [.] that the * Minde may be preferred, before the eare. And from audible sound, we ought to ascende, to the
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examination: which numbers are _Harmonious_, and which not. And why, either, the one are: or the other are not. I could at large, [.] in the heauenly * motions and distances, describe a meruailous Harmonie, of _Pythagoras_ Harpe [.] with eight stringes. Also, somwhat might be sayd of _Mercurius_ * two Harpes, [.] eche of foure Stringes Elementall. And very
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straunge matter, might be alledged of the _Harmonie_, [.] to our * Spirituall part appropriate. As in _Ptolomaus_ third boke, in the fourth and sixth Chapters may appeare. * [.] And what is the cause of the apt bonde, and frendly felowship, of the Intellectuall and Mentall part of vs, with our grosse & corruptible body: but a certaine Meane,
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and _Harmonious Spiritualitie, with both participatyng, & of both (in a maner) resultynge In [.] the * Tune of Mans voyce, and also [.] * the sound of Instrument_, what might be sayd, of _Harmonie_: No common Musicien would lightly beleue. [I. D. Read in Aristotle his . booke of Politikes: the , , and . chapters. Where you shall
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haue some occasion farder to thinke of Musike, than commonly is thought.] But of the sundry Mixture (as I may terme it) and concurse, diuerse collation, and Application of these _Harmonies_: as of thre, foure, fiue, or mo: Maruailous haue the effectes ben: and yet may be founde, and produced the like: with some proportionall consideration for our time, and
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being: in respect of the State, of the thinges then: in which, and by which, the wondrous effectes were wrought. _Democritus_ and _Theophrastus_ affirmed, that, by _Musike_, griefes and diseases of the Minde, and body might be cured, or inferred. And we finde in Recorde, that _Terpander_, _Arion_, _Ismenias_, _Orpheus_, _Amphion_, _Dauid_, _Pythagoras_, _Empedocles_, _Asclepiades_ and _Timotheus_, by _Harmonicall_ Consoncy,
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haue done, and brought to pas, thinges, more then meruailous, to here of. Of them then, making no farder discourse, in this place: Sure I am, that Common _Musike_, commonly vsed, is found to the _Musiciens_ and Hearers, to be so Commodious and pleasant, That if I would say and dispute, but thus much: That it were to be otherwise
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vsed, then it is, I should finde more repreeuers, then I could finde priuy, or skilfull of my meaning. In thinges therfore euident, and better knowen, then I can expresse: and so allowed and liked of, (as I would wish, some other thinges, had the like hap) I will spare to enlarge my lines any farder, but consequently follow my
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purpose. +Of Cosmographie+, I appointed briefly in this place, to geue you some intelligence. +Cosmographie, is the whole and perfect description of the heauenly, and also elementall parte of the world, and their homologall application, and mutuall collation necessarie.+ This Art, requireth _Astronomie_, _Geographie_, _Hydrographie_ and _Musike_. Therfore, it is no small Arte, nor so simple, as in common practise,
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it is (slightly) considered. This matcheth Heauen, and the Earth, in one frame, and aptly applieth parts Correspdent: So, as, the Heauenly Globe, may (in practise) be duely described vpon the Geographicall, and Hydrographicall Globe. And there, for vs to consider an _quonoctiall Circle_, _an Ecliptike line_, _Colures_, _Poles_, _Sterres_ in their true Longitudes, Latitudes, Declinations, and Verticalitie: also Climes,
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and Parallels: and by an _Horizon_ annexed, and reuolution of the earthly Globe (as the Heauen, is, by the _Primouant_, caried about in . quall Houres) to learne the Risinges and Settinges of Sterres (of _Virgill_ in his _Georgikes_: of _Hesiod_: of _Hippocrates_ in his _Medicinall Sphre_, to Perdicca King of the Macedonians: of _Diocles_, to King _Antigonus_, and of
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other famous _Philosophers_ prescribed) a thing necessary, for due manuring of the earth, for _Nauigation_, for the Alteration of mans body: being, whole, Sicke, wounded, or brused. By the Reuolution, also, or mouing of the Globe Cosmographicall, the Rising and Setting of the Sonne: the Lengthes, of dayes and nightes: the Houres and times (both night and day) are knowne:
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with very many other pleasant and necessary vses: Wherof, some are knowne: but better remaine, for such to know and vse: [] who of a sparke of true fire, can make a wonderfull bonfire, by applying of due matter, duely. +Of Astrologie+, here I make an Arte, seuerall from _Astronomie_: not by new deuise, but by good reason and authoritie:
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for, +Astrologie, is an Arte Mathematicall, which reasonably demonstrateth the operations and effectes, of the naturall beames, of light, and secrete influence: of the Sterres and Planets: in euery element and elementall body: at all times, in any Horizon assigned.+ This Arte is furnished with many other great Artes and experiences: As with perfecte _Perspectiue_, _Astronomie_, _Cosmographie_, _Naturall Philosophie_ of
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