I Introduction. II From Castelli to Borelli. The scientific scene in the Italian "Seicento"; The birth of the science of river hydraulics; Further debates up to Castelli's Book II Della misura dell'acque correnti; The law of efflux; In the steps of Torricelli; The fading of princely patronage: the fate of Borelli. III Along the Waters 1675-1700. Montanari at Bologna; At the school of Monanari; Guglielmini's search for independence; The birth of hydrometry; A new opening towards Europe; The physics of rivers. IV Along the Waters 1700-1725. Padua & Venice in the early 18th century; Skirmishes on the Po: Venice vs. Bologna; The building of an academic career in science; Poleni's lagoon hydraulics and fluid mechanics; Riccati's critical role. V New Patterns in Science. Out of Galileo; The thread of the waters.

