Six rules for the quadrature of the circle
Multiplying circumference and diameter fractions to get a circle's area
Under the heading "De quadratura circuli," Leonardo lists six arithmetic recipes for computing a circle's area from its circumference and diameter. Each pairs different fractions of the two — half against half, whole against quarter, quarter against whole, whole with whole (then subtract three quarters), half against whole (then subtract half), and whole against the quarter — all yielding a square equal to the circle. Short marginal notes stand in the right margin alongside the rules; the transcription does not cover them, so further untranscribed text is present on the sheet.
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Half against half: the base rule
Multiply half the circumference of the circle by half of its diameter, and the result is the squaring (area) of the circle. This is the first of six equivalent formulas Leonardo tabulates for the quadrature of the circle.
Whole-with-whole, then subtract three quarters
Multiply the whole circumference by the whole diameter and take away three quarters of the result, and the remainder is the answer. A companion rule multiplies half the circumference by the whole diameter (or half the diameter by the whole circumference) and removes half.
