taticall,
here rehearsed: that, the Superficies of the water, is Sphaericall.
Wherein, vse your discretion: to the first line, adding a small heare
breadth, more: and to the second, halfe a heare breadth more, to his
length. For, you will easily perceaue, that the difference can be no
greater, in any Pyramis or Cone, of you to be handled. Which you shall
thus trye. _For finding the swelling of the water aboue leuell._
[->]
"Square the Semidiameter, from the Centre of the earth, to your first
Waters Superficies. Square then, halfe the Subtendent of that watry
Superficies (which Subtendent must haue the equall partes of his
measure, all one, with those of the Semidiameter of the earth to your
watry Superficies): Subtracte this square, from the first: Of the
residue, take the Rote Square. That Rote, Subtracte from your first
Semidiameter of the earth to your watry Superficies: that, which
remaineth, is the heith of the water, in the middle, aboue the leuell."
Which, you will finde, to be a thing insensible. And though it were
greatly sensible, *
[* Note.]
yet, by helpe of my sixt Theoreme vpon the last Proposition of Euclides
twelfth booke, noted: you may reduce all, to a true Leuell. But, farther
diligence, of you is to be vsed, against accidentall causes of the
waters swelling: as by hauing (somwhat) with a moyst Sponge, before,
made moyst your hollow Pyramis or Cone, will preuent an accidentall
cause of Swelling, &c. Experience will teach you abundantly: with great
ease, pleasure, and commoditie.
Thus, may you Double the Cube Mechanically, Treble it, and so forth, in
any proportion.
[Note this Abridgement of Dubbling the Cube. &c.]
Now will I Abridge your paine, cost, and Care herein. Without all
preparing of your Fundamentall Cubes: you may (alike) worke this
Conclusion. For, that, was rather a kinde of Experimentall
demonstration, then the shortest way: and all, vpon one Mathematicall
Demonstration depending. "Take water (as much as conueniently will serue
your turne: as I warned before of your Fundamentall Cubes bignes) Way it
precisely. Put that water, into your Pyramis or Cone. Of the same kinde
of water, then take againe, the same waight you had before: put that
likewise into the Pyramis or Cone. For, in eche time, your marking of
the lines, how the Water doth cut them, shall geue you the proportion
betwen the Radicall sides, of any two Cubes, wherof the one is Double to
the other: w
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