irst.
Marke now againe, in what number or place of the lines, the water
Cutteth them. Two wayes you may conclude your purpose: it is to wete,
either by numbers or lines. By numbers: as, if you diuide the side of
your Fundamentall Cube into so many aequall partes, as it is capable of,
conueniently, with your ease, and precisenes of the diuision. For, as
the number of your first and lesse line (in your hollow Pyramis or
Cone,) is to the second or greater (both being counted from the vertex)
so shall the number of the side of your Fundamentall Cube, be to the
number belonging to the Radicall side, of the Cube, dubble to your
Fundamentall Cube: Which being multiplied Cubik wise, will sone shew it
selfe, whether it be dubble or no, to the Cubik number of your
Fundamentall Cube. By lines, thus: As your lesse and first line, (in
your hollow Pyramis or Cone,) is to the second or greater, so let the
Radical side of your Fundamentall Cube, be to a fourth proportionall
line, by the 12. proposition, of the sixth boke of _Euclide_. Which
fourth line, shall be the Rote Cubik, or Radicall side of the Cube,
dubble to your Fundamentall Cube: which is the thing we desired.

[-> God be thanked for this Inuention, & the fruite ensuing.]

For this, may I (with ioy) say, #EURE:KA, EURE:KA, EURE:KA#: thanking
the holy and glorious Trinity: hauing greater cause therto, then

[* Vitruuius. Lib. 9. Cap. 3.]

* _Archimedes_ had (for finding the fraude vsed in the Kinges Crowne, of
Gold): as all men may easily Iudge: by the diuersitie of the frute
following of the one, and the other. Where I spake before, of a hollow
Cubik Coffen: the like vse, is of it: and without waight. Thus. Fill it
with water, precisely full, and poure that water into your Pyramis or
Cone. And here note the lines cutting in your Pyramis or Cone. Againe,
fill your coffen, like as you did before. Put that Water, also, to the
first. Marke the second cutting of your lines. Now, as you proceded
before, so must you here procede.

[* Note.]

* And if the Cube, which you should Double, be neuer so great: you haue,
thus, the proportion (in small) betwene your two litle Cubes: And then,
the side, of that great Cube (to be doubled) being the third, will haue
the fourth, found, to it proportionall: by the 12. of the sixth of
Euclide.

[Note, as concerning the Sphaericall Superficies of the Water.]

Note, that all this while, I forget not my first Proposition S