Geometric construction for the origin of a reflected ray
Tangents, curves and the point of incidence on a circle
The leaf carries a lettered geometric figure, a circle crossed by lines and arcs, with a matching set of instructions for locating the point of incidence and the origin of a reflected ray. Leonardo draws the tangents b o and a p to the circle, forms the curves o q and p r from them, and joins the line a v through their intersection, which cuts the arc drawn about the centre c. Transferring the space m p to n o and joining a m with b n gives the point of incidence at r; more briefly, where the line a v cuts the circle at r is where the reflected ray is born. The construction treats reflection as a problem of pure geometry.
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Finding where the reflected ray is born
Transferring the space m p into n o and drawing the lines a m and b n, their intersection at r gives the point of incidence; put more briefly, where the line a v cuts the circle at r is the origin of the reflected ray. The circle stands for the reflecting body and the construction fixes the ray's starting point.
Tangents and curves of the construction
From point b the straight line b o is drawn tangent to the circle, and from a the line a p tangent to it; with b o the curve o q is made and with a p the curve p r, and the line a v is drawn through their intersection, cutting the curve made about the centre c.