The bird's eye and the angle of incidence on a sphere
Two eyelids shield the eye in fast flight; geometric construction of reflection
The sheet mixes the anatomy of the bird's eye with the geometry of reflection: a small shaded drawing of an eye sits at the upper right, surrounded by circle-and-tangent constructions with lettered points. Leonardo describes two lids, an opaque lower lid closing from below and a transparent nictitating membrane closing from the tear duct backward, which together protect the eye from raptors and let the bird keep its eyes open against the wind in swift flight, while the pupil widens and narrows with the light. The remaining notes solve, on a sphere n o m, how to find the angle of incidence by drawing right angles and tangents to a circle, and how to locate a sought point c from perpendiculars dropped to the centre h. Several lettered diagram labels appear on the sheet beyond those transcribed.
On this page
The opaque lower lid and the transparent front lid
a b n is the lower lid that closes the eye from below upward with an opaque covering, while q c e closes the eye from front to back with a transparent covering. The lower lid closes upward because danger descends from above.
How a bird's eye is protected in flight
When a bird closes its eye it first draws the nictitating membrane from the tear duct toward the outer corner, keeping the upper part in reserve against birds of prey that descend from above and behind. The transparent membrane also lets it hold its eyes open against the wind that strikes them in the fury of swift flight, while the pupil grows and shrinks with a lesser or greater light.
Finding the angle of incidence o on the sphere n o m
Given two points a and p on the sphere n o m, the angle of incidence o is found by making the right angle p q o below p and the right angle a b o below a, so that the line b q is tangent to the circle. The proof is the circle r t s, which makes the angle r o v equal to the angle p o q.
Fixing the point of tangency with right angle p o f
Let p be the head of the perpendicular p q, and at q make the right angle p q o, which touches the circle with the side p o; at that contact is the angle of tangency. That point is fixed precisely by the right angle p o f.
Locating the sought point c through the centre h
Draw the lines f e and d g, then from each drop a perpendicular to the centre h. Take on the circle the midpoint between the ends of those perpendiculars a b, which gives c, the point sought.
Shaded drawing of an eye
At the upper right of the sheet a small eye is drawn in dense hatching, showing the globe and its lids, the object of the surrounding notes on how a bird's eye closes and protects itself. It anchors the lettered lids described in the text.