[LIST] OF TITLES

V. Through tubes of equal height and equal openings original: "luminum." Literally "lights," this term refers to the internal diameter or the clear opening of the tube., which are not always kept full, an equal quantity of water flows in the same amount of time; however, one tube flows for a longer duration than the other in proportion to how much more water it contains. 115

VI. Through tubes that are not always kept full and are not of equal height, even if they have equal openings, an equal quantity of water does not flow in the same or equal time. ibid. original: "ibidem," meaning "in the same place" or on the same page.

VII. A tube four feet high, with a base diameter of one Parisian inch The Parisian foot and inch were standard units of measurement in 17th-century science, slightly larger than the English imperial units., if kept always full of water, pours out one pound of water in the span of thirteen seconds through a linear opening located at its base. 116

VIII. Waters flowing from tubes, whether they are kept always full or not always full, which have equal openings but unequal heights, have a subduplicate ratio A "subduplicate ratio" is what modern mathematics calls a square root ratio. Schott is describing an early form of Torricelli's Law, where the flow velocity depends on the square root of the height of the water column. of the heights of the tubes; and the said tubes have a duplicate ratio A "duplicate ratio" refers to the square of a value. of the waters they pour out. 117

IX. Water descending by natural motion and flowing out through tubes imitates the laws of other heavy bodies original: "gravium." In the physics of this period, "heavy bodies" refers to solid objects falling under the influence of gravity. descending by natural motion. 120

X. The velocities of the motion of water descending and flowing out through tubes of equal openings but unequal heights have a subduplicate ratio of the heights. 125

XI. To assign the cause of why waters flowing through tubes of equal openings but unequal heights have a subduplicate ratio of the heights of the tubes. 126

XII. The times in which an equal quantity of water flows out from tubes of equal openings but unequal heights have a subduplicate ratio of the tubes. ibid.

XIII. If tubes, whether they are kept always full or not always full, are of the same height but have unequal openings, the ratio of water to water is the same as the ratio of opening to opening, physically or according to the senses. 127

XIV. Tubes that are not always kept full, which are of equal height and equal openings but have unequal bases, are emptied in unequal times, and the ratio of the times is the same as the ratio of the bases. 129

XV. The times in which tubes that are not always kept full, being of equal width but not equal height, are emptied through equal openings are in the subduplicate ratio of the heights. 131

XVI. The times in which similar tubes In geometry and mechanics, "similar" refers to objects that have the same proportions regardless of their absolute size. that are not always kept full, which are equal in height and bases, are emptied through similar unequal openings are reciprocal to the openings. ibid.

XVII. Given the height and the opening of a tube kept always full, to find the quantity of water it pours out in a given time; or, given the same factors, to find the size of a cistern original: "cisterna," a tank or reservoir for storing water. that would be filled in a given time. 132