Mechanical measurements, a ruler, breathing, and mathematics
A ruling instrument, wheel-and-hub dimensions, a note on breathing, and the maxim that no science is certain without mathematics.
A mixed page of late notes that pairs short technical studies with two memorable observations. At the top a metallurgical recipe describes treating a lead bath with vinegar and 'Sol', skimming it, adding sulphur and reheating a ball at the furnace so the lead adheres within it; nearby stands Leonardo's terse maxim that no science holds true certainty unless a mathematical science can be applied to it. The lower half is given to mechanical dimensions, a horizontal rod on a vertical support with a crank-wheel and hub, and a small ruling instrument (a) for scoring lines with pen or knife, while a central note argues that one cannot breathe through nose and mouth at the same time. The sheet carries the oval stamp of the Bibliotheque de l'Institut de France.
On this page
Maxim: no science is certain without mathematics
A concise methodological statement in the left margin: no science holds true certainty unless one of the mathematical sciences can be applied to it, or unless it is united with those mathematics. It stands apart from the surrounding technical measurements as a general principle.
Why one cannot breathe through nose and mouth at once
Leonardo asserts that a person cannot draw breath through the nose and the mouth at the same moment. As proof he describes breathing in through an open mouth and expelling the air through the nose, noting that a sound is always heard at the passage set near the uvula as it opens and closes.
A ruler for scoring lines with pen or knife (a)
A small drawing tool labelled a is described as a straightedge, or riga, for ruling lines with either a pen or a knife. The note reads as a caption to the sketch of the instrument.
Rod on a vertical support with crank-wheel, dimensioned
A horizontal rod carried on a vertical support is lettered n m r and c a b. The segment c n is 1/4 wide and 1/2 thick, a b measures 3 braccia and a c measures 2 braccia; r b is 1 1/2 thick and 2 ounces wide, while m r is 6 ounces, as is the handle of the wheel (manico della rota).
Dimensions of a wheel and its hub
Further measurements record a wheel (rota) that is one ounce and 3 degrees at the head and one ounce and nine wide. The hub (mozzo) is given as 4 ounces and 9 minuti thick and 9 1/2 ounces long.
A square with segments and measurements
Beside a small square divided by segments Leonardo notes the figures 9 ounces and 3 degrees, with a height of 1/6. The numbers dimension the drawn figure.