XVIII. Given the height and the opening original: "lumine." In hydraulics, this refers to the diameter or clear aperture of a pipe. of a tube kept always full, to find the time in which it pours out a given quantity of water, or in which it fills a given cistern. 135
XIX. Given the time, the quantity of water or the size of the cistern, and the opening of the tube, to find the height of the tube which, being kept always full, would fill the cistern in the given time. 136
XX. Given a vessel and the hole through which the water flows out, to find the time in which it is emptied. 137
XXI. Given a vessel and a duration of time, to find the hole through which it may be emptied in that given time. 139
XXII. To find the height of the source original: "scaturiginis." This refers to the head of water or the rising point of a spring. of a given fountain flowing through tubes. 140
XXIII. Given the height of any tube or distribution-vessel original: "erogatorii." A vessel designed to distribute water into various channels., and the time in which it pours out a specific quantity of water from its opening, to find the height of the same or another tube which, in an equal time and through an equal opening, would pour out another specific quantity of water. 140
XXIV. To determine the spaces in a tube or vessel kept always full that are emptied in equal successive times; as well as the measure or weight of the water that flows out. 141

SUPPLEMENT TO CHAPTER III.

Schott includes this mathematical appendix because calculating flow rates required solving for geometric proportions, a standard practice before modern algebraic formulas were common.

PROPOSITION
I. To find a mean proportional between two numbers. 145
II. Given two numbers, to find a third in continuous proportion. ibid. original: "ibidem," meaning on the same page.
III. To find a third proportional between two given straight lines. ibid.
IV. Given two straight lines, to find a third proportional. 146
V. Another way to find a third proportional. 147
VI. Yet another way to find a third proportional. ibid.
VII. Given three numbers, to find a fourth proportional. 148
VIII. Given three straight lines, to find a fourth proportional. ibid.

CHAPTER IV.

This chapter concerns "leaping water," which refers to the physics of fountains and the parabolic arcs created by water jets.

PROPOSITION
I. The lengths of horizontal and middle ecdromes original: "ecdromorum." A term derived from Greek meaning "a running out," used here to describe the trajectory or path of a water jet. leaping over the same horizon are in a subduplicate ratio A subduplicate ratio is the ratio of the square roots. Schott is observing that the distance a jet travels depends on the square root of the water's pressure or height. of the tubes from which they spring. 151
III. Horizontal and middle leaping jets from the same tube are longer the higher the opening of the tube is above the horizon. 153