Geometric equivalences and ornamental circle studies
Helices worth triangles, lunes of circles, and interlaced rosette motifs
Viewed upside down (the note reads 'the sheet turned over'), this leaf gathers geometric and ornamental studies down its left side. Leonardo explores equivalences between curved and rectilinear figures — four helices set equal to four triangles, the removal of lunes from circles, and an equilateral triangle whose three sides equal each side of the square built on one of them — alongside simple arithmetic sums (1080 + 1080 = 2160; 180 + 180 = 360). Interlaced knots, rosettes and paired-circle motifs run down the margin, and large triangular lattices of overlapping circles fill the lower sheet; the codex's subject tags associate the circular devices with a mechanized military drum. Much of the right half of the leaf is left blank.
On this page
Four helices worth four triangles
Beside four triangles and four helices Leonardo notes, with the labels c a - d b, that 'these four helices are worth the four triangles,' equating spiral and rectilinear areas.
Removing two lunes halves the circle's value
Around four circles set within a larger circle, Leonardo writes that only the two greatest portions of the circle are taken away, because by removing the two lunes half the value of the circle is lost.
Equilateral triangle on a side of the square
For an equilateral triangle drawn on one side of a square, Leonardo observes that its three sides are each equal to every one of the four sides of the square.
Arithmetical sums
A small block of addition sits among the figures: 1080 + 1080 = 2160, and 180 + 180 = 360.
Interlace knots and rosette motifs
A column of decorative pen motifs runs down the left margin: interlaced knots, paired-circle emblems and circular rosettes with internal subdivisions.
Circular hatched devices (catalogued as a military drum)
Several circular, hatched forms with internal divisions descend the left column; the codex's subject tags identify these circular devices with a mechanized military drum.