The never-emptied barrel, rivers moving the earth, and whirlpools
Halving to infinity, erosion shifting the earth's centre, and the two kinds of retroso
Three connected arguments share the sheet. Leonardo shows that a barrel continuously topped with water as wine flows from the spigot is never wholly emptied of wine, since each hour yields half the remainder and continuous quantity is divisible to infinity. He then argues that northern rivers carry soil from a to b, weighing down b and lightening the antipodes, so shifting us from the earth's centre. Finally he classifies whirlpools (retrosi) into two kinds and describes their high and low parts, illustrated by the circular vortex figure at the centre.
On this page
The barrel never wholly emptied of wine
If as much water enters the bung-hole as wine-and-water leaves the spigot, the barrel is never entirely emptied of wine: each hour it pours out half of what remains, a quarter, and so on. Because every continuous quantity is divisible to infinity, the wine is divided over infinite hours. It is a proof by an unending halving series.
Northern rivers shifting the earth's centre
The northern rivers carry the soil from a to b, weighing down b and lightening their antipodes, which are ourselves, and so remove us from the centre. Erosion redistributes the body of the earth and displaces its centre of gravity. The lettered points a, b mark the transported ground.
The two natures of the whirlpool (retroso)
The lowest part of a whirlpool is the one furthest from its extremity, the highest the one furthest from its centre. Whirlpools are of two kinds: the first made by one same water struck back and bounded within its bank, dividing into two contrary eddies sometimes equal and sometimes not; the second of water that sinks into a cavernous place. The circular vortex figure illustrates the eddy.