When the natural motion of the pouring vessel is equal to the transverse motion of the poured thing, then the hypotenuse will cut the sides equal to its right angle. When the transverse motion of the pouring vessel is, in speed, equal to the natural motion of the poured thing, then the lines of the motions compose a right angle of which the hypotenuse is the poured matter. That right angle whose sides, containing its right angle, are made by the transverse motion of the pouring vessel and by the natural motion of the poured thing, will have the said poured thing for its hypotenuse. The transverse motion of the pouring vessel and the natural motion of the poured thing proceed along the two sides of the right angle, of which the hypotenuse is composed of the thing that pours. The transverse motion of the pouring vessel and the natural motion of the thing that pours have created the two sides of the right angle, and the hypotenuse is made by the poured thing.

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

See here in the figure the natural motion a c with the transverse motion a b, which is double. Therefore in this case the natural motion is double the transverse motion.

a c is found by experiment to have made, in a hundredth part of an hour, a motion of 30 braccia. Therefore the diametral line shows how a b has been of equal motion and time as were the time and motion of a c.

But if the weight a b were twice as heavy as the first, then the aforesaid motion a b would be half as short as a d, whence the diametral line of b c would transform into b d. Now you have made your instrument in which the motion a c was made in one hundredth of an hour, and it was a weight sufficient for such motion; and upon it you made an equal transverse line at a b; and with this same instrument you have found that equal sides from the hypotenuse were made by equal motions, and that you made in a hundredth of an hour 30 braccia, that is, one mile per hour.

But if the doubled velocity of a e has made another, longer motion in a d in the same aforesaid time, you will indeed return to your first triangle a b c; but the hypotenuse will no longer be created cutting the equal sides of the triangle with the motion of one mile per hour, but of two miles.

Now this investigation of such motion will seem strange to many, seeing that the hypotenuse b c cuts the sides of the rectangle with equal length in the swift motions of a c and of a b just as it would in every slow motion; for if a b made a hundredth of a braccio in an hour, and the mover a b did the like, the hypotenuse cuts those sides equally, just as if each made 100 miles per hour.