Oar in water, wing in air: the equivalence of motion
Moving the oar against still water equals moving the water against a fixed oar
Leonardo sets out his principle of relative motion: to move a body against water or air is exactly the same as to move that water or air against the body. He applies it to a rowing boat, imagining the oar held still while the water slides past it, and equally to a bird's wing in the air. With a lettered figure he shows how a boat driven by the oar veers along a curved line, so that the rudder must be turned to correct its course, and concludes that an oar or wing driven against the current can carry the boat or bird faster than the water or air itself.
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To move the oar against the water equals moving the water against the oar
Leonardo asserts that it is the same to move an object against the air or water as to move that air or water against the object. Rowing the oar from a to b, one may equally imagine the oar fixed and the water flowing from b to a. The boat's positions are lettered a, b, c, d, e.
The oared boat veers on a curve and the rudder must correct it
In an analogous lettered figure, if the oar is drawn from n to m the prow b of the boat runs from b to c, and if the oar goes from m to n the prow runs to a. The vessel therefore travels along a curved line, and to remedy this the rudder must be turned.
Oar or wing driven against the current outruns the water or air
When the oar or wing moves against the course of the water or the air, the boat or bird is made faster than that water or air by exactly the speed of the oar or wing driven against them. The same reasoning is applied indifferently to the oar in water and the wing in air.