Axioms of Statics: Equal Weights on a Balance
Numbered propositions 1a-5a on equality, power and resistance, with a balance in equilibrium
The page sets out a series of numbered propositions on statics and motion. It states that equal things do not overcome one another; that the motor is more powerful than its mobile; that equal powers moving equal bodies through equal distances in equal times prove them equal; that the heavier weight is the one with the weaker resistance; and that the part of a support farthest from its fixing resists least. A worked example treats a balance whose two equal arms a b and a c carry equal weights on pendants at right angles, so that no motion results. Balance and pulley diagrams with suspended weights accompany the text.
On this page
Five axioms on power, motion and weight
The propositions hold that equal things do not overcome one another (so unequal ones do); that the motor is more powerful than its mobile; that equal powers moving bodies through equal paths in equal times prove those bodies equal; that the heavier weight is the one with weaker resistance; and that a support resists least where it is farthest from its fixing, most where nearest.
A balance in equilibrium: arms a b and a c
The worked example takes a b and a c as the two equal arms of a balance, hence of equal power, with pendants b g and c loaded by the equal weight g h. Because the weights are equal and hang at right angles from equal arms, no motion occurs.