Angle of Incidence on a Convex Mirror
Locating the reflected image with tangent lines and equal angles of contingence
This transmitted-light plate treats the catoptrics of a convex mirror: given two points, one the object and one the eye, Leonardo seeks the site of the object's image on the mirror, which he calls the angle of incidence. He draws lines a d and b d to the mirror's centre, then tangents a e (touching at m) and b f (touching at n); where they cross at c lies the incidence angle, to be lowered if it stands too high off the circle. Supporting propositions state that unequal parts cut in the same proportion leave the remainder in that proportion, and that all angles of contingence of a circle with a straight line are equal. Being a transmitted-light image, the plate also shows large circular figures from the reverse of the leaf; these carry further untranscribed material and are visible only as bleed-through.
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Equal angles of contingence of a circle
All the angles of contingence of one and the same circle with a straight line are equal to one another, and at equal distance from the angle they make triangles of equal base. A companion lemma holds that unequal parts taken from unequal quantities in the same proportion leave the remainder in that same proportion.
Locating the image with tangents a e and b f
With a and b the object and the eye, lines a d and b d are drawn to the mirror's centre d; then tangents a e (touching the circle at m) and b f (touching at n) are drawn, and where they intersect at c lies the angle of incidence. If that angle stands too high off the circle it is lowered by the method shown alongside.
