Weights on balances, with tables of powers of two
How a weight's heaviness changes with position; virtual and real lever arms
This large double sheet is covered with balance-beam and weight diagrams together with a note that a weight shows as many different heavinesses as it has positions and as many changes as its mover. Columns and ladders of numbers work through doubling sequences (32, 16, 8, 4, 2, 1) and related progressions tied to the graduated balances. A further note states that the diminished weight relates to its counterweight as the 'spiritual arm' relates to the 'real arm' of the balance. Squares crossed by diagonals and small triangles accompany the mechanical figures.
On this page
The apparent weight varies with its position
As many varieties as the position of the weight has, and as many changes as its mover has, so many different heavinesses that same weight will display. The claim frames the many balance sketches around it.
Spiritual arm and real arm of the balance
Whatever proportion the spiritual (virtual) arm bears to the real arm, the same proportion the diminished weight bears to its counterweight. The rule is set beside a descending ladder of numbers 8 7 6 5 4 3 2 1 0.
Doubling sequences and number tables
Repeated schemes lay out geometric progressions — 32, 16, 8, 4, 2, 1 and rows such as 2 4 8 16 32 — together with grids of figures (0 16 8 4 28 32; 0 1 3 7 15) that grade the balance arms.
Squares with diagonals and triangles
Several small squares crossed by their diagonals and outline triangles are drawn among the weight diagrams on the right and lower parts of the sheet; these figures are not transcribed.