Dividing circular portions; the arc and irrational chord
Splitting a portion into equal parts, and squaring portions by exchanging wedges and remainders.
The page, drawn in faint line with circles, sectors, an octagon and dome-like shapes, pursues the squaring of circular portions. One note shows how returning 'first portions' divides a portion d into equal parts, illustrated by two half-portion figures n and m drawn below. A second note, headed 'On the arc and irrational chord,' sets a square m equal to a circle n and manipulates a wedge and portions (o, f, r, S) to leave squarable remainders, insisting only that the borrowed portion r share the same capacity, not the same length, as S.
On this page
Dividing portion d into equal parts
Since a b and c d are equal, returning to them the 'first portions' divides portion d into equal parts. Two figures n and m are then drawn below, each representing a half portion of the a above.
On the arc and irrational chord
With square m equal to circle n, Leonardo gives an arbitrary arc o, throws away wedge n and as much of m, leaving a part equal to the two portions o f that is double o; so half that remaining square equals portion o. A portion S is matched to its squared companion, and a part r of the circle is detached equal in capacity, though not length, to S.