Falling Bodies and the Paradox of a Pouring River
Velocity gained in arithmetical proportion, yet the liquid still reaches the ground
Leonardo states that a discontinuous quantity gains one degree of velocity at each degree of motion, and that in every harmonic 'time' the separated bodies gain distance from one another in arithmetical proportion. He then asks how to treat continuous quantities such as liquids: since at each degree of motion the same poured weight grows longer and thinner, it would seem to end in a point like a pyramid and so hang in the air rather than fall, however large the river. Yet experience shows the contrary, because as much liquid as leaves the top strikes below in equal time. The page continues his sustained analysis of the descent of bodies through air.
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Discontinuous bodies gain a degree of velocity per degree of motion
A discontinuous quantity acquires one degree of velocity at each degree of its motion. In every harmonic 'time' the separated bodies also gain length of distance between one another.
The gain of distance follows arithmetical proportion
The increase of distance that falling separated bodies gain in each harmonic 'time' is in arithmetical proportion. The spacing between the bodies grows by regular steps as the fall proceeds.
The paradox of a continuously pouring liquid
Because a poured liquid grows longer and thinner at every degree of motion, it seems it should taper to a point like a pyramid and remain suspended in the air, however great the river. Yet experience shows the contrary, for as much as departs from above strikes below in equal time.