Accelerated fall and the force of falling water

Natural powers are 'pyramidal' and grow in geometric proportion

Natural-violent motion thrusts a heavy body downward with an increase that holds constant to the end of the motion. All natural powers are to be called pyramidal, having grades in continuous proportion in decrease as in increase; a free weight gains grades in continuous geometric proportion at every degree of its descent, as does force in the lever.

The 'sixth': the more a weight descends, the faster and heavier

Under the heading of accidental motion, the sixth proposition states that the weight which descends more becomes faster and heavier. A triangle figure marks a 'falling weight' b a passing to a 'fallen weight.'

A falling water column strikes less hard than a solid body

The percussion of continuously descending water (marked 7-6-5-4-3-2-1) is never as strong as that of a hard body of equal weight, because when the first grade has fallen ten braccia the second has made 9, the third 8, and so on, so that as the first strikes the last has not yet begun to descend. A hard body instead moves as one.

Why a falling jet takes a pyramidal form

Water falling through air must take a pyramidal shape even though it leaves a pipe of uniform bore, because lower portions fall faster (by the sixth proposition) and so stretch apart in continuous geometric proportion, growing longer below and thicker above, unless the air breaks them up; the same holds in rivers of equal width, depth and straightness.

Uniform channels into and out of a lake keep its level

With uniform channels feeding and draining a lake (a, b c, d), the motion at the end of the feeding channel equals that at the start of the discharging one, or the lake would rise or fall greatly. Falling water lifts more than its own weight in proportion to the force of its percussion, less the power lost to friction at the instrument's pivots.

A doubling table from 256 to 536,870,912

A column of successively doubled numbers runs crosswise along the lower margin, from 256 through 536870912, closing with the note '150 thousand miles, when one exceeds by a braccio.'

In alto da destra a sinistra.

Da sinistra a destra. Figura di bilancia e figura di linee divergenti e quindi convergenti:

Figura di triangolo con un peso dal vertice al centro della base:

Figura con:

Colonna d'acqua, divisa in spazi eguali e numerati, cadente in un recipiente controbilanciato da un contrappeso:

Figura di due palline che cadono:

Figura, nel margine, di vena d'acqua ' piramidata ' :

Figura, nel margine, di canale che entra e esce da un lago, colle lettere:

Traversalmente sul margine inferiore:

Above, from right to left:

From left to right. Figure of a balance and figure of lines diverging and then converging:

Figure of a triangle with a weight from the apex to the centre of the base:

Figure with:

A column of water, divided into equal numbered spaces, falling into a vessel counterbalanced by a counterweight:

Figure of two little balls falling:

Figure, in the margin, of a 'pyramided' vein of water:

Figure, in the margin, of a channel entering and leaving a lake, with the letters:

Crosswise on the lower margin: