Balance Diagrams with Studies of Circular Proportion
Beam-balance schemes, a semicircle divided into portions, and a circle circumscribed on a hexagon
Four fragments are mounted together. A tall strip carries several schematic beam-balances, their arms lettered a-e and marked with weights 4 and 1. Other pieces treat geometry of the circle: a semicircle divided into portions where a equals b and c is double both, and a pair of figures of a circle circumscribed about a hexagon, arguing that similar parts stand in the same proportion as their similar wholes and that two circles in double proportion carry portions in like ratio. A square fragment of abacus-like number symbols and columns of figures accompanies them.
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Schematic beam-balances with weights
A strip shows successive balance schemes, their beams lettered c b a and e d, n a and m, with weight-marks 4 and 1 (and the reversal 1 4 - 4 1). They test equilibrium of a beam loaded on either arm.
Circle circumscribed about a hexagon; proportion of parts to wholes
Two figures of a circle circumscribed on a hexagon are lettered b a and d c. Leonardo argues that similar parts stand in the same proportion to one another as their similar wholes, so that two circles of double proportion carry portions (on the sixth of their circumference, or on their semidiameters) in the same ratio as the whole circles.
Semicircle divided into portions
A semicircle with portions struck out is lettered a and b c, with the note that a equals b and that c is worth double both b and a, a being born of the eighth of the semicircle, eightfold to the semicircle of b.
Columns of figures and abacus-like symbols
A ruled table sets successive figures (1st through 11th) against columns of the numbers 4, 8, 2, 1 and 3, headed as a fifth proposition. A separate square fragment carries rows of abacus-like numeral symbols.
