Working a Tower in Water, with Studies of Area Equivalence
A caisson-like tower to work as on dry land, beside geometry of semicircles and coronas and columns of figures
The sheet opens with a note on building around a tower set in water: caulking its cracks with stones and hay, laying a course of stone every braccio, then filling the bottom beside the tower so that one may labour on it as on firm ground and mount a crane there to unload ships, sketched above with a mound of loose stones and structures. Below, a run of geometrical diagrams treats the equivalence of areas among semicircles, circular coronas (annuli), triangles and portions, each labelled with letters. Two blocks of arithmetical figures and a hooked mechanical device drawn at upper right accompany them. Further untranscribed writing and sketches are present on the worn lower part of the leaf.
On this page
Building around a tower standing in water
Rest against the tower and caulk its cracks with stones and hay, laying a single course of stone at every braccio. Finish first the protective wall, which has a foundation, then fill the bottom beside the tower so you can work as if on dry land and fix a crane above to unload the ships.
Equivalence of areas: semicircles, coronas and portions
A semicircle on the lower sheet is lettered a - f - b, d - e - c, with the claim that a b c equals d e f and that a c, being half portions, are worth d e taken as whole portions. Adjacent figures compare a triangle to a circular corona and a half-corona, asserting further equalities of area.
Columns of numerical calculation
Two clusters of figures set out multiplications and sums, among them 24, 10000, 2555, 400 and 22, and a second block building toward 400000000. They read as working calculations rather than a proportion rule stated in words.
Crane and hooked device drawn beside the text
The note calls for mounting a crane (falcone) on the filled base to unload ships. Beside the upper text a hooked, claw-like mechanism is drawn, one of several small untranscribed sketches on the sheet.