Number Progressions and a Weight on Pulleys
Red-chalk doubling and tripling series with a counterweight device
In red chalk Leonardo lays out geometric number progressions: an upper pair of linked circles carrying a tripling series (1, 3, 9) and a long chain of arcs carrying a doubling series (1, 2, 4, 8, 16, 32, 64, 128), each step marked with the multiplier 2. At the foot of the sheet a small mechanical sketch shows a weight and a counterweight linked over two pulleys, captioned as such. Further faint chalk figures and stray numerals accompany the diagrams.
On this page
Doubling and tripling number series
A row of linked arcs steps through the doubling series 1, 2, 4, 8, 16, 32, 64, 128, each interval marked with the multiplier 2. Above, two joined circles carry the tripling series 1, 3, 9. The figures illustrate continuous geometric proportion by successive multiplication.
Weight and counterweight over pulleys
At the foot of the page a bracket carries two pulley wheels; a ring-shaped weight hangs on one side and a block counterweight on the other, so the two loads act against each other across the pulleys. The caption names it a weight and counterweight linked over pulleys.