PROPOSITION IV
If the power shall move the weight hung from the lever, the space through which the power moves will be to the space through which the weight is moved as the distance from the fulcrum to the power is to the distance from the fulcrum to the point from which the weight is hung.
56[Figure 56]Let there be the lever AB with its fulcrum C, and let the weight D be attached at the point B, and let the power at A move the weight D by means of a leverAB.Then the space of the power at A is to the space of the weight as CA is to CB---.
But let there be the lever at AB, whose fulcrum is B, and the moving power is at A and the weight at C; I say that the space of the moved power to the space of the weight carried is as BA to BC---.
Corollary.-From these things it is evident that the ratio of the space of the power which moves to the space of the weight moved is greater than that of the weight to the same power.
57[Figure 57]For the space of the power has the same ratio to the space of the weight as that of the weight to the power which sustains the same weight.But the power that sustains is less than the power that moves; therefore the weight will have a lesser ratio to the power that moves it than to the power that sustains it.Therefore the ratio of the space of the power that moves to the space of the weight will be greater than that of the weight to the power.