The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara | Page 4

of sense, any whit credited: But onely a perfect
demonstration, of truthes certaine, necessary, and inuincible:
vniuersally and necessaryly concluded: is allowed as sufficient for "an
Argument exactly and purely Mathematical."
[Note the worde, Vnit, to expresse the Greke Monas, & not Vnitie: as
we haue all, commonly, till now, vsed.]
Of Mathematicall thinges, are two principall kindes: namely, Number,
and Magnitude.
[Number.]
Number, we define, to be, a certayne Mathematicall Summe, of Vnits.
And, an Vnit, is that thing Mathematicall, Indiuisible, by participation
of some likenes of whose property, any thing, which is in deede, or is
counted One, may resonably be called One. We account an Vnit, a thing
Mathematicall, though it be no Number, and also indiuisible: because,
of it, materially, Number doth consist: which, principally, is a thing
Mathematicall.
[Magnitude.]
Magnitude is a thing Mathematicall, by participation of some likenes of

whose nature, any thing is iudged long, broade, or thicke. "A thicke
Magnitude we call a Solide, or a Body. What Magnitude so euer, is
Solide or Thicke, is also broade, & long. A broade magnitude, we call a
Superficies or a Plaine. Euery playne magnitude, hath also length. A
long magnitude, we terme a Line. A Line is neither thicke nor broade,
but onely long: Euery certayne Line, hath two endes:
[A point.]
The endes of a line, are Pointes called. A Point, is a thing
Mathematicall, indiuisible, which may haue a certayne determined
situation." If a Poynt moue from a determined situation, the way
wherein it moued, is also a Line: mathematically produced, whereupon,
of the auncient Mathematiciens,
[A Line.]
a Line is called the race or course of a Point. A Poynt we define, by the
name of a thing Mathematicall: though it be no Magnitude, and
indiuisible: because it is the propre ende, and bound of a Line: which is
a true Magnitude.
[Magnitude.]
And Magnitude we may define to be that thing Mathematicall, which is
diuisible for euer, in partes diuisible, long, broade or thicke. Therefore
though a Poynt be no Magnitude, yet Terminatiuely, we recken it a
thing Mathematicall (as I sayd) by reason it is properly the end, and
bound of a line. Neither Number, nor Magnitude, haue any Materialitie.
First, we will consider of Number, and of the Science Mathematicall, to
it appropriate, called Arithmetike: and afterward of Magnitude, and his
Science, called Geometrie. But that name contenteth me not: whereof a
word or two hereafter shall be sayd. How Immateriall and free from all
matter, Number is, who doth not perceaue? yea, who doth not
wonderfully wonder at it? For, neither pure Element, nor Aristoteles,
Quinta Essentia, is hable to serue for Number, as his propre matter.
Nor yet the puritie and simplenes of Substance Spirituall or Angelicall,
will be found propre enough thereto. And therefore the great & godly

Philosopher Anitius Boetius, sayd: Omnia quaecun[que] a primaeua
rerum natura constructa sunt, Numerorum videntur ratione formata.
Hoc enim fuit principale in animo Conditoris Exemplar. That is: +All
thinges (which from the very first originall being of thinges, haue bene
framed and made) do appeare to be Formed by the reason of Numbers.
For this was the principall example or patterne in the minde of the
Creator.+ O comfortable allurement, O rauishing perswasion, to deale
with a Science, whose Subiect, is so Auncient, so pure, so excellent, so
surmounting all creatures, so vsed of the Almighty and
incomprehensible wisdome of the Creator, in the distinct creation of all
creatures: in all their distinct partes, properties, natures, and vertues, by
order, and most absolute number, brought, from Nothing, to the
Formalitie of their being and state. By Numbers propertie therefore, of
vs, by all possible meanes, (to the perfection of the Science) learned,
we may both winde and draw our selues into the inward and deepe
search and vew, of all creatures distinct vertues, natures, properties, and
Formes: And also, farder, arise, clime, ascend, and mount vp (with
Speculatiue winges) in spirit, to behold in the Glas of Creation, the
Forme of Formes, the Exemplar Number of all thinges Numerable:
both visible and inuisible, mortall and immortall, Corporall and
Spirituall. Part of this profound and diuine Science, had Ioachim the
Prophesier atteyned vnto: by Numbers Formall, Naturall, and Rationall,
forseyng, concludyng, and forshewyng great particular euents, long
before their comming. His bookes yet remainyng, hereof, are good
profe: And the noble Earle of Mirandula, (besides that,) a sufficient
witnesse: that Ioachim, in his prophesies, proceded by no other way,
then by Numbers Formall. And this Earle hym selfe, in Rome,
[Ano. 1488.]
* set vp 900. Conclusions, in all kinde of Sciences, openly to be
disputed of: and among the rest, in his Conclusions Mathematicall, (in
the eleuenth Conclusion) hath in Latin, this English sentence. By
Numbers, a way is