De Moivre's (1650 AD) Approximation

yatsankhyaaatra harane krte nivrtta hrtis tu jamitaya tasya

urdhvagatasyas samasankhya taddalam guno ante syat tadvargai

rupahato haaro vyasabdhighatata: pragvat tasyam aptam svamrne krte

dhane sodhanan cha karaniyam sukhma: paridhi:

sa syat bahukrtvo haranato atisukshmas cha

………. Let the process stop at a certain stage, giving rise to a finite sum, multiply four times the diameter by half the even integer subsequent to the last odd integer used as divisor and then divide by the square of the integer increased by unity. The result is the correction to be added to or subtracted from finite sum. The choice of addition or subtraction is depending on sign of the last term in the sum. The final result is the circumference determined more accurately than by taking a large number of terms:]]>

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