Balance beams and graduated weights, with arithmetic
Schemes of balances, a rod hung by several cords, and worked calculations
The sheet is filled with schemes of balance beams whose arms are subdivided and loaded with fractional weights, worked out through columns of numbers and fractions. One diagram shows a rod suspended from several cords, dividing its load along the beam. Turned the other way up, the sheet also carries arithmetical operations, multiplications and divisions supporting the weight ratios.
On this page
Schemes of balance beams with graduated weights
Horizontal beams are graduated and loaded with weights expressed as fractions (4 4 4 3; 6 2/5 against 1 3/5, with 8/5 the part; and so on down the columns). The tables set the excess of one arm against the other to find the point of balance. A further scheme repeats the analysis with sixty-thirds and eighths.
Rod suspended by several cords
A beam is shown hung from several cords, its span marked '6 ÷ 6 ÷ 6 ÷ 6 ÷' to divide the load into equal bays. Fifths (1/5, 3/5, 4/5) note how the suspended weight distributes along the rod. It is a statics study of how many supports share a load.
Arithmetic operations worked on the inverted sheet
Turned upside-down, the sheet carries worked multiplications and divisions (63 by 16, 321 into a product, 512, 1008, 945) with terms marked 'part' and 'whole'. The figures support the fractional weights of the balance schemes. They read as scratch calculations rather than a finished argument.