Mathematicall magick, or, The vvonders that may be performed by mechanicall geometry in two books, concerning mechanicall povvers, motions, being one of the most easie, pleasant, usefull (and yet most neglected) part of mathematicks, not before treated of in this language / by I.W. ...

CAP. VI. Concerning the Wheel.

THe third Mechanicall faculty is commonly styled axis in peritro∣chio. It consists of an axis or cylin∣der, having a rundle about it, where∣in there are fastned divers spokes, by which the whole may bee turned round; according to this figure.

[illustration]

Where BC, does represent the Cy∣linder which is supposed to move up∣on a smaller Axis at E, (this being all one in comparison to the severall proportions, as if it were a meere Mathematicall line) LG, is the run∣dle or wheel, HFIK, severall spokes or handles that are fastned in it; D, the place where the cord is fastned for the drawing or lifting up of any weight.

The force of this instrument doth consist in that dis-proportion of di∣stance, which there is betwixt the Semidiameter of the Cylinder AB, and the Semidiameter of the rundle with the spokes FA. For let us con∣ceive the line FB, to be as a Leaver, wherein A, is the center or fulciment, B, the place of the weight, and F, of the power. Now it is evident from the former principles, that by how much the distance FA, is greater then AB, by so much lesse need the power be at F, in respect of the weight at B. Suppose AB, to be as the tenth part of AF, then that pow∣er

or strength, which is but as a hun∣dred pound at F, will be equall to a thousand pound at B.

For the clearer explication of this faculty, it will not be amisse to con∣sider the form of it, as it will appear being more fully exposed to the view. As in this other Diagram.

[illustration]

Suppose AB, for the Semidiame∣ter of the Axis or Cylinder, and AC, for the Semidiameter of the rundle, with the spokes; then the power

at C, which will be able to support the weight D, must bear the same proportion unto it, as AB, doth to AC: so that by how much shorter the distance AB, is in comparison to the distance AC, by so much lesse need the pow••r be at C, which may be able to support the weight D, hanging at B.

And so likewise is it for the other spokes or handles EFGH, at either of which, if we conceive any power, which shall move according to the same circumference wherin these han∣dles are placed, then the strength of this power will be all one, as if it were at C. But now supposing a dead weight hanging at any of them, (as at E,) then the disproportion will vary. The power being so much lesse then that at C, by how much the line AC, is longer then AI. The weight K, being of the same force at E, as if it were hung at I, in which point the perpendicular of its gravity doth cut the Diameter.

The chief advantage which this

instrument doth bestow, above that of the Leaver, doth consist in this particular. In a Leaver, the motion can bee continued onely for so short a space, as may be answerable to that little distance betwixt the fulciment and the weight: which is always by so much lesser, as the disproportion betwixt the weight and the power is greater, and the motion it self more easie: But now in this invention, that inconvenience is remedied; for by a frequent rotation of the axis, the weight may be moved for any height or length, as occasion shall require.

Unto this faculty may we referre the force of all those engines which consist of wheels with teeth in them.

Hence also may wee discerne the reason why sundry instruments in common use, are framed after the like form with these following fi∣gures.

[illustration]

All which are but severall kinds of this third Mechanicall faculty. In which the points ABC, doe represent the places of the power, the fulci∣ment, and the weight. The power being in the same proportion unto the weight, as BC is unto BA.

Notes

• Called likewise 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉. Arist. Mechan. c. 14.