Why Two Vertical Towers Lean and Topple Together
Verticals raised on the curved earth converge; a walker crosses a plain downhill then up
Leonardo reasons that structures built truly vertical on the curved earth are not parallel but converge toward its center, so two equally raised towers must eventually pull one another down. He shows that the lines through their inner angles b c cut each tower unevenly at c g and b f, leaving the larger portion (K L c g) heavier than its remainder and so dragging the whole tower against its neighbor. He extends the same result to two pyramids with parallel axes, and adds a note that a man crossing a flat site really goes first downhill and then equally uphill, moving faster with his head than his feet.
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A walker crosses a plain downhill then uphill, head faster than feet
Because the ground curves, a man crossing a whole flat site really goes first downhill and then just as much uphill. Leonardo also notes that the walker moves faster with his head than with his feet, the head describing the wider path.
Two equally built towers pull each other down (a i K L, f g, b c)
If two towers are raised in continuous straight line with a parallel gap between them and built always to equal height, they must fall one against the other. The central lines of the angles b c cut the towers at c g and b f, so those lines miss the center of gravity of each tower's length; the larger part K L c g outweighs its remainder c g d, and each tower's heavier piece drags the whole against the opposite tower.
Two pyramids with parallel axes topple together as well
If the axes of two pyramids are parallel and the pyramids are of great height, they too will fall one against the other, by the same reasoning as the towers.