How a flat board falls through the air
Perpendicular fall in uniform air, and the sinuous descent of an unbalanced board
Leonardo studies how a board of uniform thickness and weight falls through air. He argues that in perfectly uniform air, with its opposite ends equally distant from the center of the world, it descends along a perpendicular line and strikes the plane below all at once. Dividing the board into cubes and invoking Euclid's Elements, he shows how an unequally loaded board presses the air far harder on one side, so its front swerves and the descent becomes sinuous and arched. Sketches of a box, an inclined board and boards of various shapes accompany the reasoning.
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A uniform board falls perpendicularly in uniform air
A board of uniform thickness and weight, released in still air whose resistance is uniform, with its opposite ends equally distant from the center of the world, descends along a perpendicular line and strikes the plane beneath all at once. The equal weights are equally disposed to descend, and the air yields equally to them.
The heavy body descends by the line of least resistance
A marginal note states that the heavy body descends along the line that finds least resistance, and that this line resists least which is overcome by the greater power.
Dividing the board into cubes; the unequal load on the air
Imagining the axis a-e b d c divided into cubes, and citing the fifth proposition of the second book of the Elements, Leonardo assigns 3/8 of the weight to a and 5/8 to b. The lowest cube presses its air with the weight of sixteen cubes at 3/4 each (twelve whole cubes), so the front swerves from a to f and the descent becomes curvilinear, arched beneath the straight chord.
Symmetry of the front decides perpendicular or oblique fall
When the middle of the descending board's front lies between similar and equal sides it falls perpendicularly, as a b c; but if it divides parts of unequal obliquity, the descent follows the lesser obliquity, as r s t.