Equal arms and the spaces from centre to pole of a balance
The distances centre-to-pole share the proportion of the arms' weights
The page opens with a definition: to speak of the arms of a balance is to assume them equal in thickness and weight when they are equal in length. A single proposition, illustrated by a beam labelled a m n f with a hanging weight, states that the spaces lying between the centre of each arm and the pole are in the same proportion as the opposite weights the arms exert as counterweights, and equally as the proportion of the arms' weights together with their length.
On this page
What 'arms of a balance' presupposes
Whoever speaks of the arms of a balance understands them to be of equal thickness and weight, provided they are of equal length. This definition underlies the proportional reasoning that follows.
Centre-to-pole spaces proportional to the arms' weights
The spaces between the centre of the arms and the pole of the balance are in the same proportion as the opposite weights each arm gives as counterweight to the other. Equally, the spaces enclosed between the centres of the two arms and the pole share the proportion that the arms' weights, together with their length, have among themselves. The beam is labelled a m n f.