Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/218

 round upon their centres with equal velocities, so as that two moveables, which suppose for example to be two stones placed in the points B and C, come to be carried along the circumferences BG and CE, with equal velocities; so that in the same time that the stone B shall have run the arch BG, the stone C will have past the arch CE. I say now, that the whirl or vertigo of the lesser wheel is much more potent to make the projection of the stone B, than the vertigo of the bigger wheel to make that of the stone C. Therefore the projection, as we have already declared, being to be made along the tangent, when the stones B and C are to separate from their wheel, and to begin the motion of projection from the points B and C, then shall they be extruded by the impetus conceived from the vertigo by (or along) the tangents BF and CD. The two stones therefore have equal impetuosities of running along the tangents BF and CD, and would run along the same, if they were not turn'd aside by some other force: is it not so Sagredus?

In my opinion the businesse is as you say.

But what force, think you, should that be which averts the stones from moving by the tangents, along which they are certainly driven by the impetus of the vertigo.

It is either their own gravity, or else some glutinous matter that holdeth them fast and close to the wheels.

But for the diverting of a moveable from the motion to which nature inciteth it, is there not required greater or lesser force, according as the deviation is intended to be greater or lesser? that is, according as the said moveable in its deviation hath a greater or lesser space to move in the same time?

Yes certainly: for it was concluded even now, that to make a moveable to move; the movent vertue must be increased in proportion to the velocity wherewith it is to move.

Now consider, that for the deviating the stone upon the lesse wheel from the motion of projection, which it would make by the tangent BF, and for the holding of it fast to the wheel, it is required, that its own gravity draw it back the whole length of the secant FG, or of the perpendicular raised from the point G, to the line BF, whereas in the greater wheel the retraction needs to be no more than the secant DE, or the perpendicular let fall from the tangent DC to the point E, lesse by much than FG, and alwayes lesser and lesser according as the wheel is made bigger. And forasmuch as these retractions (as I may call them) are required to be made in equal times, that is, whil'st the wheels passe the two equal arches BG and CE, that of the stone B, that is, the retraction FG ought to be more swift than the other DE; and therefore much greater force will be required for