Similar triangles and the angle of incidence in mirrors
Proportion of bases to cathetes; a chord hung between two irrational heights
The sheet is filled with geometric constructions: line diagrams, a large semicircle crossed by radiating lines, and triangular figures with lettered points. The accompanying notes state that the bases of similar triangles are in the same proportion as their perpendicular legs (cathetes), and set up a problem of a single chord descending between two different irrational heights. A marginal note observes that the angle of incidence in a mirror always sits between two similar but unequal triangles. Several diagram labels shown on the sheet are not carried in the transcription.
On this page
Bases of similar triangles follow their cathetes
The proportion of the bases that similar triangles have to one another is the same as that of their cathetes, the perpendicular legs.
A chord descending between two irrational heights
Two different irrational heights stand somewhat apart, and a single chord descends from them, its opposite ends joined to those two heights.
The angle of incidence lies between two similar triangles
The angle of incidence in mirrors always has the potential to have two further angles with two further sides, so that it lies between two triangles that are similar but not equal; and this inequality... .
Semicircle crossed by radiating lines
A large semicircle on the left folio is crossed by lines radiating from points on and above it, of the kind Leonardo used to trace rays and angles of reflection. Feather-like fans of straight lines spread from small nodes beside it.