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.
7. And when the heaviest burdens are carried on poles by four or six porters at a time, they find the centres of balance at the very middle of the poles, so that, by distributing the dead weight of the burden according to a definitely proportioned division, each labourer may have an equal share to carry on his neck. For the poles, from which the straps for the burden of the four porters hang, are marked off at their centres by nails, to prevent the straps from slipping to one side. If they shift beyond the mark at the centre, they weigh heavily upon the place to which they have come nearer, like the weight of a steelyard when it moves from the point of equilibrium towards the end of the weighing apparatus.
8. In the same way, oxen have an equal draught when their yoke is adjusted at its middle by the yokestrap to the pole. But when their strength is not the same, and the stronger outdoes the other, the strap is shifted so as to make one side of the yoke longer, which helps the weaker ox. Thus, in the case of both poles and yokes, when the straps are not fastened at the middle, but at one side, the farther the strap moves from the middle, the shorter it makes one side, and the longer the other. So, if both
9. Just as smaller wheels move harder and with greater difficulty than larger ones, so, in the case of the poles and yokes, the parts where the interval from centre to end is less, bear down hard upon the neck, but where the distance from the same centre is greater, they ease the burden both for draught and carriage. As in all these cases motion is obtained by means of right lines at the centre and by circles, so also farm waggons, travelling carriages, drums, mills, screws, scorpiones, ballistae, pressbeams, and all other machines, produce the results intended, on the same principles, by turning about a rectilinear axis and by the revolution of a circle.