Subdividing a great disc into 57,600 squares, and its gilding cost
Section of the pyramid, the 'power' of small circles, and pricing the gold
Leonardo computes how a great square base four braccia to a side is subdivided into small squares: dividing the braccio into 60 ounce-fifths gives 3,600 square parts per square braccio, and multiplying by the 16 squares of the base yields 57,600 little squares (each a 'treina'), each treated as one 'section' with a numerical 'power' (230,400 for a half-treina section). Small and large circles relate these units, noting that a one-ounce circle a fits 2,304 times within the four-braccia circle and has 2,304 times its 'power'. A short reckoning prices the gilding of that circle: at 64 gold leaves to the square braccio it comes to 12 ducats in all, six for the gold and six for laying it on.
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The pyramid's base divided into 57,600 squares
The ounce divided into 5 divides the braccio of 12 ounces into 60; the side of a one-braccio square, multiplied by itself, gives 3,600 square parts. Multiplied by the 16 squares of the four-braccia base, this yields 57,600 little squares, and the 'section' is one of these, called a treina.
The 'power' of a small circle within the great one
The circle a, of one ounce diameter, fits 2,304 times into the four-braccia circle, and its 'power' is worth 2,304 times the power of the base. A half-treina section is credited with a power of 230,400.
Counts of units filling the four-braccia circle
Marginal figures record that 57,600 units fit into the circle of 4 braccia, and that 230,400 fit into the smaller circle of the same diameter. A large circle is drawn below to represent the four-braccia disc.
Cost of gilding the four-braccia circle
Sixty-four pieces of gold make one square braccio, and the circle amounts to 16 braccia, coming to 3 braccia per ducat. Six ducats gild it and another six for the laying-on, for 12 ducats in all.