192
G. Galilæus, his Systeme.
Sagr.But do you think that the velocity doth fully make good the gravity?The greater velocity exactly compensates the greater gravity. that is, that the moment and force of a moveable of v. g. four pounds weight, is as great as that of one of an hundred weight, whensoever that the first hath an hundred degrees of velocity, and the later but four onely?
Salv.Yes doubtless, as I am able by many experiments to demonstrate: but for the present, let this onely of the stiliard suffice: in which you see that the light end of the beam is then able to sustain and equilibrate the great Wool-sack, when its distance from the centre, upon which the stiliard resteth and turneth, shall so much exceed the lesser distance, by how much the absolute gravity of the Wool-sack exceedeth that of the pendent weight. And we see nothing that can cause this insufficiencie in the great sack of Wool, to raise with its weight the pendent weight so much less grave, save the disparity of the motions which the one and the other should make, whilst that the Wool-sack by descending but one inch onely, will raise the pendent weight an hundred inches: (supposing that the sack did weigh an hundred times as much, and that the distance of the small weight from the centre of the beam were an hundred times greater, than the distance between the said centre and the point of the sacks suspension.) And again, the pendent weight its moving the space of an hundred inches, in the time that the sack moveth but one inch onely, is the same as to say, that the velocity of the motion of the little pendent weight, is an hundred times greater than the velocity of the motion of the sack. Now fix it in your belief, as a true and manifest axiom, that the resistance which proceedeth from the velocity of motion, compensateth that which dependeth on the gravity of another moveable: So that consequently, a moveable of one pound, that moveth with an hundred degrees of velocity, doth as much resist all obstruction, as another moveable of an hundred weight, whose velocity is but one degree onely. And two equal moveables will equally resist their being moved, if that they shall be moved with equal velocity: but if one be to be moved more swiftly than the other, it shall make greater resistance, according to the greater velocity that shall be conferred on it. These things being premised, let us proceed to the explanation of our Problem; and for the better understanding of things, let us make a short Scheme thereof. Let two unequal wheels be described about this centre A, [in Fig. 7.] and let the circumference of the lesser be BG, and of the greater CEH, and let the semidiameter ABC, be perpendicular to the Horizon; and by the points B and C, let us draw the right lined Tangents BF and CD; and in the arches BG and CE, take two equal parts BG and CE: and let the two wheels be supposed to be turn'dround
