The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara | Page 5

had, to the searchyng out, and vnderstandyng of
euery thyng, hable to be knowen. For the verifying of which Conclusion,
I promise to aunswere to the 74. Questions, vnder written, by the way
of Numbers. Which Conclusions, I omit here to rehearse: aswell

auoidyng superfluous prolixitie: as, bycause Ioannes Picus, workes, are
commonly had. But, in any case, I would wish that those Conclusions
were red diligently, and perceiued of such, as are earnest Obseruers and
Considerers of the constant law of numbers: which is planted in thyngs
Naturall and Supernaturall: and is prescribed to all Creatures,
inuiolably to be kept. For, so, besides many other thinges, in those
Conclusions to be marked, it would apeare, how sincerely, & within my
boundes, I disclose the wonderfull mysteries, by numbers, to be
atteyned vnto.
Of my former wordes, easy it is to be gathered, that Number hath a
treble state: One, in the Creator: an other in euery Creature (in respect
of his complete constitution:) and the third, in Spirituall and Angelicall
Myndes, and in the Soule of man. In the first and third state, Number, is
termed Number Numbryng. But in all Creatures, otherwise, Number, is
termed Number Numbred. And in our Soule, Number beareth such a
swaye, and hath such an affinitie therwith: that some of the old
Philosophers taught, Mans Soule, to be a Number mouyng it selfe. And
in dede, in vs, though it be a very Accident: yet such an Accident it is,
that before all Creatures it had perfect beyng, in the Creator,
Sempiternally. Number Numbryng therfore, is the discretion discerning,
and distincting of thinges. But in God the Creator, This discretion, in
the beginnyng, produced orderly and distinctly all thinges. For his
Numbryng, then, was his Creatyng of all thinges. And his Continuall
Numbryng, of all thinges, is the Conseruation of them in being: And,
where and when he will lacke an Vnit: there and then, that particular
thyng shalbe Discreated. Here I stay. But our Seuerallyng, distinctyng,
and Numbryng, createth nothyng: but of Multitude considered, maketh
certaine and distinct determination. And albeit these thynges be
waighty and truthes of great importance, yet (by the infinite goodnes of
the Almighty Ternarie,) Artificiall Methods and easy wayes are made,
by which the zelous Philosopher, may wyn nere this Riuerish Ida, this
Mountayne of Contemplation: and more then Contemplation. And also,
though Number, be a thyng so Immateriall, so diuine, and aeternall: yet
by degrees, by litle and litle, stretchyng forth, and applying some
likenes of it, as first, to thinges Spirituall: and then, bryngyng it lower,
to thynges sensibly perceiued: as of a momentanye sounde iterated:

then to the least thynges that may be seen, numerable: And at length,
(most grossely,) to a multitude of any corporall thynges seen, or felt:
and so, of these grosse and sensible thynges, we are trayned to learne a
certaine Image or likenes of numbers: and to vse Arte in them to our
pleasure and proffit. So grosse is our conuersation, and dull is our
apprehension: while mortall Sense, in vs, ruleth the common wealth of
our litle world. Hereby we say, Three Lyons, are three: or a Ternarie.
Three Egles, are three, or a Ternarie.
[->]
Which * Ternaries, are eche, the Vnion, knot, and Vniformitie, of three
discrete and distinct Vnits. That is, we may in eche Ternarie, thrise,
seuerally pointe, and shew a part, One, One, and One. Where, in
Numbryng, we say One, two, Three. But how farre, these visible Ones,
do differre from our Indiuisible Vnits (in pure Arithmetike, principally
considered) no man is ignorant. Yet from these grosse and materiall
thynges, may we be led vpward, by degrees, so, informyng our rude
Imagination, toward the conceiuyng of Numbers, absolutely (:Not
supposing, nor admixtyng any thyng created, Corporall or Spirituall, to
support, conteyne, or represent those Numbers imagined:) that at length,
we may be hable, to finde the number of our owne name, gloriously
exemplified and registred in the booke of the Trinitie most blessed and
aeternall.
But farder vnderstand, that vulgar Practisers, haue Numbers, otherwise,
in sundry Considerations: and extend their name farder, then to
Numbers, whose least part is an Vnit. For the common Logist,
Reckenmaster, or Arithmeticien, in hys vsing of Numbers: of an Vnit,
imagineth lesse partes: and calleth them Fractions. As of an Vnit, he
maketh an halfe, and thus noteth it, 1/2. and so of other, (infinitely
diuerse) partes of an Vnit. Yea and farder, hath, Fractions of Fractions.
&c. And, forasmuch, as, Addition, Substraction, Multiplication,
Diuision and Extraction of Rotes, are the chief, and sufficient partes of
Arithmetike:
[Arithmetike.]

which is, the Science that demonstrateth the properties, of Numbers,
and all operations, in numbers to be performed:
[Note.]
"How often, therfore, these fiue sundry sortes of Operations, do, for the