Lever and Counter-Lever: Definitions and Right Angles
The proportion of powers as lengths, and the always right-angled junction of the power line
This closely written sheet gathers Leonardo's definitions of the lever and counter-lever, illustrated with small balances, wheels and angle diagrams. He states that the powers of a lever and its counter-lever stand in the proportion of their lengths, and defines them as the shortest straight lines running from the centre of rotation to the mover and to the moved body. A recurring theorem, repeated in several forms down both columns, insists that the junction of the power-line with the line of the lever is always right-angled, though the junction of lever and counter-lever may be rectilinear, right, acute or obtuse. The leaf also bears further writing not included in the transcription.
On this page
Powers in proportion to lengths
Whether two weights sit on one same arm or the counter-lever is created within its lever, the proportion of their powers is that of their lengths. Likewise the powers a lever has with its counter-lever are as the proportion of their lengths.
Lever and counter-lever as shortest lines
The lever and counter-lever are the shortest straight lines that extend between the mover and the movable, arising at the centre of their rotatable motion and always joined there. Their conjunction can take any angle and be rectilinear.
The power line meets the lever at a right angle
The junction of the power-lines of the mover and movable is always right-angled with the line of the lever and its counter-lever. Right-angled likewise is the junction of the line of the lever with the power-line of its mover.
Four modes of joining lever to counter-lever
The conjunction of the lever with its counter-lever varies in 4 ways: rectilinear, right-angled, acute or obtuse. They are the shortest lines rising at the centre of the rotatable motion and terminating at the mover and the movable.