of waightes, somewhat nere precisenes: by halfing
euer the Sand: they shall, at length, come to a least common waight.
Therein, I leaue the farder matter, to their discretion, whom nede shall
pinche.] The _Venetians_ consideration of waight, may seme precise
enough: by eight descentes progressionall, * halfing, from a grayne.

[I. D.
* For, so, haue you .256. partes of a Graine.]

Your Cube, Sphaere, apt Balance, and conuenient waightes, being ready:
fall to worke.[[*]]. First, way your Cube. Note the Number of the
waight. Way, after that, your Sphaere. Note likewise, the Number of the
waight. If you now find the waight of your Cube, to be to the waight of
the Sphaere, as 21. is to 11: Then you see, how the Mechanicien and
_Experimenter_, without Geometrie and Demonstration, are (as nerely in
effect) tought the proportion of the Cube to the Sphere: as I haue
demonstrated it, in the end of the twelfth boke of _Euclide_. Often, try
with the same Cube and Sphaere. Then, chaunge, your Sphaere and Cube, to
an other matter: or to an other bignes: till you haue made a perfect
vniuersall Experience of it. Possible it is, that you shall wynne to
nerer termes, in the proportion.

When you haue found this one certaine Drop of Naturall veritie, procede
on, to Inferre, and duely to make assay, of matter depending. As,
bycause it is well demonstrated, that a Cylinder, whose heith, and
Diameter of his base, is aequall to the Diameter of the Sphaere, is
Sesquialter to the same Sphaere (that is, as 3. to 2:) To the number of
the waight of the Sphaere, adde halfe so much, as it is: and so haue you
the number of the waight of that Cylinder. Which is also Comprehended of
our former Cube: So, that the base of that Cylinder, is a Circle
described in the Square, which is the base of our Cube. But the Cube and
the Cylinder, being both of one heith, haue their Bases in the same
proportion, in the which, they are, one to an other, in their Massines
or Soliditie. But, before, we haue two numbers, expressing their
Massines, Solidities, and Quantities, by waight: wherfore,

[* =The proportion of the Square to the Circle inscribed.=]

we haue * the proportion of the Square, to the Circle, inscribed in the
same Square. And so are we fallen into the knowledge sensible, and
Experimentall of _Archimedes_ great Secret: of him, by great trauaile of
minde, sought and found. Wherfore, to any Circle giuen, you can giue a
Square aequall: