Proportion of powers and weights (f. 79r, backlit)
Rules on how added or halved forces and weights alter a proportion
A transmitted-light (backlit) view of folio 79r, whose mirror-script notes state rules of proportion applied to moving powers and to weights: half a power moves a body half the distance in the same time, and various additions to unequal quantities either preserve or equalise their proportion. The margins carry small demonstration figures, some lettered (a for the whole power, b for the movable body) and some labelled with numbers. Pulley- and gear-like wheels with hanging weight-boxes are drawn at the top and sides to illustrate the statements. The backlighting also reveals writing and diagrams from the reverse showing through the sheet.
On this page
Half a power moves the body half the distance
If a power moves a body over a given space in a given time, half that power moves the whole body half that space in the same time. Leonardo labels a as the whole power and b as the movable body.
Adding proportional unequal quantities preserves the ratio
If to unequal things are added unequal things that stand to one another in the same proportion as the first, the total sum does not alter the original proportion.
Equal additions leave unequal weights unequal
If equal weights are added to unequal weights, the resulting sums remain unequal.
Opposite placement equalises the sums
If quantities equal in proportion and amount to the first are joined to unequal things but set in opposite positions, the sums where they meet become equal to one another.