[* =The Squaring of the Circle, Mechanically.=]
* as I haue taught, in my Annotation, vpon the first proposition of the
twelfth boke, And likewise, to any Square giuen, you may giue a Circle
aequall:
[* =To any Square geuen, to geue a Circle, equall.=]
* If you describe a Circle, which shall be in that proportion, to your
Circle inscribed, as the Square is to the same Circle: This, you may do,
by my Annotations, vpon the second proposition of the twelfth boke of
_Euclide_, in my third Probleme there. Your diligence may come to a
proportion, of the Square to the Circle inscribed, nerer the truth, then
is the proportion of 14. to 11. And consider, that you may begyn at the
Circle and Square, and so come to conclude of the Sphaere, & the Cube,
what their proportion is: as now, you came from the Sphaere to the
Circle. For, of Siluer, or Gold, or Latton Lamyns or plates (thorough
one hole drawen, as the maner is) if you make a Square figure & way it:
and then, describing theron, the Circle inscribed: & cut of, & file
away, precisely (to the Circle) the ouerplus of the Square: you shall
then, waying your Circle, see, whether the waight of the Square, be to
your Circle, as 14. to 11. As I haue Noted, in the beginning of
_Euclides_ twelfth boke. &c. after this resort to my last proposition,
vpon the last of the twelfth. And there, helpe your selfe, to the end.
And, here, Note this, by the way.
[Note Squaring of the Circle without knowledge of the
proportion betwene Circumference and Diameter.]
That we may Square the Circle, without hauing knowledge of the
proportion, of the Circumference to the Diameter: as you haue here
perceiued. And otherwayes also, I can demonstrate it. So that, many haue
cumberd them selues superfluously, by trauailing in that point first,
which was not of necessitie, first: and also very intricate. And easily,
you may, (and that diuersly) come to the knowledge of the Circumference:
the Circles Quantitie, being first knowen. Which thing, I leaue to your
consideration: making hast to despatch an other Magistrall Probleme: and
to bring it, nerer to your knowledge, and readier dealing with, then the
world (before this day,) had it for you, that I can tell of. And that
is, _A Mechanicall Dubblyng of the Cube: &c._ Which may, thus, be done:
[To Dubble the Cube redily: by Art Mechanicall: depending
vppon Demonstration Mathematicall.]
+Make of Copper plates, or Tyn plates,
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