Part 9

But wordes, and Argumentes, are no sensible certifying: nor the full and finall frute of Sciences practisable. And though some Artes, haue in them, _Experiences_, yet they are not complete, and brought to the vttermost, they may be stretched vnto, and applyed sensibly. As for example: the Naturall Philosopher disputeth and maketh goodly shew of reason: And the Astronomer, and the Opticall Mechanicien, put some thynges in _Experience_: but neither, all, that they may: nor yet sufficiently, and to the vtmost, those, which they do, There, then, the _Archemaster_ steppeth in, and leadeth forth on, the _Experiences_, by order of his doctrine _Experimentall_, to the chief and finall power of Naturall and Mathematicall Artes. Of two or three men, in whom, this Description of _Archemastry_ was _Experimentally_, verified, I haue read and hard: and good record, is of their such perfection. So that, this Art, is no fantasticall Imagination: as some Sophister, might, _Cum suis Insolubilibus_, 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. To this Science, doth the _Science Alnirangiat_, great Seruice. Muse nothyng of this name. I chaunge not the name, so vsed, and in Print published by other: beyng a name, propre to the Science. Vnder this, commeth _Ars Sintrillia_, by _Artephius_, briefly written. But the chief Science, of the Archemaster, (in this world) as yet knowen, is an other (as it were) OPTICAL Science: wherof, the name shall be told (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: (through the confidence they reposed in my long experience: and tryed sincerity) for the declaryng and reportyng somewhat, of the frute and commodity, by the +Artes Mathematicall, to be atteyned vnto+: euen they, Sore agaynst their willes, are forced, for sundry causes, to satisfie the workemans request, in endyng forthwith: He, so feareth this, so new an attempt, & so costly: And in matter so slenderly (hetherto) among the common Sorte of Studentes, considered or estemed.

And where I was willed, somewhat to alledge, why, in our vulgare Speche, this part of the 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.

[1.]

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

[2.]

Neither are their Studies, hereby, any whit hindred. No more, then the Italian _Vniuersities_, as _Academia Bononiensis_, _Ferrariensis_, _Florentina_, _Mediolanensis_, _Patauina_, _Papiensis_, _Perusina_, _Pisana_, _Romana_, _Senensis_, or any one of them, finde them selues, any deale, disgraced, or their Studies any thing hindred, by _Frater Lucas de Burgo_, or by _Nicolaus Tartalea_, who in vulgar Italian language, haue published, not onely _Euclides Geometrie_, but of _Archimedes_ somewhat: and in Arithmetike and Practicall Geometrie, very large volumes, all in their vulgar speche. Nor in Germany haue the famous _Vniuersities_, any thing bene discontent with _Albertus Durerus_, his Geometricall 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 their reputation to be decayed: or suppose any their Studies to be hindred by the Excellent _P. Nonnius_, his Mathematicall workes, in vulgare speche by him put forth. Haue you not, likewise, in the French tounge, the whole Mathematicall Quadriuie? and yet neither Paris, Orleance, or any of the other Vniuersities of Fraunce, at any time, with the Translaters, or Publishers offended: or any mans Studie thereby hindred?

[3.]

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

[4.]

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

[5.]

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

[Vniuersities.]

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

[☞]

and all Artes, necessary for the best, and most noble State of Common Wealthes.”

[6.]

Besides this, how many a Common Artificer, is there, in these Realmes of England and Ireland, that dealeth with Numbers, Rule, & 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 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 mã (I say) who either hath Charitie toward his brother (and would be glad of his furtherance in vertuous knowledge): or that hath any care & zeale for the bettering of the Cõmon 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 cõmending, or setting forth, Profitable Artes to English 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 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 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 Preface treateth,

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

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

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

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

_Written at my poore House At Mortlake._

_Anno. 1570. February. 9._

[Decoration]

[Transcriber’s 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. 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 Præface: annexed to _Euclide_ (now first)+ published in our Englishe tounge. An. 1570. Febr. 3.

+‡Sciences, and Artes Mathematicall,‡ are, either+

+‡Principall,‡ which are two, onely,+

+Arithmetike.+

+‡Simple‡+, Which dealeth with Numbers onely: 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‡ whereof, is either,+

In thinges Supernaturall, æternall, & Diuine: By Application, _Ascending_. In thinges Mathematicall: without farther Application. In thinges Naturall: both Substãtiall, & Accidentall, Visible, & Inuisible. &c. By Application: _Descending_.

The like Vses and Applications are, (though in a degree lower) in the +Artes Mathematicall Deriuatiue+.

+‡Deriuatiue‡ frõ the Principalls: of which, some haue+

+‡The names of‡ the 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 Nũbers: Simple, Compound, Mixt: And of their Fractions. --Arithmetike of Cossike Nũbers: with their Fractions: And the great Arte of Algiebar.

+_Geometrie_, vulgar: which teacheth Measuring+

+‡At hand‡+

All Lengthes.--+Mecometrie.+ All Plaines: As, Land, Borde, Glasse, &c.--+Embadometrie.+ All Solids: As, Timber, Stone, Vessels, &c.--+Stereometrie.+

+‡With distãce‡+ 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 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 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 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 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 Nũber, 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 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, Sphære, Conoïd, and Sphæroid: and their properties.

+Pneumatithmie,+--Which demonstrateth by close hollow Geometricall figures (Regular and Irregular) the straunge properties (in motion or 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: naturally, not, so, directible, or moueable.

+Hypogeiodie,+--Which demonstrateth, how, vnder the Sphæricall 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 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 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) 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 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.

+¶ Imprinted by _Iohn Day_.+

An. 1570. Feb. 25.

* * * * * * * * * * * * * *

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 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”_] τὸ ὁτὶ [_accent unchanged_] in our worldly affaires [wordly] fall to worke.❉. [_Some text readers may not display the oversized-asterisk symbol._] _Emptying the first._ [Emptyting] Απὸ τάυτης τῆς ἡμέρας, περὶ παντὸς, Αρχιμήδει λέγοντι πιϛευτεόν [ἡμήρας ... πιϛευτέομ] 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 438-439; 451-457; 463-464._]

Additional Notes:

The Greek letter η (eta) was consistently printed as if it were the ou-ligature ȣ. The Latin “-que” 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 “root” sign √ combined with symbols for the power of 2 (doubled for power of 4, or fourth root) and 3. They are shown as ²√ ³√ ⁴√.

Euclid:

The following Propositions were identified by number.

6.12: (How) to find a fourth (line) proportional to three given straight lines.

11.34: In equal parallelepipedal solids the bases are reciprocally proportional to the heights; and those parallelepipedal solids in which the bases are reciprocally proportional to the heights are equal.

11.36: If three straight lines are proportional, then the parallelepipedal solid formed out of the three equals the parallelepipedal solid on the mean which is equilateral, but equiangular with the aforesaid solid.

12.1: Similar polygons inscribed in circles are to one another as the squares on their diameters.

12.2: Circles are to one another as the squares on their diameters.

12.18 (“last”): Spheres are to one another in triplicate ratio of their respective diameters.