Propositions on the balance and its weights
Statements on weights hung from the terminals and sections of a lettered beam
Filling the sheet in Leonardo's mirror hand is a set of propositions on the balance (the libra), of the kind belonging to the medieval 'science of weights.' They argue that once certain quantities are 'given', a weight and the opposite arm, the divisions of the beam, or weights hung at a terminal and at a section, every remaining weight, arm, or the declination of the perpendicular can be determined. Small balance-beam and triangle figures are sketched in the left margin. Further short notes and diagrams at the foot of the sheet are not transcribed here.
On this page
Given a weight and the opposite arm, all is determined
If the arms of the balance are given together with the weight, and the beam is cut into a given shorter part, and the weight hangs so as to keep the balance level, that weight too is shown to be given; and if two weights depend from the shorter side, one at the terminal and one at a division, keeping the beam level with a known combined weight, each weight is given.
Weights on the sections of the longer arm
If the beam of a given weight is divided into unequal parts and given weights hung from the terminals hold it level, the arms from the centre are given; and if a weight on the section of the longer arm is made equal to one at the terminal of the shorter, then, one section being given, the other is given too.
Declination of the perpendicular at the centre of motion
With the beam set at the perpendicular centre of motion, no weight hung from any part can descend as far as the vertical of the centre; and once the distance of the centre from the middle of the beam and the attached weights are given, both the weight of the beam and the declination of the perpendicular are given.
Balance sketches in the margin
Small figures of balance beams, together with a triangular figure, are drawn down the left margin beside the propositions, illustrating the lettered arms and their divisions.