Taylor (1685 AD) Series of Sine and Cosine Discovered By Nilakanta

ista-dohkotidhanushoh svasamipasamirate jye dve saavayave

nyasya kuryaad unaadhikam dhanuh dvighna

talliptikaptaikasarasailasikhindavah nyasyacchedaaya

cha mithastatsamskaaravidhitsaya anyasyam atha taam

dvighnaam tathaa syam iti samskriti:

santha te krtasamskare svagunau dhanusas tayo:

  Placing the sine and cosine chords nearest to the arc, whose sine and cosine chords are required, get the arc difference to be subtracted or added. For making the correction, 13,751 should be divided by twice the arc difference in minutes and the quotient is to be placed as the divisor, divide the one (sine or cosine) by this divisor and add to or subtract from the other (cosine or sine) according as the arc difference is to be added or subtracted. Double this result and do as before. Add or subtract the result to or from the first sine or cosine to get the desired sine or cosine chords.

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