An Explication of the First Plate.

Figure. 1. This belongs to GalilÆo's famous Demonstration of the Velocities and Times of Bodies descending by an uniform Force, such is that of Gravity here below: And shews that they will ever fall in equal Times, 1, 2, 3, 4, &c. according to the odd Numbers, 1, 3, 5, 7, &c. or the Trapezia BCDE, DEFG, FGHI, &c. and by consequence, that their Velocity will increase uniformly in Proportion to the Lines BC, DE, FG, HI, &c. or to the Times of Descent. And that the entire Lines of their Descent will be as the Triangles ABC, ADE, AFG, AHI, &c. or as the Squares of those Times, 1, 4, 9, 16, &c.

Fig.2. This is a strong Balance for an Experiment to prove the former Proposition, by shewing that any Bullet or Ball, when it falls from four Times the Height, has twice, from nine Times the Height has thrice its former Velocity or Force; and will accordingly raise a double or triple Weight in the opposite Scale, to the same Height, and no more; and so for ever.

Fig.3. This shews how Bodies upon an inclin'd Plane will slide, if the Perpendicular through the Center of their Gravity falls within; and will rowl, if that Perpendicular fall without their common Section.

Fig.4. This shews that an oblique Body will stand, if the Perpendicular through its Center of Gravity cut the Base; and that it will fall, if it cut not the Base: As accordingly we stand when the Perpendicular through the Center of Gravity of our Bodies falls within the Base of our Feet; and we are ready to tumble when it falls without the same.

Fig.5. This is a Conick Rhombus, or two right Cones, with a common Base, rowling upwards to Appearance, or from E towards F and G: Which Points are set higher by Screws than the Point E. But so that the Declivity from C towards A and B is greater than the Aclivity from E towards F and G. Whence it is plain, that the Axis and Center of Gravity do really descend all the Way.

Fig.6. Is a Balance, in an horizontal Posture, with weights at Distances from the Center reciprocally proportional to themselves; and thereby in Æquilibrio.

Fig.7. and 8. Are two other Balances in an horizontal Posture, with several Weights on each Side, so adjusted, that the Sum of the Motion on one Side, made by multiplying each Weight by its Velocity, or Distance from the Center, and so added together, is equal to that on the other: And so all still in Æquilibrio.

Fig.9. Belongs to the Laws of Motion, in the Collision of Bodies to be tried with Pendulums, or otherwise, both as to Elastical Bodies, and to those which are not Elastical.

Fig.10. Belongs to that Famous and Fundamental Law of Motion, that if a Body be impell'd by two distinct Forces in an Proportion, it will in the same Time move along the Diagonal of that Parallelogram, whose Sides would have been describ'd by those distinct Forces; and that accordingly all Lines, in which Bodies move, be consider'd as Diagonals of Parallelograms; and so may be resolved into those two Forces, which would have been necessary for the distinct Motions along their two Sides respectively: Which grand Law includes the Composition and Resolution of all Motions whatsoever, and is of the greatest Use in Mechanical and Natural Philosophy.

Fig.11. Are two polite Plains inclined to one another, to shew that the Descent down one Plain will elevate a Ball almost to an equal Height on the other.