Proportional figures and water likened to the body's blood
Circle-and-ball geometry, balance appendages, and water in the earth's veins
The left leaf (44v) works through proportional relationships between lettered segments and a construction in which a circle m n p meets a group of semicircles at the points where balls touch them at equal angles, so that radii through the contacts point toward the centre of the world and the balls' centres of gravity lie above their resting points. A note observes that sections of a pyramid taken parallel to the triangle's base are unequal, applied to the tapering appendages of balances; nearby, written upside down, is a string of invented obscene coinages and the single word "Conception." The right leaf (59r) draws the analogy that the cause raising humors against their weight in living bodies also drives water up through the earth's veins, as blood rises and pours from the forehead.
On this page
Proportional segments o t : a n = m t : n m
The proportion that o t has to a n, m t has exactly to n m, and likewise o v to v a. It sets up equal ratios among the lettered divisions of the figure.
A circle meeting semicircles where balls touch at equal angles
The circle m n p intersects the peripheries of the semicircles at points where the balls make contact at equal angles, so that lines from the centres are radii passing through centre and contact. These radii direct themselves toward the centre of the world, placing each ball's centre of gravity above the point where it rests.
Unequal pyramid sections and balance appendages
No sections of the pyramid taken equally distant from the base of the triangle are of equal length. Leonardo applies this to the appendages of balances, which are narrower at the foot than at the head across their intervals.
Water in the earth's veins likened to blood in the body
The same cause that moves the humors against the natural course of their weight in all animate bodies moves the water through the earthly veins, succoring wherever necessity teaches. Water falling from a height, which begins every river's course, acts like blood that rises from below and pours out through the ruptures of the forehead.
A string of invented vulgar coinages
Written upside down beside the figure is a playful list of invented obscene words spun from a single vernacular root. It stands apart from the geometry and hydraulics as private word-play.