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.