The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara | Page 7

of findyng an vnknowen number, by
Addyng of a Number, & Diuision & aequation+. Here haue you the
name: and also the principall partes of the Rule, touched. To name it,
The rule, or Art of Aequation, doth signifie the middle part and the
State of the Rule. This Rule, hath his peculier Characters:
[5.]
and the principal partes of Arithmetike, to it appertayning, do differre
from the other Arithmeticall operations. This Arithmetike, hath
Numbers Simple, Compound, Mixt: and Fractions, accordingly. This
Rule, and Arithmetike of Algiebar, is so profound, so generall and so
(in maner) conteyneth the whole power of Numbers Application
practicall: that mans witt, can deale with nothyng, more proffitable
about numbers: nor match, with a thyng, more mete for the diuine force
of the Soule, (in humane Studies, affaires, or exercises) to be tryed in.
Perchaunce you looked for, (long ere now,) to haue had some particular
profe, or euident testimony of the vse, proffit and Commodity of
Arithmetike vulgar, in the Common lyfe and trade of men. Therto, then,
I will now frame my selfe: But herein great care I haue, least length of

sundry profes, might make you deme, that either I did misdoute your
zelous mynde to vertues schole: or els mistrust your hable witts, by
some, to gesse much more. A profe then, foure, fiue, or six, such, will I
bryng, as any reasonable man, therwith may be persuaded, to loue &
honor, yea learne and exercise the excellent Science of Arithmetike.
And first: who, nerer at hand, can be a better witnesse of the frute
receiued by Arithmetike, then all kynde of Marchants? Though not all,
alike, either nede it, or vse it. How could they forbeare the vse and
helpe of the Rule, called the Golden Rule? Simple and Compounde:
both forward and backward? How might they misse Arithmeticall helpe
in the Rules of Felowshyp: either without tyme, or with tyme? and
betwene the Marchant & his Factor? The Rules of Bartering in wares
onely: or part in wares, and part in money, would they gladly want?
Our Marchant venturers, and Trauaylers ouer Sea, how could they
order their doynges iustly and without losse, vnleast certaine and
generall Rules for Exchaunge of money, and Rechaunge, were, for their
vse, deuised? The Rule of Alligation, in how sundry cases, doth it
conclude for them, such precise verities, as neither by naturall witt, nor
other experience, they, were hable, els, to know? And (with the
Marchant then to make an end) how ample & wonderfull is the Rule of
False positions? especially as it is now, by two excellent
Mathematiciens (of my familier acquayntance in their life time)
enlarged? I meane Gemma Frisius, and Simon Iacob. Who can either in
brief conclude, the generall and Capitall Rules? or who can Imagine the
Myriades of sundry Cases, and particular examples, in Act and earnest,
continually wrought, tried and concluded by the forenamed Rules,
onely? How sundry other Arithmeticall practises, are commonly in
Marchantes handes, and knowledge: They them selues, can, at large,
testifie.
The Mintmaster, and Goldsmith, in their Mixture of Metals, either of
diuerse kindes, or diuerse values: how are they, or may they, exactly be
directed, and meruailously pleasured, if Arithmetike be their guide?
And the honorable Phisicians, will gladly confesse them selues, much
beholding to the Science of Arithmetike, and that sundry wayes: But
chiefly in their Art of Graduation, and compounde Medicines. And

though Galenus, Auerrois, Arnoldus, Lullus, and other haue published
their positions, aswell in the quantities of the Degrees aboue
Temperament, as in the Rules, concluding the new Forme resulting: yet
a more precise, commodious, and easy Method, is extant: by a
Countreyman of ours
[R. B.]
(aboue 200. yeares ago) inuented. And forasmuch as I am vncertaine,
who hath the same: or when that litle Latin treatise, (as the Author writ
it,) shall come to be Printed: (Both to declare the desire I haue to
pleasure my Countrey, wherin I may: and also, for very good profe of
Numbers vse, in this most subtile and frutefull, Philosophicall
Conclusion,) I entend in the meane while, most briefly, and with my
farder helpe, to communicate the pith therof vnto you.
First describe a circle: whose diameter let be an inch. Diuide the
Circumference into foure equall partes. From the Center, by those 4.
sections, extend 4. right lines: eche of 4. inches and a halfe long: or of
as many as you liste, aboue 4. without the circumference of the circle:
So that they shall be of 4. inches long (at the least) without the Circle.
Make good euident markes, at euery inches end. If you list, you may
subdiuide the inches againe into 10. or 12. smaller partes, equall. At the
endes of the lines, write the names of