The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara | Page 3

diuerse trades of these two excellent Philosophers (and am
most sure, both, that Plato right well, otherwise could teach: and that
Aristotle mought boldely, with his hearers, haue dealt in like sorte as
Plato did) I am in no little pang of perplexitie: Bycause, that, which I
mislike, is most easy for me to performe (and to haue Plato for my
example.) And that, which I know to be most commendable: and (in
this first bringyng, into common handling, the Artes Mathematicall) to
be most necessary: is full of great difficultie and sundry daungers. Yet,
neither do I think it mete, for so straunge matter (as now is ment to be
published) and to so straunge an audience, to be bluntly, at first, put
forth, without a peculiar Preface: Nor (Imitatyng Aristotle) well can I
hope, that accordyng to the amplenes and dignitie of the State
Mathematicall, I am able, either playnly to prescribe the materiall
boundes: or precisely to expresse the chief purposes, and most
wonderfull applications therof. And though I am sure, that such as did
shrinke from Plato his schole, after they had perceiued his finall
conclusion, would in these thinges haue ben his most diligent hearers
(so infinitely mought their desires, in fine and at length, by our Artes
Mathematicall be satisfied) yet, by this my Praeface & forewarnyng,
Aswell all such, may (to their great behofe) the soner, hither be allured:
as also the Pythagoricall, and Platonicall perfect scholer, and the
constant profound Philosopher, with more ease and spede, may (like
the Bee,) gather, hereby, both wax and hony.
[The intent of this Preface.]

Wherfore, seyng I finde great occasion (for the causes alleged, and
farder, in respect of my Art Mathematike generall) to vse "a certaine
forewarnyng and Praeface, whose content shalbe, that mighty, most
plesaunt, and frutefull Mathematicall Tree, with his chief armes and
second (grifted) braunches: Both, what euery one is, and also, what
commodity, in generall, is to be looked for, aswell of griff as stocke:
And forasmuch as this enterprise is so great, that, to this our tyme, it
neuer was (to my knowledge) by any achieued: And also it is most hard,
in these our drery dayes, to such rare and straunge Artes, to wyn due
and common credit:" Neuertheles, if, for my sincere endeuour to
satisfie your honest expectation, you will but lend me your thankefull
mynde a while: and, to such matter as, for this time, my penne (with
spede) is hable to deliuer, apply your eye or eare attentifely:
perchaunce, at once, and for the first salutyng, this Preface you will
finde a lesson long enough. And either you will, for a second (by this)
be made much the apter: or shortly become, well hable your selues, of
the lyons claw, to coniecture his royall symmetrie, and farder propertie.
Now then, gentle, my frendes, and countrey men, Turne your eyes, and
bend your myndes to that doctrine, which for our present purpose, my
simple talent is hable to yeld you.
All thinges which are, & haue beyng, are found vnder a triple diuersitie
generall. For, either, they are demed Supernaturall, Naturall, or, of a
third being. Thinges Supernaturall, are immateriall, simple, indiuisible,
incorruptible, & vnchangeable. Things Naturall, are materiall,
compounded, diuisible, corruptible, and chaungeable. Thinges
Supernaturall, are, of the minde onely, comprehended: Things Naturall,
of the sense exterior, ar hable to be perceiued. In thinges Naturall,
probabilitie and coniecture hath place: But in things Supernaturall,
chief demonstration, & most sure Science is to be had. By which
properties & comparasons of these two, more easily may be described,
the state, condition, nature and property of those thinges, which, we
before termed of a third being: which, by a peculier name also, are
called Thynges Mathematicall. For, these, beyng (in a maner) middle,
betwene thinges supernaturall and naturall: are not so absolute and
excellent, as thinges supernatural: Nor yet so base and grosse, as things
naturall: But are thinges immateriall: and neuerthelesse, by materiall

things hable somewhat to be signified. And though their particular
Images, by Art, are aggregable and diuisible: yet the generall Formes,
notwithstandyng, are constant, vnchaungeable, vntransformable, and
incorruptible. Neither of the sense, can they, at any tyme, be perceiued
or iudged. Nor yet, for all that, in the royall mynde of man, first
conceiued. But, surmountyng the imperfection of coniecture, weenyng
and opinion: and commyng short of high intellectuall conception, are
the Mercurial fruite of Dianoeticall discourse, in perfect imagination
subsistyng. A meruaylous newtralitie haue these thinges Mathematicall,
and also a straunge participation betwene thinges supernaturall,
immortall, intellectual, simple and indiuisible: and thynges naturall,
mortall, sensible, compounded and diuisible. Probabilitie and sensible
prose, may well serue in thinges naturall: and is commendable: In
Mathematicall reasoninges, a probable Argument, is nothyng regarded:
nor yet the testimony