Power proportioned to its load, with geometric and tube studies
The wind-filled bladder on 54r: force must match its load; with a lettered circle and 'angled-mouth' tube sketches.
On the left page (49v) a geometric note explains how, from the lines h d and g d, two curves d b and d c are drawn so that the segment of a circle enclosed between them at b c can be divided proportionally, illustrated by a lettered circle diagram. The right page (54r) carries a passage on mechanics arguing that power in excess of a fixed resistance is wasted: motion reaches the 'first degree' of its effectiveness only when the mover's power is proportioned to the body it moves. Leonardo illustrates this with a wind-filled bladder that rebounds off the condensed air as though off a wall when driven too hard. Small marginal sketches show tubular forms with an 'angled mouth' (boca aunglata) and a base line measured at 500 braccia.
On this page
Dividing a circular segment between the curves d b and d c
From the line h d the curve d b is drawn, and from the line g d the other curve d c; the space of the circle enclosed between the ends of these two curves at b c is then to be divided in the same proportion as a given ratio. A lettered circle diagram on 49v accompanies the note.
Power must be proportioned to the body it moves
Power in excess of a fixed resistance does the moving body no good; motion reaches the first degree of its strength only when the mover's power is proportioned to its load. Leonardo likens it to hurling a wind-filled bladder: driven by excess force it rebounds off the condensed air as if dashed against a wall, but moved with proportioned force it advances as far as it can slowly push aside the opposing air.
Tubes with an 'angled mouth' (boca aunglata)
Marginal sketches on 54r show tubular forms, one labelled with an 'angled mouth' (boca aunglata) and another marked 'middle, that is the half' (mezo cioe la meta). A base line drawn below is measured 'a b, 500 braccia'.