Finding the area of a circular segment
Arc and chord: multiply the arc by the quarter-circle area, then divide by the circumference
A pen sketch of a circle carrying a shallow segment across its top, its points lettered a, b, c and d, with the number 22 marking the circumference at the left. The notes give a worked rule for the 'capacity' (area) of the part of a circle bounded by an arc and its chord. Leonardo multiplies the arc a b c (5 1/2) by the quarter-circle area 38 1/2 to get 211 3/4, then divides by the circumference 22 to obtain 9 5/8, adding that the rule holds for a quarter of the circle.
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Area of the segment bounded by arc a b c and its chord
The figure isolates the region between the arc a b c and the chord drawn beneath it, set inside the full circle whose circumference is marked 22. The lettered points a, b, c fix the arc, while d marks its summit. The construction poses the classic problem of measuring the sliver cut off by an arc and its chord.
Worked rule: (arc x quarter-circle area) / circumference
Leonardo multiplies the arc a b c, taken as 5 1/2, by the circle's capacity 38 1/2 to reach 211 3/4. He then divides that product by the circumference 22, yielding 9 5/8 as the required area. A closing line states that the rule applies over one quarter of the circle.