Squaring the lunes; a water-driven template machine
Geometry of infinite lunes above; a mechanism to shape stone profiles below
The upper half of the folio pursues 'the squaring of infinite lunes': four numbered figures (First through Fourth) build crescents of unequal sides whose areas are reduced to the squares g and h by inscribing an arc a d c equal to a d b and squaring by the triangle o p q. The lower half turns to workshop mechanics. A machine for shaping a 'sagoma' (template), whose three irons are of one piece, runs along a channel with the template made of Fiesole slab-stone and water. A companion mechanism sets screw-nuts inside its pulleys, tightened by the cords d e f g, so the template lowers as it wears yet stays very firm.
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Squaring infinitely many lunes
Leonardo makes the crescent of unequal sides a b c e, squared as g. Inscribing the periphery a d c equal to a d b yields the third figure, squared by the triangle o p q; its square remains g, and the leftover lune a d e c equals the square h. The construction is meant to generalize to almost infinite lunes.
Water-driven machine for shaping a template (sagoma)
d a is the axis of the revolving part and a b c the motion of the curvature, slower when shorter and shorter when higher. The three irons are of one piece and the device runs along a channel, with the template made of Fiesole slab-stone and water.
Screw-and-pulley lowering of the template
Because the template must lower as it wears yet stand firm once lowered, the pulleys carry the nuts of the screws inside them, tightening and opening between a c as shown by b, and the little screw-nut wheels are drawn by the cords d e f g.