Axioms of power, weight, and proportion (f. 79r)
Four common-notion propositions set beside balance and weight diagrams.
Folio 79r pairs a set of short mechanical axioms with diagrams of weights hung from horizontal bars and pulleys, including a vessel at the foot of the page. The propositions treat how a driving power relates to the space and time of a body's motion, and how adding quantities or weights affects a proportion. Letters a (the whole power) and b (the movable body) key the first figure; the remaining sketches carry numbers and paired hanging loads. The notes read as Euclid-style common notions applied to weight and motion.
On this page
A power and the space it moves a body
If a power moves a body through a given space in a given time, half that power moves the same body through half that space in the same time. Leonardo lets a stand for the whole power and b for the movable body. It is a statement of proportionality between force and distance moved.
Adding proportional quantities preserves a ratio
If to unequal things are added other unequal things standing in the same proportion, the totals keep the original proportion. The claim generalizes ratio arithmetic to compound quantities. It is illustrated beside a figure carrying numbers.
Adding equal weights to unequal weights
If equal weights are added to unequal weights, the sums stay unequal. The rule is the weight-analogue of the common notion that equals added to unequals give unequals. It anchors the hanging-weight sketches on the sheet.
Equal additions in opposite positions equalize sums
If unequal things are joined by quantities equal in the same proportion, and these are placed in opposite positions, the sums where they meet become equal to one another. The proposition addresses how position, not just quantity, governs the result. It closes the page's set of axioms.