Oar and wing faster, slower, or equal to the water and air
When medium and oar move at equal speed the oar follows the current; arithmetic on the reverse
The reverse of the previous leaf continues the analysis of oar and wing acting against water and air. If the oar or wing moves faster than the medium it drives, the leftover motion of the water or air is spent against it in the opposite sense; if the medium is the faster, the oar and wing cannot move against it but are carried along with its course; and if the two speeds are equal, the oar and wing simply follow the motion of the water and air. Turned the other way, the sheet is filled with columns of arithmetical working.
On this page
Oar and wing faster, slower, or equal to the medium
Leonardo distinguishes three cases. If the oar or wing is faster than the water or air it pushes, the residual motion of the medium is spent against it in the contrary sense. If the medium is itself faster, the oar and wing cannot move against it.
When the water outpaces the oar it carries it along
In the marginal note Leonardo confirms that the oar and wing will not move against the water and air but will instead accompany their course. The reasoning treats the moving water exactly as it treats the moving air.
Wing and air moving at equal speed
If the motion of the water or air is of the same velocity as that of the oar or wing moving within it, then the oar and wing simply follow the motion of the water and the air. The rule is stated for the wing in air as for the oar in water.
Columns of calculation on the turned sheet
Rotated from the main text, the lower part of the leaf is covered with stacked arithmetical operations, columns of digits with partial products and remainders. They are working figures set down independently of the motion notes.