3Perhaps some one who may have read the works of Archimedes will say that a true level cannot be obtained by means of water, because that author says, that water is not level, but takes the form of a spheroid, whose centre is the same as that of the earth. Whether the water have a plane or spheroidal surface, the two ends of the channel on the rod right and left, when the rod is level, will nevertheless sustain an equal height of water. If it be inclined towards one side, that end which is highest will not suffer the water to reach to the edge of the channel on the rule. Hence it follows, that though water poured in may have a swelling and curve in the middle, yet its extremities to the right and left will be level. The figure of the chorobates will be given at the end of the book. If there be much fall, the water will be easily conducted, but if there be intervals of uneven ground, use must be made of substructions.
3Perhaps some reader of the works of Archimedes will say that there can be no true levelling by means of water, because he holds that water has not a level surface, but is of a spherical form, having its centre at the centre of the earth. Still, whether water is plane or spherical, it necessarily follows that when the straightedge is level, it will support the water evenly at its extremities on the right and left, but that if it slopes down at one end, the water at the higher end will not reach the rim of the groove in the straightedge. For though the water, wherever poured in, must have a swelling and curvature in the centre, yet the extremities on the right and left must be on a level with each other. A picture of the chorobates will be found drawn at the end of the book. If there is to be a considerable fall, the conducting of the water will be comparatively easy. But if the course is broken by depressions, we must have recourse to substructures.