Levers and cords raising beams; reflex motion and balances
Statics of beams lifted by cords, the three kinds of rebound, plus sums and a note of expenses
A densely worked mechanics sheet on the statics of raising beams and rods with cords: Leonardo asks which cord in a five-position setup starts a beam sliding, defines when a mover loses the load as a beam pivots upright, and distinguishes three kinds of reflex (rebound) motion. He relates accidental to natural weight as the real arm to the potential arm, working the balance examples b, a-c and the numbers 4:1. Along the margins are a rule-of-three calculation and a short note of household expenses. The sheet also carries balance sketches and many small beam-and-cord diagrams.
On this page
Which cord begins a beam's sliding motion
A cord is drawn in five positions to drag a beam, and Leonardo asks which of these cords first overcomes friction to set the beam moving. In a related note he states that once the beam's center of gravity reaches the central line of the angle on which it rests, the load vanishes for the mover raising it upright.
Three kinds of reflex (rebound) motion
For an object that strikes the ground and rebounds, Leonardo classes the reflex motions in three kinds. The first is longer than its incident motion, the second equal to it, and the third smaller.
Accidental weight to natural weight as real arm to potential arm
Leonardo sets the proportion: the accidental weight is to the natural weight as the real arm is to the potential arm. When a cord is fixed at one end of a level-lying rod and the angle between cord and beam is less than a right angle, the accidental-to-real weight ratio equals that of the counter-lever's length to its lever's.
Balance of a as 4 against b as 3
In the balance scheme a-c b, a can weigh as 4 against b's 3 with the addition of the accidental weight. That added element is power without weight, that is force, which does not press upon its fulcrum.
Rule of three and calculations
The left margin carries a worked table of numbers laid out as a rule-of-three calculation. Figures such as 7, 3, 5, 15 and 139 are arranged in the columns of the operation.
Note of expenses
A short household account lists abbreviated goods against money columns. Entries include items marked cr, sa, pes, pru and pani with their sums.
