On the motion of the moving body.

The arrow shot from the prow of a ship, against the place toward which the ship moves, will not depart from the spot from which it is loosed, the motion of the ship being equal to the motion of that arrow.

But if the arrow of such a ship is shot toward the place from which the ship is fleeing, with the aforesaid speed, then that arrow will separate from the ship by twice the motion of the arrow.

On knowing how far the ship moves per hour.

Our ancients used various devices to see what voyage a ship makes each hour, among which Vitruvius sets down one in his work on architecture; and this method is fallacious, together with the others. And this is a mill-wheel touched by the sea waves at its extremities, and by means of its whole revolutions a straight line is described, which represents the circumferential line of that wheel reduced to a straight line. But this invention is not valid except on the flat and immobile surfaces of lakes; for if the water moves together with the ship with equal motion, then the wheel stays still; and if the water is of swifter or slower motion than the motion of the ship, still the wheel does not have a motion equal to that of the ship, so that such an invention is of little worth.

There is another method made by the experience of a known distance from one island to another, and for this a light board is made, struck by the wind, which is made more or less oblique according as the wind that strikes it is more or less swift. And this is in Battista Alberti.

Battista Alberti's method, which is founded on the experience of a known distance from one island to another; but such an invention does not succeed except for a ship similar to the one on which the experience was made - and it must be with the same load, the same sail, the same set of the sail, and the same size of waves. But my method serves for every ship, whether of oars or of sail; and be it small or large, narrow or long, high or low, it always serves.