If the natural motion is equal to the transverse motion, this will be the operation carried out according to the intention of its inventor.

But if the natural motion were doubled in weight, it would be doubled in speed, whence the hypotenuse would not cut the sides of the rectangle equally; rather the side of the natural motion will be double the side of the transverse motion. Again, if the speed of the transverse motion exceeded the natural motion by double speed, the hypotenuse would cut the sides of the rectangle in double proportion, that is, the upper side would be double the natural one.

Therefore more or less speed of the transverse motion makes the lower part of the hypotenuse cut the side of the natural motion higher or lower, and more or less heaviness of the natural motion makes the said hypotenuse longer or shorter.

Given that the rectangle of equal sides has its natural side made by the said experiment, the more weight is added to the descending matter, the longer the hypotenuse becomes; and conversely it becomes shorter if the descending weight is made lighter. The heavier the hypotenuse, the greater the power of motion that makes it cut the sides of the triangle of equal length; and conversely, the lighter the hypotenuse, the less the power of motion that makes it cut the sides of the rectangle of equal length. The heavier the hypotenuse, the greater ..... the motion that makes it create the sides equal to its right angle; and conversely the light hypotenuse makes the like with lesser motions.

The degrees of the motion of the whole are measured on the side a f, which is always divided in half in whatever remains of its cut, as is seen in the figure opposite; and this is done so that the degrees and minutes 2', 3' and 4' be of equal spaces, and they are equal, because the two parts into which the line e l is divided are similar to each of the four partitions of d K, and the eight of c i are similar to the said four, and the sixteen of b h are similar to the said eight, and the thirty-two, each by itself, is similar to the said sixteen and to the said two of e l.

The transverse motion of the pouring vessel, together with the natural motion of the poured thing, have created the two sides of the right angle, of which the hypotenuse is the thing that pours. When the said transverse motion is equal to the natural motion, then the hypotenuse cuts the sides of the right angle equally.

Such will be the proportion that the transverse motion has to the natural, as that which the sides of the right angle, terminated in their hypotenuse, have between themselves.

The discontinuous hypotenuse b n will have its lower part more distant from the transverse motion, because the extremity b was the first to separate from a; and that which was the last to separate from that transverse motion of the vessel will be higher, that is, nearer to the mouth of the vessel whence such bodies descend.

Each stays enclosed in the glass, so that the percussion of the air does not impede it.

It is asked why, the continuous quantity not having this motion of descending in pieces as the discontinuous does — of which every part descends by a perpendicular line — for what cause this continuous quantity comes to place itself in its hypotenuse, in the same way as the discontinuous quantity, as is seen in c b, the extremity c finding itself in its proper place as if it had fallen from b, the motion a b being similar to the motion of the discontinuous quantity, and this hypotenuse not being of uniform heaviness like the antecedent or the succeeding ones figured above and below. Here for the present it does not seem to me possible to assign another reason, except that it seems to me, by the 7th of the 4th, that, the weight c being uniformly distributed along the cord that sustains it, such heaviness is of uniform weight beneath the quantity of the transverse motion, and uniformly keeps the distances of the weight as the discontinuous quantity does, degree by degree, according to the degrees of time that separated it from the vessel; so this secures proportionally the same distances with its united particles as with the disunited, that is, the distances from the upper transverse motion. Therefore, in this said manner, all the particles of the continuous hypotenuse fall by a perpendicular line beneath the whole line of the transverse motion, no otherwise than the discontinuous quantity falls; for this continuous quantity, being without transverse motion, directs its central line to the centre of the world, and there comes to rest. And if you move transversely, with continuous and equal velocity, the upper part of this continuous quantity, its lower part remains in the same place of the first central line, so that it stops beneath the beginning of the transverse motion, obliquely situated, and becomes the hypotenuse of the said right angle.

The weight n rises without increase of effort to its mover.