The Convex Mirror: Why Reflection Has No General Rule
The angle of contingency, with proportioned triangles and a test of hot iron and filings
A short note first proposes an experiment to test whether hot iron draws iron filings to itself. The main passage, illustrated by a large arc diagram at the top, argues that no general rule or true science can be given for locating the image of a luminous point b as seen by the eye c upon a convex mirror p q c, because the angle of contingency (the angle of contact at the curve) makes the bases and curved sides of equal angles fall out of regular proportion. A small right-triangle figure in the right margin illustrates two triangles a b c and d e c whose straight sides stand in a clean double ratio, the very regularity the curved case lacks.
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Test: does hot iron attract iron filings?
A brief experimental note proposes to test whether heated iron draws iron filings toward itself.
No general rule for the image on a convex mirror
Given convex mirror p q c, luminous point b, and eye c, Leonardo argues it is impossible to give a general rule for finding the reflected image, since the angle of contingency prevents the bases and curved sides of equal angles (o c n and t c S) from holding regular proportion to their straight sides.
Two triangles in double ratio, sides all straight
A marginal figure shows triangles a b c and d e c, proportioned by having all their sides straight so that every side of the larger is double that of the smaller, the orderly correspondence that the curved mirror case destroys.