Dividing a portion of a circle into equal parts by halving
A general rule for splitting a circular segment, repeated to a half, quarter, eighth and sixteenth
A tan sheet of pure geometry. Leonardo gives a general rule for dividing a portion of a circle into equal parts: bisect the segment by drawing the chord of its arc and the perpendicular sagitta directed to the circle's centre, then draw a line parallel to the chord, a construction repeated to yield a half, quarter, eighth and sixteenth, shown in a row of shrinking figures. Larger arc and semicircle constructions divided by radiating lines fill the centre and lower half of the sheet.
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General rule for dividing a circular portion using chord and sagitta
A portion of a circle is divisible infinitely into similar and equal parts. Given half the portion b a f as a sector, draw the chord a f of arc a d f and, perpendicular to it, the sagitta d e directed to the whole circle's centre h; then from the sector's angle c draw the line c g parallel to that chord. This serves as a general rule for all divisions of such portions.
Successive halving: half, quarter, eighth, sixteenth
A row of shrinking figures labels the successive divisions: first a half (a, b c, d, e); second a quarter (f, g S, h); third an eighth (i, K t, L); fourth a sixteenth.
Large arc and semicircle divided by radiating lines
Larger constructions fill the centre and lower half of the sheet: a broad arc crossed by many concentric curves and radiating lines, and a large semicircle divided into sectors by lines drawn from its base, with a small shaded lune at the left.