Compound motion: the right triangle of fall and cross-motion

Figure with letters.

Beside the figure:

If the natural motion is equal to the transversal motion, this will be the function performed according to the intention of its inventor.

Figure with letters.

Beside the figure:

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 would be double the side of the transversal motion. Again, if the speed of the transversal 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.

Figure with letters.

Beside the figure:

Therefore more or less speed of the transversal 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.

Figure with writing.

Beside the figure:

Given a rectangle of equal sides, such that the natural side is made by the said experiment: the more weight is added to the descending matter, the longer the hypotenuse will become, and conversely it will become shorter if the descending weight is made lighter. The heavier the hypotenuse, the greater the power of motion needed to make it cut the sides of the triangle of equal length; and conversely, the lighter the hypotenuse, the less power of motion will make 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 will make the same with lesser motions.

Figure with letters.

Beside the figure:

The degrees of the whole motion will be measured on the side a f, which is always divided in half in every remainder of its cutting, as is seen in the figure opposite; and this is done so that the degrees and minutes, that is 2', 3' and 4', may be of equal spaces, and they are equal, because the 2 parts into which the line e l is divided are similar to each of the 4 divisions of d K, and the 8 of c i are similar to the said 4, and the 16 of b h are similar to the said 8, and the 32, each by itself, is similar to the said 16 and to the said 2 of e l.

Figure with writing.

Beside the figure:

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

Figure with letters and writing.

Beside the figure:

Such will be the proportion that the transversal motion has to the natural as is that which the sides of the right angle, created by these motions and terminated at their hypotenuse, have between themselves.

Figure with letters and writing.

Beside the figure:

The discontinuous hypotenuse b n will have its lower part farther from the transversal motion, because the extreme b was the first that divided from a, and that which was the last to divide from the transversal motion of the vessel will be higher, that is, nearer to the mouth of the vessel from which such bodies descend.

Figure with letters and writing:

Each one is enclosed in glass, so that the buffeting of the air may not impede it.

Beside the figure:

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 the continuous quantity comes to place itself on its hypotenuse in the same way as the discontinuous quantity, as is seen in c b, the extreme c being found 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 subsequent figured above and below. Here for the present it does not seem to me that I can assign any other 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 transversal motion, and uniformly observes the distances of the weight, as the discontinuous quantity does degree by degree, according to the degrees of time in which it divided from the vessel; thus this assures proportionally the same distances with its united particles as with the disunited, that is, the distances from the upper transversal motion. Therefore, according to this said manner: all the particles of the continuous hypotenuse fall by a perpendicular line beneath the whole line of the transversal motion, not otherwise than the discontinuous quantity falls; because this continuous quantity, being without transversal motion, directs its central line to the centre of the world, and there it comes to rest. And if you move transversally, with continuous and equal speed, 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 transversal motion, obliquely situated, and makes itself the hypotenuse of the said right angle.

Lower right, a group of three figures with letters and writing.

Beside the figure at the centre of the group:

The weight n is raised without any increase of effort to its mover.

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Figura con lettere.

A lato della figura:

Figura con lettere.

A lato della figura:

Figura con lettere.

A lato della figura:

Figura con scritte.

A lato della figura:

Figura con lettere.

A lato della figura:

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Figura con scritte.

A lato della figura:

Figura con lettere e scritte.

A lato della figura:

Figura con lettere e scritte.

A lato della figura:

Figura con lettere e scritte:

A lato della figura:

In basso a destra gruppo di tre figure con lettere e scritte.

A lato della figura al centro del gruppo:

Figure with letters.

Beside the figure:

Figure with letters.

Beside the figure:

Figure with letters.

Beside the figure:

Figure with writing.

Beside the figure:

Figure with letters.

Beside the figure:

Figure with writing.

Beside the figure:

Figure with letters and writing.

Beside the figure:

Figure with letters and writing.

Beside the figure:

Figure with letters and writing:

Beside the figure:

Lower right, a group of three figures with letters and writing.

Beside the figure at the centre of the group:

On this page

Natural and transversal motion combine on a right triangle

Doubling weight or cross-speed shifts the hypotenuse

The proportion of the sides equals the proportion of the motions

Degrees of motion halved along the line a f

A continuous poured stream falls like separate drops

A weight raised without added effort