The Mathematicall Praeface to Elements of Geometrie of Euclid of MegaraDee, John
Philosophy
The Mathematicall Praeface to Elements of Geometrie of Euclid of Megara
Dee, John
Geometry -- Early works to 1800; Mathematics -- Early works to 1800; Philosophy -- Early works to 1800
“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 cõmoditie.
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 demõstration,
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:
working as before I haue taught you:
[* ☞ Note.]
* sauing that for you Fundamentall Cube his Radicall side: here, you may
take a right line, at pleasure.”
Yet farther proceding with our droppe of Naturall truth:
[To giue Cubes one to the other in any proportion,
Rationall or Irrationall.]
Public-domain text, read in full here on John Shaqi.
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