Burning mirrors: focusing sunlight in a concave mirror
Geometry of the reflected ray-pyramid, its focal point, and a copper bar drawn to a set curvature
The left leaf (84v) argues that solar rays entering a concave mirror converge in a pyramid pointing toward the sun's centre, and relates the mirror's flatness or hollowness to how far and how tightly the reflected rays gather; a margin gives a worked case where a mirror one braccio across, drawn from a 400-braccia circle, throws its rays about 100 braccia, a quarter of the diameter. A lower drawing shows a copper bar pulled through a draw-plate and a lathe for jars, noting that the bar's curvature depends on the spacing of its supports. The right leaf (88r) is a large ray diagram of a burning mirror on line c d, tracing parallel solar rays to the focal point b at equal angles of incidence and reflection. Faint fractions and calculations in the left margin are not part of the supplied transcription.
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Solar rays converge in a pyramid toward the sun's centre
The solar rays entering the lips of the concave mirror reach the top of the half-sphere. Because the rays converge on the centre of the sun's body, their meeting is necessarily pyramidal, so the base of that pyramid can begin within the lips of the mirror.
Flatter mirrors gather more rays; hollower ones curve the pyramid
The flatter the ordinary concave mirror, the greater the sum of reflected rays it brings to one spot; the more hollow it is, the fewer. A less hollow mirror gives the reflected pyramid straighter hypotenuses, while greater concavity makes the hypotenuse more curved.
Focal throw reaches a quarter of the sphere's diameter
A mirror one braccio across, derived from a circle 400 braccia in diameter, is barely curved and casts its rays 100 braccia, a quarter of the diameter. A mirror of ordinary concavity throws the furthest reflected rays to the fourth part of the diameter of the sphere it came from, and the smaller the pyramid's angle, the smaller its base.
Copper bar drawn through a draw-plate; lathe for jars
A copper bar drawn through a draw-plate can be given the curvature of a circle of 400 braccia. Its curvature here is greater or smaller as its supports stand farther apart or nearer. A lathe for jars is drawn alongside.
Burning mirror: equal angles of incidence and reflection at focus b
The burning mirror lies on line c d; the parallel lines from a b are the solar rays falling on it, meeting at the point of convergence b, where each pair of contingent angles is equal. Because the sun is so distant, the rays here may be taken as parallel; the construction begins at angle f d b with the perpendicular solar ray g n, which descends to n and rebounds to b.