Colliding Winds; Doubling Squares, Circles and Lunes
Reflected wind against incident wind, then the geometry of doubled figures
The page opens with a study of colliding winds, sketched at the top right, then turns to geometry. Leonardo argues that a reflected wind overcomes the incident wind through the condensation it gains where it strikes, while a marginal note observes that water does the same not by condensing but by rising into the air and gaining weight. The lower diagrams treat doubled figures: two squares (the larger's side equal to the smaller's diagonal), two circles containing them, and a lune a c d b shown equal to two triangles a n e and b e g toward its quadrature.
On this page
Doubling a square: side of the larger equals the diagonal of the smaller
Two squares are double one another when the side of the larger equals the diagonal of the smaller. The diagonals bisect each square, and the larger's diagonals cross at the centre dividing it into four equal triangles, of which half the smaller square equals one. Circles containing such squares are likewise double one another.
The lune a c d b equal to two triangles
Of circles double one another, half the larger equals the whole smaller. Where two equal plane surfaces partly overlap, the parts in contact are equal and so are the excesses; thus with circle a b c e equal to semicircle n d g overlapped at a b c, the lune a c d b equals the two triangles a n e and b e g, opening the way to square such excesses.
Reflected wind overcoming the incident wind
The reflected wind that turns back against its coming overcomes the incident wind until it weakens, then regains force when it rejoins the incident motion. This power arises from the condensation acquired where it struck, which penetrates the incident wind until it disperses and slows the motion.
Water rises into the air and gains weight
A marginal note observes that water does the same as the colliding wind, not by condensation but because it rises up amid the air and acquires weight.