Converting years to months using counting rods, the “Suppose-you-have” procedure 今有術, and the Metonic "rule" 章.
Résumé
The “Suppose-you-have” procedure behind the Sifen li’s “[5.] Procedure for calculating astronomical month I” as performed with counting rods on a physical calculating surface for the year 2020, i.e. 52×235⁄19 (reconstruction after Chemla, “Mathematics, Nature and Cosmological Inquiry”). Note, on the left, how the multiplier in step a gradually disappears in “making” 為 the product in step m, on the right, how the dividend in step n likewise disappears but for the “little remainder” in “making” the quotient in step z, and, lastly, how the steps of multiplication and division, left and right, mirror one another at each step.
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