A classification of motions: straight, curved, and spiral
Definitions of motion, the four kinds of cochlear (screw) spirals, and why gliding descends then rises higher
Leonardo defines straight motion as the shortest line between two points and curved motion as one containing some part of straight motion, then classifies 'cochlear' (screw-like) motion, drawn as four spirals in the margin, into convex, plane, concave, and columnar kinds. He adds circular motion, always at equal distance about a point and called 'revoluble,' and the infinite irregular motions compounded from all the rest. Applying the scheme to flight, he notes that in simple motion the incident begins higher than the reflected ends, whereas in composite motion the bird pressing under the wind lowers the incident path while the reflected rise above the wind climbs higher. Four spiral coils and a small bird are sketched in the upper margin, with further notes running down the side of the sheet.
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The four kinds of cochlear (spiral) motion
Cochlear motion is composed of an oblique and curved line, whose radii drawn from the middle to the circumference are all of various lengths. It is of four kinds: convex cochlear, plane cochlear, concave cochlear, and columnar cochlear; to which are added circular ('revoluble') motion about a point and the infinite irregular motions compounded from them all.
Definitions of straight and curved motion
Straight motion is that which extends from one point to another by the shortest line. Curved motion is that in which some part of straight motion is found.
Composite gliding: incident lowered, reflected raised
In simple motion the beginning of the incident is always higher than the end of the reflected, the moving body being still in motionless air. But in composite motion the opposite holds: the bird generating the incident motion under the wind presses and lowers its course, while the reflected motion, generated with open wings above the wind, rises much higher than the start of the incident.