Mirrors and the simulacrum, with a note on Roger Bacon
Locating a reflected image between convex and concave mirrors; an interlace and columns of sums
On f. 70r Leonardo studies mirrors ('De' spechi'): diagrams show how the image (simulacrum) of a point c seen at b in an upper mirror is located on a lower mirror by drawing from the angle of contingence b through the mirror's centre f. A short note observes that the straight line n c makes no angle of contingence at b even though it touches the convex mirror a b m. The facing leaf (f. 71v) carries only the reminder 'Roger Bacon, put into print,' but also bears an untranscribed interlace of overlapping circles and columns of figures totalling 753. Those numeric and ornamental elements are noted from the image only, not read.
On this page
Locating the reflected image between two mirrors
Of mirrors. If the image of c is seen at b by the eye n upon the mirror n b m, the same image is seen at o by that same eye upon the mirror g o h. So, to find the image anywhere on the lower mirror, make the notional mirror a b m touch the straight line n c (which always touches at b), draw from the angle of contingence b to the mirror's centre f, and where line b f cuts the mirror g o h at o, there the image of c is seen by the eye n.
The line n c and the angle of contingence
The straight line n c does not make an angle of contingence at the point b, even though it is in contact with the convex mirror a b m. The remark distinguishes mere contact from the tangential angle that governs reflection.
A reminder about Roger Bacon in print
At the top of f. 71v Leonardo notes 'Roger Bacon, put into print,' a memorandum of a printed book he wished to consult or acquire. It stands apart from the optical diagrams on the facing page.
An interlace of overlapping circles
The lower left of f. 71v is filled with a shaded design of nine overlapping circles forming a knot-like grid of interlace. It is drawn but not transcribed in the bundle, and is noted here only from the image.
Columns of figures totalling 753
The upper part of f. 71v carries columns of untranscribed figures that are added down to a total of 753, with further large numbers across the top of both leaves. They are noted from the image only, not read. Their purpose is not stated in the transcribed text.