On Architecture

3. For, as the shorter fore part of the lever goes under the weight from the fulcrum that forms the centre, the head of it, which is farther away from that centre, on being depressed, is made to describe a circular movement, and thus by pressure brings to an equilibrium the weight of a very great load by means of a few hands. Again, if the tongue of an iron lever is placed under a weight, and its head is not pushed down, but, on the contrary, is heaved up, the tongue, supported on the surface of the ground, will treat that as the weight, and the edge of the weight itself as the fulcrum. Thus, not so easily as by pushing down, but by motion in the opposite direction, the weight of the load will nevertheless be raised. If, therefore, the tongue of a lever lying on a fulcrum goes too far under the weight, and its head exerts its pressure too near the centre, it will not be able to elevate the weight, nor can it do so unless, as described above, the length of the lever is brought to equilibrium by the depression of its head.

4. This may be seen from the balances that we call steelyards. When the handle is set as a centre close to the end from which the scale hangs, and the counterpoise is moved along towards the other arm of the beam, shifting from point to point as it goes farther or even reaches the extremity, a small and inferior weight becomes equal to a very heavy object that is being weighed, on account of the equilibrium that is due to the levelling of the beam. Thus, as it withdraws from the centre, a small and comparatively light counterpoise, slowly turning the scale, makes a greater amount of weight rise gently upwards from below.

5. So, too, the pilot of the biggest merchantman, grasping the steering oar by its handle, which the Greeks call o)/iac, and with one hand bringing it to the turning point, according to the rules of his art, by pressure about a centre, can turn the ship, although she may be laden with a very large or even enormous burden of merchandise and provisions. And when her sails are set only halfway up the mast, a ship cannot run quickly; but when the yard is hoisted to the top, she makes much quicker progress, because then the sails get the wind, not when they are

6. As a lever thrust under a weight is harder to manage, and does not put forth its strength, if the pressure is exerted at the centre, but easily raises the weight when the extreme end of it is pushed down, so sails that are only halfway up have less effect, but when they get farther away from the centre, and are hoisted to the very top of the mast, the pressure at the top forces the ship to make greater progress, though the wind is no stronger but just the same. Again, take the case of oars, which are fastened to the tholes by loops,—when they are pushed forward and drawn back by the hand, if the ends of the blades are at some distance from the centre, the oars foam with the waves of the sea and drive the ship forward in a straight line with a mighty impulse, while her prow cuts through the rare water.