Trisecting a Circular Segment by Construction
Dividing the portion a b c d into three equal parts with sector b c n and line b h
Leonardo divides a circular portion into three equal parts by construction. With the cut b h he obtains the parts b h c, c h d and a b e, and states the general aim: each part should have for one side a third of the curved edge, the other sides being straight. Drawing the sector b c n to the centre n and the line b h yields two equal, similar triangles b c h and c d h, leaving triangle b e h — the excess of square b c e h over triangle c d h — to be further divided into three at e f g h. A labelled segment with its central triangle running down to n accompanies the text.
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Cutting the portion into three parts with b h
The cut b h makes 3 equal parts in the portion — b h c, c h d and a b e — leaving triangle b e h, which is itself divided into 3 so each receives its part. Each part is to have a third of the curved side, its other sides rectilinear.
Sector b c n, line b h, and the residual triangle b e h
For portion a b c d, drawing sector b c n to the centre n and line b h at point h gives 2 equal similar triangles b c h and c d h; the residual triangle b e h — by which square b c e h exceeds triangle c d h — is divided into 3 equal at e f g h.