The works of the Honourable Robert Boyle, Esq., epitomiz'd by Richard Boulton ... ; illustrated with copper plates.

CHAP. XXII. An Explication of the Rota Aristotelica.

NOT to mention all those Absurdities which Mr. Boyle hath shew'd in the Author's Explanation of the Rota Aristotelica,* 1.1 I shall pass on to lay down what Explanation Mr. Boyle himself gives of it; for Mr. Boyle conceiving no such Difficulties in it, as our Author would represent, says, that it is so far from containing any Obscurities in it, that it is plain and easie. For if the Wheel A B C D. be mov'd in a di∣rect Motion from A I C. to K L M. each of the Points A E I G C. will either on a Plain, or in the Medium it passes through, form so many parallel Lines to I L. But if instead of that direct Progres∣sive Motion, it have a Circulation, each Point in one Revolution, whilst mov'd from G to L. will form a Cyclorid. Besides, each Point of the Circle acquires various Degrees of Celerity in its Pro∣gression by this complex Motion, according to its various Position to a Point, which is always to be found in some part of the Line, drawn from the Center of the circular Motion Perpendicu∣lar to the Progressive; for as the Circumfe∣rence to the Radius, so is the Line of the Pro∣gressive

Motion to the distance of the Point from the Center; because the Line of Progression is equal to the Circle, describ'd on that distance as Radius; and therefore, each Point of the smal∣ler Circle, when it touches the Perpendicular, will in respect of its Progressive Motion stand still: This Point therefore, will be the Center of the complex Motion.

* 1.2But since it may sufficiently explain the Rota Aristotelica, if we only consider those Points which pass across the Perpendicular, we shall suppose in our Example that A is the Center or immoveable Point; and then the Circumference A B C D will be equal to I L or A K by our Hy∣pothesis. And since the Point I hath only one motion, viz. that of Lation, the Point C which hath two Motions, must have double the Velo∣city of I, and the Point F having the same De∣gree of Lation with I, and put half the Distance of C from the Center I, it must have one Degree of Motion and a half.

And further, the Point E having the same Progressive Motion with I, and being mov'd backwards with half the Velocity, loses half the Progressive Motion forwards. And the Point A being by its Progression mov'd forwards, with an equal Velocity with I, and by its Rotation (the Circle A B C D being equal to the Line I L) being carri'd back with equal Celerity, must ne∣cessarily stand still as to the Progressive Mo∣tion.

Now from hence it appearing, that the Point A, (being at Rest, by reason of its two oppo∣site Motions) only touch a Point of the Line A K, without being in the least mov'd upon it,

and that the Point E, (moving forwards as fast again as it is carri'd backwards by its Rotation, and consequently mov'd half as fast as the Point I) not only touches the Line E K, but is mov'd upon it with a progressive Motion, half as quick as that of I, it will consequently follow, that each Point in E must make a small Line, which is a Part of the whole E C; so that the Contact of the former, and the Contact and the Progression of the latter, being perform'd by an infinite Suc∣cession of Points, in an infinite Succession of Instants, the Difficulties represented by our Author's Explaining it, are taken off, all that he says coming to no more, than that in such a determinate Moment or minutes Space of time, such a determirate minutes Corpuscle, will successively pass over such a determinate Space or Length.

Notes

• * 1.1

  See Plate the second Fig. 5.
• * 1.2

  Our Au∣thor's Ex∣plication of the Rota Aristotelica.