The Ten Books on Architecture, 10.3.3

Vitruvius  Parallel editions

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Gwilt translation

3This is accounted for by the fore part of the lever being under the weight, and at a shorter distance from the fulcrum or centre of motion; whilst the longest part, which is from the centre of motion to the head being brought into circular motion, the application of few hands to it will raise a great weight. So if the tongue of the lever be placed under the weight, and instead of the end being pressed downward it be lifted up, the tongue then having the ground for a fulcrum, will act on that as in the first instance it did on the weight, and the tongue will press against the side thereof as it did on the fulcrum: though by this means the weight will not be so easily raised, yet it may be thus moved. If the tongue of the lever lying on the fulcrum be placed too far under the weight, and the end be too near the centre of pressure, it will be without effect; so, as hath been already mentioned, will it be, unless the distance from the fulcrum to the end of the lever be greater than from the fulcrum to the tongue thereof.

Morgan translation

3For, 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.