A windmill, a wedge's centre of gravity, and mean proportionals
A 30-braccia mill braced by eight struts, with weight and proportion studies
Folio 55 verso combines a machine design with two mathematical studies. At upper left a tall mill (molino) is drawn, described as gripped at mid-height by eight struts n m so the wind cannot overturn it, with a vane 20 braccia high and detailed dimensions totalling exactly 30 braccia. A lower note treats the centre of gravity of a wedge (conio) a b c g and its half-wedge, balancing weights about the common centre. A semicircle construction at the foot demonstrates finding the two mean proportionals 2 and 4 between 1 and 8.
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A windmill braced at mid-height by eight struts
The mill is held at the middle of its height by the 8 struts n m so the wind does not throw it upside down. Its vane is 20 braccia high and one and a half braccia wide (a breadth of linen), with a shaft half a braccio thick; the whole mill, house included, stands exactly 30 braccia tall.
Centre of gravity of a wedge and half-wedge
e is the middle of the natural weight of the wedge (conio) a b c g, and d the middle of the weight of the half-wedge a b c. Because the half-wedge is one half of the wedge, weight is apportioned beyond the common centre at e, with the whole weight taken at f.
Two mean proportionals 2 and 4 between 1 and 8
The semicircle construction finds the 2 mean proportionals between one and 8, namely 2 and 4, so that 2 is to one as 8 is to 4. The proportion is read off the lines a c, a b c and b e, d e of the lettered figures.