Balance of the Lever and a List of Household Expenses
Centre-of-gravity and balance calculations paired with an account of goods bought
The left leaf (213v) carries large circle diagrams with lettered points and a mechanics text on the position of the centre of gravity relative to the pole of a wheel, worked out through weights and the rule of three (a i to i b as 18 to 17). The right leaf (212r) is dominated by an elaborate figure of many small circles arranged within a great circle, flanked by columns of numerical calculation, and lower down bears a short household account of goods with a total. The transcription covers the balance text and the expense list; the circular diagram and the marginal arithmetic on the right leaf are drawn but not transcribed.
On this page
Centre of gravity, pole and the excess of one side (a, b, f, h)
From the centre of the wheel to the centre of gravity a is 1/12 of a braccio more distant from the pole than is the pole f from the centre of gravity of the weight b. One pound placed at b stands equal to that excess against a; and if a whole pound cannot be there, half a pound set at h below serves for a pound and a half, so that a half pound is the excess or advantage of one side.
The rule of three applied to the balance arms
The arm a i stands to the arm i b as 18 to 17; therefore 18 at b will stand equal with 17 at a. And if a were 18, what would the 17 of b amount to correspondingly? Work it by the rule of three to find the result.
Account of household goods and their costs
A list of purchases and their prices in soldi: a bed at 70, a ring at 70, crockery at 25, the gardener 12, Mainardo 28, porters 21, glasses 10, fire-irons 36, locks 10, summing to 327 and reckoned as 16 lire 7 soldi.
Great circle filled with lesser circles
The upper right leaf is filled by a large circle enclosing many smaller circles set about crossed axes, with a second, simpler circular figure below it and columns of figures alongside. This drawing is not addressed by the transcribed text.