Tides and river mouths, with circle-quadrature figures
Leonardo argues the tides are born from waves, not the moon or the sun
Most of this sheet argues a theory of the tides: the sea's flux and reflux, Leonardo insists, is born not from the moon or the sun but from the greatest incident and reflected waves, sustained by the water dammed back and returned by the rivers. A labelled diagram of a river mouth (points n, m, g h p, o, near Antwerp) shows the incident descent of the river striking back the reflected wave against the islands. At the top, geometric figures set circles in a cross within a square, carrying the rule that if a squarable figure is removed from a square the remainder is squarable.
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The tides are born from waves, not the moon or sun
The flux and reflux of the sea, Leonardo states, is born neither from the moon nor from the sun but from the greatest incident and reflected wave. Because the reflected wave is weaker, the wavering motion would exhaust itself were it not renewed by the rivers, whose dammed-back water is added to the reflux and rebounds against the facing islands — a claim he grounds in continual experience of rivers.
River mouth n–m–g h p–o near Antwerp
In the labelled river-mouth diagram, the incident descent of the river g h, by its percussion, strikes and beats back the reflected wave m h, while the front of the greatest flood-wave n p o strikes upon the islands and is reflected backward — the incident motion being greater in power than the reflected.
Flux and reflux caused by the rivers' slower flow
The sea's flux and reflux, at another river mouth, is caused by the course of the rivers, which deliver their water to the sea more slowly than the river moves, so that necessity makes the water rise; the river covers its course with the swift reflected wave running against its own oncoming flow.
Circles in a cross within a square (quadrature)
At the top of the sheet circles are arranged in a cross within a square, accompanied by the maxim that if from a square you take away a squarable figure, the remainder is squarable.